CN112989756A - Coarse grain parallel iteration method and device for dynamically applying coupling between layers of integrated circuit - Google Patents

Coarse grain parallel iteration method and device for dynamically applying coupling between layers of integrated circuit Download PDF

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CN112989756A
CN112989756A CN202110425242.5A CN202110425242A CN112989756A CN 112989756 A CN112989756 A CN 112989756A CN 202110425242 A CN202110425242 A CN 202110425242A CN 112989756 A CN112989756 A CN 112989756A
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CN112989756B (en
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唐章宏
邹军
王芬
汲亚飞
黄承清
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Beijing Wisechip Simulation Technology Co Ltd
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Abstract

The invention provides a coarse grain parallel iteration method and a coarse grain parallel iteration device for interlayer coupling dynamic application of an integrated circuit, wherein the coarse grain parallel iteration method comprises the following steps: firstly, dividing iterative computation of interlayer coupling of an integrated circuit into parallel computation particles, and combining the parallel computation particles into parallel computation coarse particles according to CPU weighted time; secondly, distributing a calculation task by taking parallel calculation particles as a unit, performing iteration on current distribution of the source layer in parallel, calculating the influence of other layers on the source layer through a parallel vector Green function during each iteration, accumulating the influence as a source item of the source layer, applying a two-dimensional finite element to the source layer to calculate field distribution of the source layer so as to update the field and current distribution of the source layer, obtaining the change amount of the field of the source layer, and dynamically modifying the range of an action layer of the source layer influenced by other layers; and repeating the iteration until the change amount of the fields of all the layers is smaller than a specified threshold value, and finishing the iteration. According to the method and the device, the electromagnetic response calculation time of the three-dimensional multilayer integrated circuit is linearly reduced along with the parallel process number.

Description

Coarse grain parallel iteration method and device for dynamically applying coupling between layers of integrated circuit
Technical Field
The invention relates to the technical field of integrated circuits, in particular to a coarse grain parallel iteration method and device for interlayer coupling dynamic application of an integrated circuit.
Background
When the integrated circuit works, a high-frequency alternating electromagnetic field can be formed on a multilayer layout of the integrated circuit due to the transmission of high-speed signals, and meanwhile, in order to improve the performance of electronic equipment, reduce the volume and reduce the cost, transistors, other components and circuits are integrated on a small semiconductor substrate. In order to realize more functions, the ultra-large scale integrated circuit has a structure from tens of layers to hundreds of layers, each layer of structure is extremely complex, millions or even tens of millions of transistors are integrated, and the ultra-large scale integrated circuit has a multi-scale structure from a centimeter level to the latest nanometer level at present. In order to ensure that the integrated circuit can normally work and realize the function designed in advance, the power integrity and the signal integrity of the integrated circuit need to be ensured firstly, so that the power integrity and the signal integrity of the integrated circuit with a multi-scale structure of tens of layers and hundreds of layers need to be accurately analyzed by adopting an electromagnetic field analysis method, which is a great problem of the electromagnetic field analysis of the ultra-large scale integrated circuit.
The method comprises the steps of performing electromagnetic field analysis on a three-dimensional large-scale integrated circuit by adopting a traditional method, further calculating the electromagnetic response of the three-dimensional large-scale integrated circuit, generally determining the whole three-dimensional integrated circuit and a limited region outside the integrated circuit as a calculation region after setting a truncation error of a certain region, then performing mesh division on the whole calculation region, calculating the electromagnetic field distribution of the whole calculation region, and further calculating the electromagnetic response of each layer of the integrated circuit, such as the electromagnetic field distribution, the current voltage of a designated port and the like. However, the characteristic dimensions of the via holes, the wires and the like of the integrated circuit are nano-scale, the dimension of the whole integrated circuit is centimeter-scale, the calculation area determined according to the truncation error is decimeter-scale and meter-scale, and hundreds of millions of grids and unknown quantities can be generated by carrying out uniform grid subdivision on the multi-scale space and then analyzing the space electromagnetic radiation of the multi-scale space, so that the hardware (memory) cost and the CPU time cost are overlarge. Therefore, the electromagnetic response of the three-dimensional large-scale integrated circuit can be calculated by adopting a method combining a finite element method and a moment method. In the three-dimensional large-scale integrated circuit area, a finite element method is adopted; in a large-scale area outside the integrated circuit, a moment method is adopted; the finite element method and the moment method are coupled at the interface of the integrated circuit and the external space. Because the moment method only integrates aiming at the interface, a large number of grid units and unknowns can be reduced, but because the scale range of the integrated circuit is from nano-scale to centimeter-scale, the finite element method directly used for solving the integrated circuit can generate a huge sparse matrix, and because the finite element method and the moment method are coupled, the formed coupling matrix is a dense matrix at the interface, the non-zero element number of the whole sparse matrix and the solving complexity of the sparse matrix are greatly increased, and the calculation time is still long.
Disclosure of Invention
Objects of the invention
Based on the problems, the invention provides a coarse grain parallel iteration method and a coarse grain parallel iteration device dynamically applied by interlayer coupling of an integrated circuit, on one hand, the communication among processes is reduced to the maximum extent in the process of iterative computation of interlayer coupling of a multilayer ultra-large scale integrated circuit, the hard disk read-write bottleneck caused by the fact that the peak value of a memory is larger than the available physical memory during the multi-process parallel computation is avoided, the problem of process waiting caused by the fact that the complexity of different computation examples is not equal is perfectly solved, and the parallel computation efficiency is greatly improved; on the other hand, according to the characteristics of interlayer coupling of the integrated circuit, all the calculation particles are combined into two-stage parallel calculation coarse particles with calculation task sets in different ranges, and calculation processes are distributed according to the two-stage parallel calculation coarse particles; finally, based on the attenuation rules of electromagnetic fields and electromagnetic waves in space, when a parallel iteration solving method is designed, the influence of other layers on the source layer is calculated through a parallel vector Green function in each iteration, the influence is accumulated to be used as a source item of the source layer, a two-dimensional finite element is applied to the source layer to calculate the field distribution of the source layer so as to update the field and current distribution of the layer, the change quantity of the source layer field is obtained, the range of an action layer of the source layer influenced by other layers is dynamically modified, and the iteration solving time is greatly accelerated. The present application discloses the following technical solutions.
(II) technical scheme
As a first aspect of the invention, the invention discloses a coarse grain parallel iteration method for the interlayer coupling dynamic application of an integrated circuit, which comprises the following steps:
step S100, dividing iterative computation of coupling between integrated circuit layers into parallel computation particles, combining the parallel computation particles into two-stage parallel computation coarse particles according to weighted CPU time of the parallel computation particles, wherein the first-stage parallel computation coarse particles are used for computing electromagnetic field and current distribution of each source layer, and the first-stage parallel computation coarse particles comprise the steps of updating source items acting on the source layers in a coupling mode by computing influences of other layers on the source layers and computing the electromagnetic field and current distribution of the source layers by utilizing two-dimensional finite elements; the second level of parallel computing coarse grains is used for computing the layer-layer mutual influence of the integrated circuit;
step S200, the large scale integrated circuit is summarizedN+1 layer, each layer numbered
Figure 248013DEST_PATH_IMAGE001
When considering the second aspect of LSImWhen the current source of the layer is in the current source of the layer, the layer is called the first layermA source layer provided with a secondmActive layer of source layer
Figure 368415DEST_PATH_IMAGE002
Is divided bymOthers of the source layerNLayer integrated circuits, i.e.
Figure 616994DEST_PATH_IMAGE003
Wherein
Figure 949887DEST_PATH_IMAGE004
The 0 th layer is a bottom layer; setting the number of iterations
Figure 466056DEST_PATH_IMAGE005
；
Step S300, if
Figure 757360DEST_PATH_IMAGE006
Computing the first based on the coarse grain of the first stage parallel computingmThe electromagnetic field and current distribution of the source layer are calculated, and the change amount of the electromagnetic field of the layer is calculateddE m And a firstlLayer to layer ofInfluence value of layer-by-layer vector green's functionG lm Maximum value ofG m,maxAnd minimum valueG m,minWherein 0 is less than or equal tom≤N；
Step S400, if
Figure 962077DEST_PATH_IMAGE007
And is
Figure 364239DEST_PATH_IMAGE008
And (5) finishing the iteration, and outputting electromagnetic fields and current distributions of each layer, wherein
Figure 501960DEST_PATH_IMAGE009
The iteration precision is preset;
step S500, if
Figure 698586DEST_PATH_IMAGE010
Merging all the influence values of the dyadic Green function obtained by the parallel calculation of the coarse grains at the first stage, and obtaining the maximum value of the influence values of all the dyadic Green functions of the current iterationG maxAnd minimum valueG minCalculating the effective influence value of the dyadic Green function
Figure 145923DEST_PATH_IMAGE011
Here, thethredsholdA discarding threshold value for the influence of a preset dyadic Green function;
step S600, if
Figure 86198DEST_PATH_IMAGE010
Calculating satisfy
Figure 812845DEST_PATH_IMAGE012
Of the conditionG lm Middle distance layermNearest layerl near Will be
Figure 445952DEST_PATH_IMAGE013
Is updated to
Figure 890840DEST_PATH_IMAGE014
；
Step S700, setting
Figure 634805DEST_PATH_IMAGE015
The process proceeds to step S300.
Further, in step S100, the formula for calculating the weighted CPU time of the parallel calculation grain is:
Figure 980073DEST_PATH_IMAGE016
in the formula:
Figure 518502DEST_PATH_IMAGE017
is as followsiThe weighted CPU times of the particles are calculated in parallel,
Figure 450686DEST_PATH_IMAGE018
is as followsiThe CPU time of a single calculation of a grain is calculated in parallel,
Figure 998342DEST_PATH_IMAGE019
is as followsiThe number of particle executions is calculated in parallel.
Furthermore, the first-stage parallel computing coarse grains and the second-stage parallel computing coarse grains are computing task sets in different ranges, the first-stage parallel computing coarse grains comprise a plurality of second-stage parallel computing coarse grains and a computing task for computing electromagnetic fields and current distribution of an integrated circuit layer by using two-dimensional finite elements, the parallel computing grains belonging to the same stage can be computed in parallel, the first-stage parallel computing grains can be distributed with a plurality of computing processes, and the second-stage parallel computing grains can be distributed with only one computing process.
Further, the step S300 includes:
step S310, calculating coarse grains based on the second-stage parallel calculation, and calculating the second stage by utilizing a dyadic Green functionlLayer to layermInfluence of the Source layer, isG lm Wherein, in the step (A),
Figure 699582DEST_PATH_IMAGE020
(ii) a All will beG lm Overlapping to obtain the other layer pairs within the range of the action layermSum of influence of source layers:
Figure 175956DEST_PATH_IMAGE021
(ii) a Finishing the second-stage parallel calculation of coarse grains;
step S320, ifiter>0, willG m As a firstmAdditional sources of source layers added to the secondmIn the source item of the source layer;
step S330, for the secondmThe source layer applies two-dimensional finite element to calculate the electromagnetic field distribution so as to update the electromagnetic field and current distribution of the layer, and the change quantity of the electromagnetic field of the layer is calculateddE m ；
Step S340, according tolInfluence value of layer on dyadic Green function of layerG lm CalculatingG lm Maximum value ofG m,maxAnd minimum valueG m,min。
Further, the specific steps of the second-stage parallel computation of coarse grains include:
step S311, calculating the electric field generated by the point current source at the field point, wherein the electric field expression generated by the point current source at the field point is a special analytic expression formed according to the layered special structure of the integrated circuit, and the current sources of the multilayer integrated circuit are layered, that is, the current density distributed on each metal layer of the integrated circuit layout with the complex shape is only equal to that of each metal layer of the integrated circuit layout with the complex shapexAndyis related tozIndependently, the current density distribution is onlyx, yA function of (a);
step S312, taking an electric field expression generated by the point current source at the field point as an integrand of two-dimensional gaussian integration, and calculating a field generated by the surface current source of the simple-shaped polygon at the same position based on a field linear superposition principle, including: the field generated by the current source in the two-dimensional plane S at any point in space can be calculated by the two-dimensional gaussian integral:
Figure 329856DEST_PATH_IMAGE022
；
wherein the content of the first and second substances,
Figure 415624DEST_PATH_IMAGE023
at any point in space for the current source within the two-dimensional plane S (x,y,z) The field that is generated is,
Figure 971370DEST_PATH_IMAGE024
is an arbitrary position within the two-dimensional surface S: (u,v) At any point in space (a)x,y,z) The expression of the field that is generated,
Figure 117181DEST_PATH_IMAGE025
representing a gaussian integration point corresponding to a two-dimensional gaussian integration in the two-dimensional plane S,p,qrespectively representu,vIn the first directionpA first, aqThe number of the Gaussian integration points is equal to the total number of the points,
Figure 758378DEST_PATH_IMAGE026
is the weight factor corresponding to the gaussian integral point;
step S313, calculating fields generated by the current on the simple-shaped polygon at different positions of other layers of the integrated circuit, and determining the fields generated by the current on the simple-shaped polygon divided on the layout of other layers of the integrated circuit based on the linear superposition principle of the fields;
step S314, determining the second step based on the linear superposition principle of the fieldlIs layered onmThe electric field generated by the source layer.
Further, influence values according to the dyadic Green function in the iteration processGDetermines a layer that can be ignored, adaptively adjustsmExtent of influence of source layer by other layers adjacent thereto
Figure 880792DEST_PATH_IMAGE027
。
The other side fully discloses a coarse grain parallel iteration device for the interlayer coupling dynamic application of the integrated circuit, which comprises a parallel calculation grain division module, a parallel calculation coarse grain division module and a parallel calculation coarse grain operation module;
the parallel computing particle dividing module is used for dividing iterative computing of interlayer coupling of the integrated circuit into parallel computing particles;
the parallel computing coarse grain dividing module is used for acquiring weighted CPU time of each parallel computing grain and total CPU time of an iteration method for coupling real-time updating between layers of an integrated circuit based on one-time complete serial iterative computation, and combining the parallel computing grains into two-stage parallel computing coarse grains according to the ratio of the weighted CPU time to the total CPU time; the first stage of parallel coarse grain calculation is to calculate the electromagnetic field and current distribution of each source layer, and the first stage of parallel coarse grain calculation comprises the steps of calculating the influence of other layers on the source layer to update source items acting on the source layer in a coupling mode and calculating the electromagnetic field and current distribution of the source layer by utilizing two-dimensional finite elements; the second level of parallel computing coarse grains is used for computing the layer-layer mutual influence of the integrated circuit;
the parallel computing coarse grain operation module is used for randomly disordering the sequences of all computing tasks executed by the parallel computing coarse grains at the same level in the process of executing the parallel computing coarse grains to form a new computing task sequence, and dynamically distributing the new computing task sequence to different computing processes to complete the parallel computing of the computing tasks.
Furthermore, the first-stage parallel computing coarse grains and the second-stage parallel computing coarse grains are computing task sets in different ranges, the first-stage parallel computing coarse grains comprise a plurality of second-stage parallel computing coarse grains and a computing task for computing electromagnetic fields and current distribution of an integrated circuit layer by using two-dimensional finite elements, the parallel computing grains belonging to the same stage can be computed in parallel, the first-stage parallel computing grains can be distributed with a plurality of computing processes, and the second-stage parallel computing grains can be distributed with only one computing process.
Further, the specific steps of the second-stage parallel computation of coarse grains include:
step 1, calculating an electric field generated by a point current source at a field point, wherein an electric field expression generated by the point current source at the field point is formed according to a layered special structure of an integrated circuitAnalyzing the expression, the current sources of the multilayer integrated circuit are distributed in a layered way, namely, the current density distributed on each metal layer of the integrated circuit layout with the complex shape is only equal to that of the current density distributed on each metal layer of the integrated circuit layout with the complex shapexAndyis related tozIndependently, the current density distribution is onlyx, yA function of (a);
step 2, taking an electric field expression generated by the point current source at the field point as an integrand function of two-dimensional Gaussian integration, and calculating fields generated by the surface current source of the simple-shaped polygon at the same position based on a linear superposition principle of the fields, wherein the field expression comprises the following steps: the field generated by the current source in the two-dimensional plane S at any point in space can be calculated by the two-dimensional gaussian integral:
Figure 556624DEST_PATH_IMAGE022
；
wherein the content of the first and second substances,
Figure 873336DEST_PATH_IMAGE023
at any point in space for the current source within the two-dimensional plane S (x,y,z) The field that is generated is,
Figure 1829DEST_PATH_IMAGE024
is an arbitrary position within the two-dimensional surface S: (u,v) At any point in space (a)x,y,z) The expression of the field that is generated,
Figure 429399DEST_PATH_IMAGE025
representing a gaussian integration point corresponding to a two-dimensional gaussian integration in the two-dimensional plane S,p,qrespectively representu,vIn the first directionpA first, aqThe number of the Gaussian integration points is equal to the total number of the points,
Figure 195624DEST_PATH_IMAGE026
is the weight factor corresponding to the gaussian integral point;
step 3, calculating fields generated by the current on the simple-shaped polygon at different positions of other layers of the integrated circuit, and determining the fields generated by the current on the simple-shaped polygon divided on the layout of other layers of the integrated circuit based on the linear superposition principle of the fields;
step 4, determining the first step based on the linear superposition principle of the fieldlIs layered onmThe electric field generated by the source layer.
Further, the calculation formula of the weighted CPU time of the parallel calculation grain is:
Figure 417657DEST_PATH_IMAGE016
in the formula:
Figure 33447DEST_PATH_IMAGE017
is as followsiThe weighted CPU times of the particles are calculated in parallel,
Figure 264708DEST_PATH_IMAGE018
is as followsiThe CPU time of a single calculation of a grain is calculated in parallel,
Figure 649553DEST_PATH_IMAGE019
is as followsiThe number of particle executions is calculated in parallel.
(III) advantageous effects
In the process of dynamically applying the calculation by coupling among the integrated circuit layers, the invention greatly reduces the communication among the processes and the waiting time generated by synchronization, and simultaneously, because of adopting a random dynamic allocation method of the calculation tasks, the invention ensures that the calculation models with unequal complexity are randomly and uniformly distributed on each calculation node, and avoids the bottleneck of hard disk reading and writing caused by virtual memory access due to overhigh peak memory.
Drawings
The embodiments described below with reference to the drawings are exemplary and intended to be used for explaining and illustrating the present invention and should not be construed as limiting the scope of the present invention.
FIG. 1 is a block diagram of the main steps of a first embodiment of the present invention;
FIG. 2 is a flow chart of the second stage parallel computation coarse grain in the first embodiment of the present invention;
FIG. 3 is a block diagram of the modules of a second embodiment of the present invention;
fig. 4 is an exploded view of the electric field generated at the field point of the point source of the present invention.
Detailed Description
In order to make the implementation objects, technical solutions and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention will be described in more detail below with reference to the accompanying drawings in the embodiments of the present invention.
It should be noted that: in the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described are some embodiments of the present invention, not all embodiments, and features in embodiments and embodiments in the present application may be combined with each other without conflict. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the description of the present invention, it is to be understood that the terms "central," "longitudinal," "lateral," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," and the like are used in the orientation or positional relationship indicated in the drawings, which are used for convenience in describing the invention and for simplicity in description, and are not intended to indicate or imply that the referenced device or element must have a particular orientation, be constructed and operated in a particular orientation, and are not to be considered limiting of the scope of the invention.
The following describes in detail a first embodiment of the coarse grain parallel iterative method and apparatus for integrated circuit interlayer coupling dynamic application provided by the present invention with reference to fig. 1, 2 and 4. The coarse grain parallel iteration method for the interlayer coupling dynamic application of the integrated circuit provided by the embodiment, as shown in fig. 1 and 2, includes the following steps:
step S100, dividing iterative computation of coupling between integrated circuit layers into parallel computation particles, combining the parallel computation particles into two-stage parallel computation coarse particles according to weighted CPU time of the parallel computation particles, wherein the first-stage parallel computation coarse particles are used for computing electromagnetic field and current distribution of each source layer, and the first-stage parallel computation coarse particles comprise the steps of updating source items acting on the source layers in a coupling mode by computing influences of other layers on the source layers and computing the electromagnetic field and current distribution of the source layers by utilizing two-dimensional finite elements; the second level of parallel computing coarse grains is used for computing the layer-layer mutual influence of the integrated circuit;
furthermore, the first-stage parallel computing coarse grains and the second-stage parallel computing coarse grains are computing task sets in different ranges, the first-stage parallel computing coarse grains comprise a plurality of second-stage parallel computing coarse grains and a computing task for computing electromagnetic fields and current distribution of an integrated circuit layer by using a two-dimensional finite element, the parallel computing grains belonging to the same stage can be computed in parallel, the first-stage parallel computing coarse grains can be distributed with a plurality of computing processes, and the second-stage parallel computing coarse grains can be distributed with only one computing process.
Specifically, the weighted CPU time of each parallel computation grain is sorted in descending order and sequentially accumulated until the accumulated sum exceeds 90% of the total CPU time, and each parallel computation grain in the accumulated sum is taken as a parallel computation coarse grain. Wherein, the calculation formula of the weighted CPU time of the parallel calculation particles is as follows:
Figure 541023DEST_PATH_IMAGE016
in the formula:
Figure 644108DEST_PATH_IMAGE017
is as followsiThe weighted CPU times of the particles are calculated in parallel,T i the CPU time of a single calculation for the ith parallel-calculated grain,
Figure 679060DEST_PATH_IMAGE019
is as followsiThe number of times the parallel computation particles are executed; the calculation formula of the total CPU time in the whole calculation process is as follows:
Figure 183991DEST_PATH_IMAGE028
wherein, in the step (A),Tfor the total CPU time of the entire calculation process,mparallel computing grain partitioned for an entire computing programThe number of the first and second groups is,
Figure 747828DEST_PATH_IMAGE017
is as followsiThe weighted CPU times of the particles are calculated in parallel.
For example: if the iterative computation of the integrated circuit interlayer coupling immediate update is divided into 3 parallel computation particles of c1, c2 and c3 according to the definition of the parallel computation particles, the 3 parallel computation particles can execute the computation task of the whole operation process; if c1 executes 500 computation tasks, c2 executes 200 computation tasks, and c3 executes 5 computation tasks; then 705 total computing tasks constitute the whole computation process, which only needs 3 parallel computing granules of c1, c2 and c 3. The whole operation process is executed by 3 parallel computing particles of c1, c2 and c3, and each of c1, c2 and c3 comprises at least 1 independent operation (computing task).
Sorting according to the weighted CPU time obtained by each parallel computing grain operation, wherein if the c1 weighted CPU time is 0.1s, the c2 weighted CPU time is 100s and the c3 weighted CPU time is 0.2s, the final sorting result is c2> c3> c 1; the weighted CPU times for the 3 parallel-calculated particles add sequentially from large to small, i.e., T (c2) + T (c3) + …, until the sum of the times is greater than 90% of the total CPU time; if T (c2) + T (c3) > 90%, then c2, c3 are each taken as a parallel calculation coarse grain; if T (c2) > 90% of the total CPU time, then c2 is parallel computing coarse grain.
The parallel computing coarse grains are classified, the similar parallel computing coarse grains are mutually independent, the corresponding computing task sequences can be randomly disordered, in the process of executing the parallel computing coarse grains, the sequences of all computing tasks executed by the similar parallel computing coarse grains are randomly disordered to form new computing task sequences, and the new computing task sequences are dynamically distributed to different computing processes to complete the parallel computing of the computing tasks.
Specifically, the way of randomly scrambling the operation task sequence is as follows:
firstly, the sequence of operation tasks
Figure 603788DEST_PATH_IMAGE029
Correspondingly generating random number sequences
Figure 678317DEST_PATH_IMAGE030
，m＝1,2,3,…,M. Then to the sequence
Figure 37754DEST_PATH_IMAGE030
The sequences are sorted from small to large, and the sorted sequences are
Figure 38071DEST_PATH_IMAGE031
. Finally, generating new non-repeated operation task sequence
Figure 850169DEST_PATH_IMAGE032
，
Figure 492503DEST_PATH_IMAGE033
Is composed of
Figure 706447DEST_PATH_IMAGE034
In that
Figure 376200DEST_PATH_IMAGE035
Of (c) is used.
The key point is to make all the operation tasks in the parallel particles in sequence
Figure 941174DEST_PATH_IMAGE036
Randomly disorganized to generate new non-repetitive operation task sequence
Figure 856040DEST_PATH_IMAGE037
And then distributing the operation tasks according to the sequence, namely equivalently distributing the original operation tasks randomly, wherein the random distribution strategy is characterized in that a random distribution scheme can completely disturb the distribution sequence of all the operation tasks, so that the sum of the peak value memory occupied by the tasks operated by all the operation nodes at the same time is determined by the average value of the process number and the peak value memory occupied by all the models (calculation particles) rather than the maximum value.
And the main process distributes all the operation tasks required to be executed by the parallel coarse grain calculation to all the processes including the main process according to the formed new calculation task sequence, and completes the parallel operation of all the operation tasks executed by the parallel coarse grain calculation.
In addition, if a certain operation task in the parallel computing coarse grain is distributed to a process, a mark file which is used for indicating that the operation task is already distributed to the operation task is generated; when applying for distributing a certain calculation task, the other process tries to generate a mark file of the calculation task, and automatically applies for distributing the next calculation task by the other process under the condition that the mark file exists.
In the multi-process parallel operation process, the chances of allocating a certain operation task to each process are equal, if no measure is taken, multiple processes may be allocated to the same operation task, and the waste of operation resources is caused, so that some measure must be taken, and all operation tasks are uniquely allocated to a certain process. The simplest and most intuitive measure for achieving this is to assign a task a time stamp, i.e. a task is assigned to a process at the same time as it is marked so that other processes are no longer assigned the task. However, because the variables of each process are generally independent of each other during parallel operation, the operation tasks are asymmetric, the operation states of each process are different, and information distributed by any process through the variable marking task cannot be immediately transmitted to other processes, an external explicit marking method is needed to be adopted so that all processes can obtain the information once the operation tasks are marked. Therefore, if the operation tasks in the parallel computation coarse grains are distributed to the processes, the mark files of the operation tasks are immediately generated; when a process applies for distributing a certain operation task, the process will try to generate a mark file of the operation task, if the mark file exists, the operation task is indicated to be distributed, and the process will automatically apply for distributing the next operation task.
The specific implementation steps for realizing the correct allocation of the operation tasks by utilizing the marker files are as follows:
step A1, a process applies for distributioniAn arithmetic task;
step A2,Judgment ofiSign file of individual operation taskFiIf the current state does not exist, jumping to the step A8, and if the current state does not exist, jumping to the step A3;
step A3, judging the flag file FiWhether the lock is locked or not, jumping to the step A8 if the lock is locked, and jumping to the step A4 if the lock is not locked;
step A4, locking the logo fileFi；
Step A5, generating a logo fileFi；
Step A6, marking fileFiUnlocking;
step A7, completing the first stepiCalculating the operation tasks;
step A8, judging whether all the operation tasks in the parallel computation coarse grain are completed or not, if not, theni＝i+1 and returning to step a1, if finished, jumping to step a 9;
all operation tasks required to be executed by the parallel calculation coarse grain are all distributed to all processes, and the distribution of the parallel calculation coarse grain is finished; it returns to performing all the computational tasks that the other parallel computing coarse grains need to perform individually.
Step S200, the large scale integrated circuit is summarizedN+1 layer, each layer numbered
Figure 924490DEST_PATH_IMAGE038
When considering the second aspect of LSImWhen the current source of the layer is in the current source of the layer, the layer is called the first layermA source layer provided with a secondmActive layer of source layer
Figure 532189DEST_PATH_IMAGE039
Is divided bymOthers of the source layerNLayer integrated circuits, i.e.
Figure 318880DEST_PATH_IMAGE040
Wherein
Figure 97541DEST_PATH_IMAGE041
The 0 th layer is a bottom layer; setting the number of iterations
Figure 551656DEST_PATH_IMAGE042
；
Step S300, if
Figure 64677DEST_PATH_IMAGE043
Computing the first based on the coarse grain of the first stage parallel computingmThe electromagnetic field and current distribution of the source layer are calculated, and the change amount of the electromagnetic field of the layer is calculateddE m And a firstlInfluence value of layer on dyadic Green function of layerG lm Maximum value ofG m,maxAnd minimum valueG m,minWherein 0 is less than or equal tom≤N；
Further, the step S300 includes:
step S310, calculating coarse grains based on the second-stage parallel calculation, and calculating the second stage by utilizing a dyadic Green functionlLayer to layermInfluence of the Source layer, isG lm Wherein, in the step (A),
Figure 604243DEST_PATH_IMAGE020
(ii) a All will beG lm Overlapping to obtain the other layer pairs within the range of the action layermSum of influence of source layers:
Figure 860912DEST_PATH_IMAGE021
(ii) a Finishing the second-stage parallel calculation of coarse grains;
step S320, ifiter>0, willG m As a firstmAdditional sources of source layers added to the secondmIn the source item of the source layer;
step S330, for the secondmThe source layer applies two-dimensional finite element to calculate the electromagnetic field distribution so as to update the electromagnetic field and current distribution of the layer, and the change quantity of the electromagnetic field of the layer is calculateddE m ；
Step S340, according tolInfluence value of layer on dyadic Green function of layerG lm CalculatingG lm Maximum value ofG m,maxAnd minimum valueG m,min。
Step S400, if
Figure 903954DEST_PATH_IMAGE010
And is
Figure 351991DEST_PATH_IMAGE044
And (5) finishing the iteration, and outputting electromagnetic fields and current distributions of each layer, wherein
Figure 50957DEST_PATH_IMAGE009
The iteration precision is preset;
step S500, if
Figure 783421DEST_PATH_IMAGE010
Merging all the influence values of the dyadic Green function obtained by the parallel calculation of the coarse grains at the first stage, and obtaining the maximum value of the influence values of all the dyadic Green functions of the current iterationG maxAnd minimum valueG minCalculating the effective influence value of the dyadic Green function
Figure 448013DEST_PATH_IMAGE011
Here, thethredsholdA discarding threshold value for the influence of a preset dyadic Green function;
step S600, if
Figure 302837DEST_PATH_IMAGE010
Calculating satisfy
Figure 551416DEST_PATH_IMAGE012
Of the conditionG lm Middle distance layermNearest layerl near Will be
Figure 415467DEST_PATH_IMAGE013
Is updated to
Figure 167522DEST_PATH_IMAGE014
(ii) a Because the influence of the point source on any point in the space is weakened along with the distance between the point source and the point as known by the attenuation rule of the electromagnetic field and the electromagnetic wave in the space, the influence value is in inverse proportion to the distance, and the influence value of the layer interface isReflection makes the electromagnetic wave from the source point to the field point in the space weaken faster, therefore, when using the dyadic Green function to calculate the effect of the point source to the space point, it can be considered that the effect of the point source to the space point can be ignored after the distance between the space point and the point source is greater than a certain degree, or the number of the medium layers separated from each other reaches a certain degree. Therefore, in the iteration process, a layer capable of being ignored is determined according to the magnitude of the influence value G of the dyadic Green function, and the second step of self-adaptive adjustment is carried outmExtent of influence of source layer by other layers adjacent thereto
Figure 458826DEST_PATH_IMAGE013
。
Step S700, settingiter=iter+1, the process proceeds to step S300.
Further, the specific steps of parallel coarse grain calculation in the second stage as shown in fig. 2 include:
step S311, calculating an electric field generated by the point current source at the field point, where an electric field expression generated by the point current source at the field point is a special analytic expression formed according to a special structure of the integrated circuit layer, as shown in fig. 4, the concrete analytic expression is as follows: aiming at the frequency domain electromagnetic field of the multilayer integrated circuit layout, the electric field intensity generated by the point source at any layer of field point is calculated by adopting a dyadic Green function, and the electric field intensity in nine directions of any point of any layer of the multilayer integrated circuit layout can be solved through the following formula to express that the electric field expression of the point source to the field point is solved:
the electric field expression generated by the point current source at the field point is as follows:
Figure 693236DEST_PATH_IMAGE046
Figure 95398DEST_PATH_IMAGE047
Figure 701960DEST_PATH_IMAGE048
Figure 429745DEST_PATH_IMAGE050
Figure 387337DEST_PATH_IMAGE051
Figure 327611DEST_PATH_IMAGE052
Figure 555723DEST_PATH_IMAGE053
Figure 454409DEST_PATH_IMAGE054
wherein the content of the first and second substances,
Figure 633718DEST_PATH_IMAGE056
Figure 643262DEST_PATH_IMAGE058
Figure 489995DEST_PATH_IMAGE060
Figure 28424DEST_PATH_IMAGE061
Figure 724722DEST_PATH_IMAGE063
Figure 6799DEST_PATH_IMAGE065
iis the unit of an imaginary number,i 2=-1；
Figure 442460DEST_PATH_IMAGE066
representing a Bessel function of order 0;
Figure 886210DEST_PATH_IMAGE067
representing a Bessel function of order 1;
Figure 275997DEST_PATH_IMAGE068
expressed as a function of the Bessel integral coefficient,
Figure 830606DEST_PATH_IMAGE069
；x, y, zthe coordinates of the field points are represented,
Figure 120773DEST_PATH_IMAGE070
,
Figure 735425DEST_PATH_IMAGE071
,
Figure 875157DEST_PATH_IMAGE072
representing source point coordinates; angular frequency
Figure 233457DEST_PATH_IMAGE073
，
Figure 643710DEST_PATH_IMAGE074
Represents a frequency;
Figure 429263DEST_PATH_IMAGE075
indicating that the site is at the second
Figure 781923DEST_PATH_IMAGE075
A layer of a material selected from the group consisting of,
Figure 943914DEST_PATH_IMAGE076
is as follows
Figure 474253DEST_PATH_IMAGE075
At layer boundarieszCoordinates;
Figure 696287DEST_PATH_IMAGE077
,
Figure 312076DEST_PATH_IMAGE078
respectively represent
Figure 776293DEST_PATH_IMAGE075
The number of complex waves in the horizontal and vertical directions of the layer;
Figure 161138DEST_PATH_IMAGE079
respectively represent
Figure 554073DEST_PATH_IMAGE075
A layer horizontal dielectric constant, a vertical dielectric constant;
Figure 860421DEST_PATH_IMAGE080
,
Figure 131258DEST_PATH_IMAGE081
respectively representlHorizontal magnetic conductivity and vertical magnetic conductivity of the layer;
Figure 370610DEST_PATH_IMAGE082
is shown aslThe anisotropy coefficient of the layer;
Figure 200026DEST_PATH_IMAGE083
,
Figure 790407DEST_PATH_IMAGE084
respectively representlIntegral coefficients of complex wave numbers of the horizontal and vertical layers;
Figure 97892DEST_PATH_IMAGE085
respectively representlThe undetermined coefficient of a layer,A l , B l the following linear equation is solved:
Figure 955864DEST_PATH_IMAGE086
T1is 2n×2nThe complex number matrix of (a) is,
Figure 690602DEST_PATH_IMAGE087
is of length 2nA complex vector of (a);
Figure 502700DEST_PATH_IMAGE089
Figure 879455DEST_PATH_IMAGE090
Figure 827819DEST_PATH_IMAGE091
Figure 500502DEST_PATH_IMAGE092
Figure 799897DEST_PATH_IMAGE093
the following linear equation is solved:
Figure 449184DEST_PATH_IMAGE094
T2is 2n×2nThe complex number matrix of (a) is,
Figure 783213DEST_PATH_IMAGE095
is of length 2nA complex vector of (a);
Figure 125333DEST_PATH_IMAGE097
Figure 144979DEST_PATH_IMAGE098
Figure 597957DEST_PATH_IMAGE099
Figure 786493DEST_PATH_IMAGE100
the following linear equation is solved:
Figure 565093DEST_PATH_IMAGE101
T3is 2n×2nThe complex number matrix of (a) is,
Figure 839080DEST_PATH_IMAGE102
is of length 2nA complex vector of (a);
Figure 597214DEST_PATH_IMAGE103
Figure 905835DEST_PATH_IMAGE104
Figure 589757DEST_PATH_IMAGE105
Figure 85461DEST_PATH_IMAGE107
Figure 145821DEST_PATH_IMAGE108
to representxOriented electric dipole in the second placelOf said electric field generated by said field points of the layerxA component;
Figure 43369DEST_PATH_IMAGE109
to representxOriented electric dipole in the second placelOf said electric field generated by said field points of the layeryA component;
Figure 396728DEST_PATH_IMAGE110
to representxOriented electric dipole in the second placelOf said electric field generated by said field points of the layerzA component;
Figure 379728DEST_PATH_IMAGE111
to representyOriented electric dipole in the second placelOf said electric field generated by said field points of the layerxA component;
Figure 978199DEST_PATH_IMAGE112
to representyOriented electric dipole in the second placelOf said electric field generated by said field points of the layeryA component;
Figure 730255DEST_PATH_IMAGE113
to representyOriented electric dipole in the second placelOf said electric field generated by said field points of the layerzA component;
Figure 21559DEST_PATH_IMAGE114
to representzOriented electric dipole in the second placelOf said electric field generated by said field points of the layerxA component;
Figure 739459DEST_PATH_IMAGE115
to representzOriented electric dipole in the second placelOf said electric field generated by said field points of the layeryA component;
Figure 876042DEST_PATH_IMAGE116
to representzOriented electric dipole in the second placelOf said electric field generated by said field points of the layerzAnd (4) components.
The current sources of the multilayer integrated circuit are distributed in a layered manner, namely the current density distributed on each metal layer of the integrated circuit layout with the complex shape is only equal to that of the current density distributed on each metal layer of the integrated circuit layout with the complex shapexAndyis related tozIndependently, the current density distribution is onlyx, yAs a function of (c).
Step S312, taking an electric field expression generated by the point current source at the field point as an integrand of two-dimensional gaussian integration, and calculating a field generated by the surface current source of the simple-shaped polygon at the same position based on a field linear superposition principle, including: the field generated by the current source in the two-dimensional plane S at any point in space can be calculated by the two-dimensional gaussian integral:
Figure 748183DEST_PATH_IMAGE118
；
wherein the content of the first and second substances,E(x,y,z) At any point in space for the current source in the two-dimensional plane Sx,y,z) The field that is generated is,
Figure 210388DEST_PATH_IMAGE119
is an arbitrary position within the two-dimensional surface S: (u,v) At any point in space (x,y,z) The expression of the dyadic green function of the generated field,
Figure 902401DEST_PATH_IMAGE120
representing a gaussian integration point corresponding to a two-dimensional gaussian integration in the two-dimensional plane S,p,qrespectively representu,vIn the first directionpA first, aqThe number of the Gaussian integration points is equal to the total number of the points,
Figure 341210DEST_PATH_IMAGE026
is the weight factor corresponding to the gaussian integral point;
step S313, calculating fields generated by the current on the simple-shaped polygon at different positions of other layers of the integrated circuit, and determining the fields generated by the current on the simple-shaped polygon divided on the layout of other layers of the integrated circuit based on the linear superposition principle of the fields;
step S314, determining the second step based on the linear superposition principle of the fieldlIs layered onmThe electric field generated by the source layer.
Further, influence values according to the dyadic Green function in the iteration processGDetermines a layer that can be ignored, adaptively adjustsmExtent of influence of source layer by other layers adjacent thereto
Figure 333437DEST_PATH_IMAGE027
。
Further, the coarse grains of the first-stage parallel computation are computed by two-dimensional finite element methodmThe electromagnetic field and current distribution of the source layer are as follows:
for the direct current electric field model, the three-dimensional model of the multilayer integrated circuit refers to the conductivity in the direct current electric field model
Figure 576331DEST_PATH_IMAGE121
Potential of the electrodeuAll the distributions of (A) and (B) are three-dimensional space coordinatesx,y,z) I.e.:
Figure 257104DEST_PATH_IMAGE122
，
Figure 1069DEST_PATH_IMAGE123
the function of the three-dimensional model satisfies the following equation (1):
Figure 847802DEST_PATH_IMAGE124
in the equation (1),
and boundary condition (2):
Figure 651810DEST_PATH_IMAGE125
in the formula
Figure 318415DEST_PATH_IMAGE126
Is a boundary of the first type and is,nis normal to the boundary of the second type,
Figure 630185DEST_PATH_IMAGE127
represents a potentialuAt the first kind boundary
Figure 331425DEST_PATH_IMAGE126
Value of above, using
Figure 40755DEST_PATH_IMAGE128
It is shown that,
Figure 460235DEST_PATH_IMAGE129
bulk current density for external circuits;
the dimension of an actual PCB or a chip packaged board in the multilayer super large scale integrated circuit is far larger than the thickness of the metal layer, so that the three-dimensional direct current field problem of the multilayer integrated circuit is simplified into a two-dimensional direct current field problem;
the field solving equation set established by the finite element method for the two-dimensional model is an equation set (3):
Figure 811582DEST_PATH_IMAGE131
in the formula (I), theI(u) In order to be a functional function,tis the thickness of the metal layer or layers,
Figure 367328DEST_PATH_IMAGE132
as a grid celleThe electrical conductivity of (a) a (b),
Figure 749025DEST_PATH_IMAGE133
as a grid celleThe potential of (a) is set to be,
Figure 655801DEST_PATH_IMAGE134
as a grid celleThe area of (a) is,
Figure 545259DEST_PATH_IMAGE135
as the density of the surface current, the current density,
Figure 955512DEST_PATH_IMAGE136
representing grid cellseThe edge of (1);
for the alternating electromagnetic field model, the three-dimensional model of the multilayer integrated circuit refers to the dielectric constant in the three-dimensional model of the electromagnetic response characteristic in the frequency domain simulation of the multilayer VLSI
Figure 537803DEST_PATH_IMAGE137
Magnetic permeability of
Figure 666296DEST_PATH_IMAGE138
Electric field intensityEMagnetic field intensityHAll the distributions of (A) and (B) are three-dimensional space coordinatesx,y,z) I.e.:
Figure 592402DEST_PATH_IMAGE139
,
Figure 388319DEST_PATH_IMAGE140
,
Figure 875932DEST_PATH_IMAGE141
，
Figure 226142DEST_PATH_IMAGE142
the function of the three-dimensional model satisfies the following equation:
Figure 457403DEST_PATH_IMAGE143
in the formulaJFor the purpose of the applied current density distribution,
Figure 842248DEST_PATH_IMAGE144
for the angular frequency simulated for the integrated circuit,
Figure 736648DEST_PATH_IMAGE145
indicating the strength of the magnetic fieldHRotation of，
Figure 839734DEST_PATH_IMAGE146
Indicates the electric field intensityEThe degree of rotation of the screw is reduced,jis the unit of an imaginary number,j 2=-1；
the board size of the actual PCB or chip package in the multilayer VLSI is far larger than the metal layer spacing, the three-dimensional model of the electromagnetic response characteristics in the frequency domain simulation of the multilayer VLSI is simplified into a two-dimensional model, and the dielectric constant in the model is at the moment
Figure 609107DEST_PATH_IMAGE137
Magnetic permeability of
Figure 848458DEST_PATH_IMAGE138
Electric field intensityEMagnetic field intensityHAll the distributions are two-dimensional plane coordinates (x,y) I.e.:
Figure 910830DEST_PATH_IMAGE147
，
Figure 235632DEST_PATH_IMAGE148
，
Figure 808696DEST_PATH_IMAGE149
，
Figure 168133DEST_PATH_IMAGE150
distribution thereof andzindependent of and potential in the fielduAnd surface current densityJ sSatisfies the following conditions:
Figure 902871DEST_PATH_IMAGE151
in the formula (I), the compound is shown in the specification,
Figure 204715DEST_PATH_IMAGE152
respectively representx, y, zThe unit vector of the direction is,E zof electric field strengthzThe direction component of the light beam is,H xandH yrespectively of magnetic field strengthxAndythe direction component of the light beam is,his the metal layer spacing;
through the simplification from the three-dimensional model to the two-dimensional model, the two-dimensional finite element functional extreme value formula corresponding to the two-dimensional model is obtained as follows:
Figure 315890DEST_PATH_IMAGE153
in the formula (I), the compound is shown in the specification,
Figure 264255DEST_PATH_IMAGE155
in order to be a functional function,
Figure 435473DEST_PATH_IMAGE156
it is shown that the extreme value is taken for the functional,
Figure 734867DEST_PATH_IMAGE157
as a grid celliThe surface admittance of the first and second electrodes,
Figure 148269DEST_PATH_IMAGE158
is a boundary
Figure 747878DEST_PATH_IMAGE159
The boundary condition of the opening of (a),u kis a boundary
Figure 89997DEST_PATH_IMAGE160
The distribution of the electric potential on the upper side,
Figure 611108DEST_PATH_IMAGE161
indicating a position to the right of the boundary and infinitely close to the boundary,
Figure 329666DEST_PATH_IMAGE162
indicating a position to the left of the boundary and infinitely close to the boundary,
Figure 518202DEST_PATH_IMAGE163
representing grid cellsiThe area of (a) is,
Figure 267108DEST_PATH_IMAGE164
as a grid celliThe current density of (a) is,
Figure 275515DEST_PATH_IMAGE165
as a grid celliThe surface resistance of the glass substrate is higher than the surface resistance of the glass substrate,
Figure 266605DEST_PATH_IMAGE166
as a grid celliThe potential of (a) is set to be,kis referred to askAnd (4) a boundary.
From the above iteration steps, it can be seen that each iteration updates the electromagnetic field distribution and current distribution of each layer, rather than actively calculating the influence of the source layer on other layers. When the electromagnetic field distribution and the current distribution of each layer are calculated, the source item of the layer is determined to be the excitation source corresponding to the external circuit and the source item corresponding to the influence of other layers on the excitation source. The influence of other layers on the electromagnetic field and the electromagnetic wave can be determined according to the attenuation rule of the electromagnetic field and the electromagnetic wave in the space. And meanwhile, in the iteration process, the range of the influence exerted on other layers by each source layer is adaptively adjusted according to the magnitude of the influence value of the dyadic Green function of each layer.
Particularly, when the voltage drop and the current distribution of a power supply layer of the integrated circuit are analyzed, the working frequency is low frequency, the direct current field model is adopted for analysis, no space coupling exists between the integrated circuit layers at the moment, only physical coupling exists, namely, the layers which are connected with each other through the through hole and the external circuit are mutually coupled, at the moment, the mutual influence layers between the integrated circuit layers are determined, and iteration is not needed to influence the influence rangeN eff，m And (6) correcting.
A second embodiment of the coarse grain parallel iterative method and apparatus for interlayer coupling dynamic application of an integrated circuit provided by the present invention is described in detail below with reference to fig. 3 and 4. As shown in fig. 3 and 4, the coarse grain parallel iteration apparatus for interlayer coupling dynamic application of an integrated circuit provided in this embodiment includes, as shown in fig. 3, a parallel calculation grain division module, a parallel calculation coarse grain division module, and a parallel calculation coarse grain operation module;
the parallel computing particle dividing module is used for dividing iterative computing of interlayer coupling of the integrated circuit into parallel computing particles;
the parallel computing coarse grain dividing module is used for acquiring weighted CPU time of each parallel computing grain and total CPU time of an iteration method for coupling real-time updating between layers of an integrated circuit based on one-time complete serial iterative computation, and combining the parallel computing grains into two-stage parallel computing coarse grains according to the ratio of the weighted CPU time to the total CPU time; the first stage of parallel coarse grain calculation is to calculate the electromagnetic field and current distribution of each source layer, and the first stage of parallel coarse grain calculation comprises the steps of calculating the influence of other layers on the source layer to update source items acting on the source layer in a coupling mode and calculating the electromagnetic field and current distribution of the source layer by utilizing two-dimensional finite elements; the second level of parallel computing coarse grains is used for computing the layer-layer mutual influence of the integrated circuit;
specifically, the weighted CPU time of each parallel computation grain is sorted in descending order and sequentially accumulated until the accumulated sum exceeds 90% of the total CPU time, and each parallel computation grain in the accumulated sum is taken as a parallel computation coarse grain. Wherein, the calculation formula of the weighted CPU time of the parallel calculation particles is as follows:
Figure 44068DEST_PATH_IMAGE016
in the formula:
Figure 960946DEST_PATH_IMAGE017
is as followsiThe weighted CPU times of the particles are calculated in parallel,
Figure 456650DEST_PATH_IMAGE018
is as followsiThe CPU time of a single calculation of a grain is calculated in parallel,
Figure 985851DEST_PATH_IMAGE019
is as followsiThe number of times the parallel computation particles are executed; the calculation formula of the total CPU time in the whole calculation process is as follows:
Figure 883400DEST_PATH_IMAGE028
wherein, in the step (A),Tfor the total CPU time of the entire calculation process,mthe number of parallel computing grains divided for the entire computing program,
Figure 974109DEST_PATH_IMAGE017
is as followsiThe weighted CPU times of the particles are calculated in parallel.
For example: if the iterative computation of the integrated circuit interlayer coupling immediate update is divided into 3 parallel computation particles of c1, c2 and c3 according to the definition of the parallel computation particles, the 3 parallel computation particles can execute the computation task of the whole operation process; if c1 executes 500 computation tasks, c2 executes 200 computation tasks, and c3 executes 5 computation tasks; then 705 total computing tasks constitute the whole computation process, which only needs 3 parallel computing granules of c1, c2 and c 3. The whole operation process is executed by 3 parallel computing particles of c1, c2 and c3, and each of c1, c2 and c3 comprises at least 1 independent operation (computing task).
Sorting according to the weighted CPU time obtained by each parallel computing grain operation, wherein if the c1 weighted CPU time is 0.1s, the c2 weighted CPU time is 100s and the c3 weighted CPU time is 0.2s, the final sorting result is c2> c3> c 1; the weighted CPU times for the 3 parallel-calculated particles add sequentially from large to small, i.e., T (c2) + T (c3) + …, until the sum of the times is greater than 90% of the total CPU time; if T (c2) + T (c3) > 90%, then c2, c3 are each taken as a parallel calculation coarse grain; if T (c2) > 90% of the total CPU time, then c2 is parallel computing coarse grain.
The parallel computing coarse grains are classified, the similar parallel computing coarse grains are mutually independent, the corresponding computing task sequences can be randomly disordered, in the process of executing the parallel computing coarse grains, the sequences of all computing tasks executed by the similar parallel computing coarse grains are randomly disordered to form new computing task sequences, and the new computing task sequences are dynamically distributed to different computing processes to complete the parallel computing of the computing tasks.
Furthermore, the first-stage parallel computing coarse grains and the second-stage parallel computing coarse grains are computing task sets in different ranges, the first-stage parallel computing coarse grains comprise a plurality of second-stage parallel computing coarse grains and a computing task for computing electromagnetic fields and current distribution of an integrated circuit layer by using two-dimensional finite elements, the parallel computing grains belonging to the same stage can be computed in parallel, the first-stage parallel computing grains can be distributed with a plurality of computing processes, and the second-stage parallel computing grains can be distributed with only one computing process.
The parallel computing coarse grain operation module is used for randomly disordering the sequences of all computing tasks executed by the parallel computing coarse grains at the same level in the process of executing the parallel computing coarse grains to form a new computing task sequence, and dynamically distributing the new computing task sequence to different computing processes to complete the parallel computing of the computing tasks.
Specifically, the way of randomly scrambling the operation task sequence is as follows:
firstly, the sequence of operation tasks
Figure 691530DEST_PATH_IMAGE029
Correspondingly generating random number sequences
Figure 290001DEST_PATH_IMAGE030
，m＝1,2,3,…,M. Then to the sequence
Figure 42057DEST_PATH_IMAGE030
The sequences are sorted from small to large, and the sorted sequences are
Figure 300737DEST_PATH_IMAGE031
. Finally, generating new non-repeated operation task sequence
Figure 505454DEST_PATH_IMAGE032
，
Figure 642037DEST_PATH_IMAGE033
Is composed of
Figure 248599DEST_PATH_IMAGE034
In that
Figure 445225DEST_PATH_IMAGE035
Of (c) is used.
The key point is to make all the operation tasks in the parallel particles in sequence
Figure 638702DEST_PATH_IMAGE036
Randomly disorganized to generate new non-repetitive operation task sequence
Figure 844556DEST_PATH_IMAGE037
And then distributing the operation tasks according to the sequence, namely equivalently distributing the original operation tasks randomly, wherein the random distribution strategy is characterized in that a random distribution scheme can completely disturb the distribution sequence of all the operation tasks, so that the sum of the peak value memory occupied by the tasks operated by all the operation nodes at the same time is determined by the average value of the process number and the peak value memory occupied by all the models (calculation particles) rather than the maximum value.
And the main process distributes all the operation tasks required to be executed by the parallel coarse grain calculation to all the processes including the main process according to the formed new calculation task sequence, and completes the parallel operation of all the operation tasks executed by the parallel coarse grain calculation.
In addition, if a certain operation task in the parallel computing coarse grain is distributed to a process, a mark file which is used for indicating that the operation task is already distributed to the operation task is generated; when applying for distributing a certain calculation task, the other process tries to generate a mark file of the calculation task, and automatically applies for distributing the next calculation task by the other process under the condition that the mark file exists.
In the multi-process parallel operation process, the chances of allocating a certain operation task to each process are equal, if no measure is taken, multiple processes may be allocated to the same operation task, and the waste of operation resources is caused, so that some measure must be taken, and all operation tasks are uniquely allocated to a certain process. The simplest and most intuitive measure for achieving this is to assign a task a time stamp, i.e. a task is assigned to a process at the same time as it is marked so that other processes are no longer assigned the task. However, because the variables of each process are generally independent of each other during parallel operation, the operation tasks are asymmetric, the operation states of each process are different, and information distributed by any process through the variable marking task cannot be immediately transmitted to other processes, an external explicit marking method is needed to be adopted so that all processes can obtain the information once the operation tasks are marked. Therefore, if the operation tasks in the parallel computation coarse grains are distributed to the processes, the mark files of the operation tasks are immediately generated; when a process applies for distributing a certain operation task, the process will try to generate a mark file of the operation task, if the mark file exists, the operation task is indicated to be distributed, and the process will automatically apply for distributing the next operation task.
The specific implementation steps for realizing the correct allocation of the operation tasks by utilizing the marker files are as follows:
step A1, a process applies for distributioniAn arithmetic task;
step A2, judgmentiSign file of individual operation taskFiIf the current state does not exist, jumping to the step A8, and if the current state does not exist, jumping to the step A3;
step A3, judging the mark fileFiWhether the lock is locked or not, jumping to the step A8 if the lock is locked, and jumping to the step A4 if the lock is not locked;
step A4, locking the logo fileFi；
Step A5, generating a logo fileFi；
Step A6, marking fileFiUnlocking;
step A7, completing the first stepiCalculating the operation tasks;
step A8, judging whether all the operation tasks in the parallel computation coarse grain are completed or not, if not, theni＝i+1 and returning to step a1, if finished, jumping to step a 9;
all operation tasks required to be executed by the parallel calculation coarse grain are all distributed to all processes, and the distribution of the parallel calculation coarse grain is finished; it returns to performing all the computational tasks that the other parallel computing coarse grains need to perform individually.
Further, the specific steps of the second-stage parallel computation of coarse grains include:
step 1, calculating an electric field generated at a field point by a point current source, wherein an electric field expression generated at the field point by the point current source is a special analytical expression formed according to a special layered structure of an integrated circuit, as shown in fig. 4, the analytical expression is as follows: aiming at the frequency domain electromagnetic field of the multilayer integrated circuit layout, the electric field intensity generated by the point source at any layer of field point is calculated by adopting a dyadic Green function, and the electric field intensity in nine directions of any point of any layer of the multilayer integrated circuit layout can be solved through the following formula to express that the electric field expression of the point source to the field point is solved:
the electric field expression generated by the point current source at the field point is as follows:
Figure DEST_PATH_IMAGE167
Figure 40045DEST_PATH_IMAGE047
Figure 407572DEST_PATH_IMAGE048
Figure 616574DEST_PATH_IMAGE168
Figure 360539DEST_PATH_IMAGE051
Figure 941693DEST_PATH_IMAGE052
Figure 745701DEST_PATH_IMAGE053
Figure 677885DEST_PATH_IMAGE054
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE169
Figure 207566DEST_PATH_IMAGE170
Figure DEST_PATH_IMAGE171
Figure 846489DEST_PATH_IMAGE061
Figure 86978DEST_PATH_IMAGE062
Figure 240879DEST_PATH_IMAGE064
iis the unit of an imaginary number,i 2=-1；
Figure 326646DEST_PATH_IMAGE066
representing a Bessel function of order 0;
Figure 646507DEST_PATH_IMAGE067
representing a Bessel function of order 1;
Figure 792318DEST_PATH_IMAGE068
expressed as a function of the Bessel integral coefficient,
Figure 433514DEST_PATH_IMAGE069
；x, y, zthe coordinates of the field points are represented,
Figure 588552DEST_PATH_IMAGE070
,
Figure 202067DEST_PATH_IMAGE071
,
Figure 692348DEST_PATH_IMAGE072
representing source point coordinates; angular frequency
Figure 86420DEST_PATH_IMAGE073
，
Figure 513990DEST_PATH_IMAGE074
Represents a frequency;
Figure 44329DEST_PATH_IMAGE075
indicating that the site is at the second
Figure 30477DEST_PATH_IMAGE075
A layer of a material selected from the group consisting of,
Figure 646266DEST_PATH_IMAGE076
is as follows
Figure 877527DEST_PATH_IMAGE075
At layer boundarieszCoordinates;
Figure 262372DEST_PATH_IMAGE077
,
Figure 186466DEST_PATH_IMAGE078
respectively represent
Figure 23972DEST_PATH_IMAGE172
The number of complex waves in the horizontal and vertical directions of the layer;
Figure 294810DEST_PATH_IMAGE079
respectively represent
Figure 65320DEST_PATH_IMAGE172
A layer horizontal dielectric constant, a vertical dielectric constant;
Figure 894735DEST_PATH_IMAGE080
,
Figure 219538DEST_PATH_IMAGE081
respectively representlHorizontal magnetic conductivity and vertical magnetic conductivity of the layer;
Figure 792601DEST_PATH_IMAGE082
is shown aslThe anisotropy coefficient of the layer;
Figure 417618DEST_PATH_IMAGE083
,
Figure 916470DEST_PATH_IMAGE084
respectively representlIntegral coefficients of complex wave numbers of the horizontal and vertical layers;
Figure 994147DEST_PATH_IMAGE085
respectively representlThe undetermined coefficient of a layer,A l , B l the following linear equation is solved:
Figure 105323DEST_PATH_IMAGE086
T1is 2n×2nThe complex number matrix of (a) is,
Figure 319266DEST_PATH_IMAGE087
is of length 2nA complex vector of (a);
Figure DEST_PATH_IMAGE173
Figure 959326DEST_PATH_IMAGE174
Figure DEST_PATH_IMAGE175
Figure 697869DEST_PATH_IMAGE092
Figure 612735DEST_PATH_IMAGE093
the following linear equation is solved:
Figure 681185DEST_PATH_IMAGE094
T2is 2n×2nThe complex number matrix of (a) is,
Figure 757726DEST_PATH_IMAGE095
is of length 2nA complex vector of (a);
Figure 42951DEST_PATH_IMAGE176
Figure 761508DEST_PATH_IMAGE098
Figure 684465DEST_PATH_IMAGE099
Figure 931907DEST_PATH_IMAGE100
the following linear equation is solved:
Figure 205893DEST_PATH_IMAGE101
T3is 2n×2nThe complex number matrix of (a) is,
Figure 952308DEST_PATH_IMAGE102
is of length 2nA complex vector of (a);
Figure 995351DEST_PATH_IMAGE103
Figure DEST_PATH_IMAGE177
Figure 616956DEST_PATH_IMAGE105
Figure 378239DEST_PATH_IMAGE178
Figure 671555DEST_PATH_IMAGE108
to representxOriented electric dipole in the second placelOf said electric field generated by said field points of the layerxA component;
Figure 569103DEST_PATH_IMAGE109
to representxOriented electric dipole in the second placelOf said electric field generated by said field points of the layeryA component;
Figure 423927DEST_PATH_IMAGE110
to representxOriented electric dipole in the second placelOf said electric field generated by said field points of the layerzA component;
Figure 406926DEST_PATH_IMAGE111
to representyOriented electric dipole in the second placelSaid field of the layerOf said electric field generated by the dotsxA component;
Figure 270977DEST_PATH_IMAGE112
to representyOriented electric dipole in the second placelOf said electric field generated by said field points of the layeryA component;
Figure 790077DEST_PATH_IMAGE113
to representyOriented electric dipole in the second placelOf said electric field generated by said field points of the layerzA component;
Figure 815802DEST_PATH_IMAGE114
to representzOriented electric dipole in the second placelOf said electric field generated by said field points of the layerxA component;
Figure 286097DEST_PATH_IMAGE115
to representzOriented electric dipole in the second placelOf said electric field generated by said field points of the layeryA component;
Figure 953839DEST_PATH_IMAGE116
to representzOriented electric dipole in the second placelOf said electric field generated by said field points of the layerzAnd (4) components.
The current sources of the multilayer integrated circuit are distributed in a layered manner, namely the current density distributed on each metal layer of the integrated circuit layout with the complex shape is only equal to that of the current density distributed on each metal layer of the integrated circuit layout with the complex shapexAndyis related tozIndependently, the current density distribution is onlyx, yAs a function of (c).
Step 2, taking an electric field expression generated by the point current source at the field point as an integrand function of two-dimensional Gaussian integration, and calculating fields generated by the surface current source of the simple-shaped polygon at the same position based on a linear superposition principle of the fields, wherein the field expression comprises the following steps: the field generated by the current source in the two-dimensional plane S at any point in space can be calculated by the two-dimensional gaussian integral:
Figure DEST_PATH_IMAGE179
；
wherein the content of the first and second substances,E(x,y,z) At any point in space for the current source in the two-dimensional plane Sx,y,z) The field that is generated is,
Figure 29242DEST_PATH_IMAGE119
is an arbitrary position within the two-dimensional surface S: (u,v) At any point in space (x,y,z) The expression of the dyadic green function of the generated field,
Figure 724404DEST_PATH_IMAGE120
representing a gaussian integration point corresponding to a two-dimensional gaussian integration in the two-dimensional plane S,p,qrespectively representu,vIn the first directionpA first, aqThe number of the Gaussian integration points is equal to the total number of the points,
Figure 681995DEST_PATH_IMAGE026
is the weight factor corresponding to the gaussian integral point;
step 3, calculating fields generated by the current on the simple-shaped polygon at different positions of other layers of the integrated circuit, and determining the fields generated by the current on the simple-shaped polygon divided on the layout of other layers of the integrated circuit based on the linear superposition principle of the fields;
step 4, determining the first step based on the linear superposition principle of the fieldlIs layered onmThe electric field generated by the source layer.
Further, influence values according to the dyadic Green function in the iteration processGDetermines a layer that can be ignored, adaptively adjustsmExtent of influence of source layer by other layers adjacent thereto
Figure 622269DEST_PATH_IMAGE027
。
Further, the above-mentionedThe coarse grains are calculated in parallel in the first stage through two-dimensional finite element calculationmThe electromagnetic field and current distribution of the source layer are as follows:
for the direct current electric field model, the three-dimensional model of the multilayer integrated circuit refers to the conductivity in the direct current electric field model
Figure 348917DEST_PATH_IMAGE121
Potential of the electrodeuAll the distributions of (A) and (B) are three-dimensional space coordinatesx,y,z) I.e.:
Figure 982024DEST_PATH_IMAGE122
，
Figure 662797DEST_PATH_IMAGE123
the function of the three-dimensional model satisfies the following equation (1):
Figure 141183DEST_PATH_IMAGE124
in the equation (1),
and boundary condition (2):
Figure 987916DEST_PATH_IMAGE125
in the formula
Figure 526345DEST_PATH_IMAGE126
Is a boundary of the first type and is,nis normal to the boundary of the second type,
Figure 458529DEST_PATH_IMAGE127
represents a potentialuAt the first kind boundary
Figure 239141DEST_PATH_IMAGE126
Value of above, using
Figure 674801DEST_PATH_IMAGE128
It is shown that,
Figure 649711DEST_PATH_IMAGE129
bulk current density for external circuits;
the dimension of an actual PCB or a chip packaged board in the multilayer super large scale integrated circuit is far larger than the thickness of the metal layer, so that the three-dimensional direct current field problem of the multilayer integrated circuit is simplified into a two-dimensional direct current field problem;
the field solving equation set established by the finite element method for the two-dimensional model is an equation set (3):
Figure 803611DEST_PATH_IMAGE180
in the formula (I), theI(u) In order to be a functional function,tis the thickness of the metal layer or layers,
Figure 889379DEST_PATH_IMAGE132
as a grid celleThe electrical conductivity of (a) a (b),
Figure 946590DEST_PATH_IMAGE133
as a grid celleThe potential of (a) is set to be,
Figure 92401DEST_PATH_IMAGE134
as a grid celleThe area of (a) is,
Figure 733598DEST_PATH_IMAGE135
as the density of the surface current, the current density,
Figure 91898DEST_PATH_IMAGE136
representing grid cellseThe edge of (1);
for the alternating electromagnetic field model, the three-dimensional model of the multilayer integrated circuit refers to the dielectric constant in the three-dimensional model of the electromagnetic response characteristic in the frequency domain simulation of the multilayer VLSI
Figure 767730DEST_PATH_IMAGE137
Magnetic permeability of
Figure 317397DEST_PATH_IMAGE138
Electric field intensityEMagnetic field intensityHAre all distributedAs three-dimensional space coordinates (x,y,z) I.e.:
Figure 445890DEST_PATH_IMAGE139
,
Figure 607882DEST_PATH_IMAGE140
,
Figure 872641DEST_PATH_IMAGE141
，
Figure 607858DEST_PATH_IMAGE142
the function of the three-dimensional model satisfies the following equation:
Figure 958068DEST_PATH_IMAGE143
in the formulaJFor the purpose of the applied current density distribution,
Figure 189329DEST_PATH_IMAGE144
for the angular frequency simulated for the integrated circuit,
Figure 574174DEST_PATH_IMAGE145
indicating the strength of the magnetic fieldHThe degree of rotation of the screw is reduced,
Figure 701530DEST_PATH_IMAGE146
indicates the electric field intensityEThe degree of rotation of the screw is reduced,jis the unit of an imaginary number,j 2=-1；
the board size of the actual PCB or chip package in the multilayer VLSI is far larger than the metal layer spacing, the three-dimensional model of the electromagnetic response characteristics in the frequency domain simulation of the multilayer VLSI is simplified into a two-dimensional model, and the dielectric constant in the model is at the moment
Figure 303151DEST_PATH_IMAGE137
Magnetic permeability of
Figure 806944DEST_PATH_IMAGE138
Electric field intensityEMagnetic field intensityHAll the distributions are two-dimensional plane coordinates (x,y) I.e.:
Figure 311875DEST_PATH_IMAGE147
，
Figure 610132DEST_PATH_IMAGE148
，
Figure 311765DEST_PATH_IMAGE149
，
Figure 88092DEST_PATH_IMAGE150
distribution thereof andzindependent of and potential in the fielduAnd surface current densityJ sSatisfies the following conditions:
Figure 946064DEST_PATH_IMAGE151
in the formula (I), the compound is shown in the specification,
Figure 946381DEST_PATH_IMAGE152
respectively representx, y, zThe unit vector of the direction is,E zof electric field strengthzThe direction component of the light beam is,H xandH yrespectively of magnetic field strengthxAndythe direction component of the light beam is,his the metal layer spacing;
through the simplification from the three-dimensional model to the two-dimensional model, the two-dimensional finite element functional extreme value formula corresponding to the two-dimensional model is obtained as follows:
Figure 758479DEST_PATH_IMAGE153
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE181
in order to be a functional function,
Figure 338496DEST_PATH_IMAGE156
it is shown that the extreme value is taken for the functional,
Figure 818019DEST_PATH_IMAGE157
as a grid celliThe surface admittance of the first and second electrodes,
Figure 490702DEST_PATH_IMAGE158
is a boundary
Figure 790097DEST_PATH_IMAGE159
The boundary condition of the opening of (a),u kis a boundary
Figure 704963DEST_PATH_IMAGE160
The distribution of the electric potential on the upper side,
Figure 773413DEST_PATH_IMAGE161
indicating a position to the right of the boundary and infinitely close to the boundary,
Figure 381112DEST_PATH_IMAGE162
indicating a position to the left of the boundary and infinitely close to the boundary,
Figure 167802DEST_PATH_IMAGE163
representing grid cellsiThe area of (a) is,
Figure 119316DEST_PATH_IMAGE164
as a grid celliThe current density of (a) is,
Figure 573431DEST_PATH_IMAGE165
as a grid celliThe surface resistance of the glass substrate is higher than the surface resistance of the glass substrate,
Figure 86452DEST_PATH_IMAGE166
as a grid celliThe potential of (a) is set to be,kis referred to askAnd (4) a boundary. From the above iteration steps, it can be seen that each iteration updates the electromagnetic field distribution and current distribution of each layer, rather than actively calculating the influence of the source layer on other layers. When the electromagnetic field distribution and the current distribution of each layer are calculated, determining the source item of the layer as an excitation source corresponding to an external circuitAnd source items for which other layers affect it. The influence of other layers on the electromagnetic field and the electromagnetic wave can be determined according to the attenuation rule of the electromagnetic field and the electromagnetic wave in the space. And meanwhile, in the iteration process, the range of the influence exerted on other layers by each source layer is adaptively adjusted according to the magnitude of the influence value of the dyadic Green function of each layer.
Particularly, when the voltage drop and the current distribution of a power supply layer of the integrated circuit are analyzed, the working frequency is low frequency, the direct current field model is adopted for analysis, no space coupling exists between the integrated circuit layers at the moment, only physical coupling exists, namely, the layers which are connected with each other through the through hole and the external circuit are mutually coupled, at the moment, the mutual influence layers between the integrated circuit layers are determined, and iteration is not needed to influence the influence range
Figure 360438DEST_PATH_IMAGE027
And (6) correcting.
The above description is only for the specific embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.

Claims (10)

1. A coarse grain parallel iteration method for coupling dynamic application between layers of an integrated circuit is characterized by comprising the following steps:
step S100, dividing iterative computation of coupling between integrated circuit layers into parallel computation particles, combining the parallel computation particles into two-stage parallel computation coarse particles according to weighted CPU time of the parallel computation particles, wherein the first-stage parallel computation coarse particles are used for computing electromagnetic field and current distribution of each source layer, and the first-stage parallel computation coarse particles comprise the steps of updating source items acting on the source layers in a coupling mode by computing influences of other layers on the source layers and computing the electromagnetic field and current distribution of the source layers by utilizing two-dimensional finite elements; the second level of parallel computing coarse grains is used for computing the layer-layer mutual influence of the integrated circuit;
step S200, the large scale integrated circuit is summarizedN+1 layer, each layer numbered
Figure DEST_PATH_IMAGE001
When considering the second aspect of LSImWhen the current source of the layer is in the current source of the layer, the layer is called the first layermA source layer provided with a secondmActive layer of source layer
Figure 190815DEST_PATH_IMAGE002
Is divided bymOthers of the source layerNLayer integrated circuits, i.e.
Figure DEST_PATH_IMAGE003
Wherein
Figure 803193DEST_PATH_IMAGE004
The 0 th layer is a bottom layer; setting the number of iterations
Figure DEST_PATH_IMAGE005
；
Step S300, if
Figure 201944DEST_PATH_IMAGE006
Computing the first based on the coarse grain of the first stage parallel computingmThe electromagnetic field and current distribution of the source layer are calculated, and the change amount of the electromagnetic field of the layer is calculateddE m And a firstlInfluence value of layer on dyadic Green function of layerG lm Maximum value ofG m,maxAnd minimum valueG m,minWherein 0 is less than or equal tom≤N；
Step S400, if
Figure DEST_PATH_IMAGE007
And is
Figure 507155DEST_PATH_IMAGE008
And (5) finishing the iteration, and outputting electromagnetic fields and current distributions of each layer, wherein
Figure 545518DEST_PATH_IMAGE010
The iteration precision is preset;
step S500, if
Figure DEST_PATH_IMAGE011
Merging all the influence values of the dyadic Green function obtained by the parallel calculation of the coarse grains at the first stage, and obtaining the maximum value of the influence values of all the dyadic Green functions of the current iterationG maxAnd minimum valueG minCalculating the effective influence value of the dyadic Green function
Figure 696008DEST_PATH_IMAGE012
Here, thethredsholdA discarding threshold value for the influence of a preset dyadic Green function;
step S600, if
Figure 277162DEST_PATH_IMAGE011
Calculating satisfy
Figure DEST_PATH_IMAGE013
Of the conditionG lm Middle distance layermNearest layerl near Will be
Figure 222115DEST_PATH_IMAGE014
Is updated to
Figure DEST_PATH_IMAGE015
；
Step S700, setting
Figure 560824DEST_PATH_IMAGE016
The process proceeds to step S300.
2. The method of claim 1, wherein in step S100, the parallel computing of the coarse grain is performedThe formula for calculating the weighted CPU time is as follows:
Figure DEST_PATH_IMAGE017
in the formula:
Figure 108480DEST_PATH_IMAGE018
is as followsiThe weighted CPU times of the particles are calculated in parallel,
Figure 278561DEST_PATH_IMAGE019
is as followsiThe CPU time of a single calculation of a grain is calculated in parallel,
Figure DEST_PATH_IMAGE020
is as followsiThe number of particle executions is calculated in parallel.
3. The integrated circuit interlayer coupling dynamic applied coarse grain parallel iteration method according to claim 2, wherein the first-stage parallel computation coarse grains and the second-stage parallel computation coarse grains are a set of computation tasks in different ranges, the first-stage parallel computation coarse grains comprise a plurality of second-stage parallel computation coarse grains and a computation task for computing electromagnetic fields and current distributions of the integrated circuit layer by using two-dimensional finite elements, parallel computation grains belonging to the same stage can be computed in parallel, the first-stage parallel computation grains can be allocated with a plurality of computation processes, and the second-stage parallel computation grains can be allocated with only one computation process.
4. The integrated circuit interlayer coupling dynamic applied coarse grain parallel iterative method of claim 1, wherein said step S300 comprises:
step S310, calculating coarse grains based on the second-stage parallel calculation, and calculating the second stage by utilizing a dyadic Green functionlLayer to layermInfluence of the Source layer, isG lm Wherein, in the step (A),
Figure 394416DEST_PATH_IMAGE021
(ii) a All will beG lm Overlapping to obtain the other layer pairs within the range of the action layermSum of influence of source layers:
Figure DEST_PATH_IMAGE022
(ii) a Finishing the second-stage parallel calculation of coarse grains;
step S320, ifiter>0, willG m As a firstmAdditional sources of source layers added to the secondmIn the source item of the source layer;
step S330, for the secondmThe source layer applies two-dimensional finite element to calculate the electromagnetic field distribution so as to update the electromagnetic field and current distribution of the layer, and the change quantity of the electromagnetic field of the layer is calculateddE m ；
Step S340, according tolInfluence value of layer on dyadic Green function of layerG lm CalculatingG lm Maximum value ofG m,maxAnd minimum valueG m,min。
5. The method of claim 4, wherein the step of performing parallel coarse grain computation at the second stage comprises:
step S311, calculating the electric field generated by the point current source at the field point, wherein the electric field expression generated by the point current source at the field point is a special analytic expression formed according to the layered special structure of the integrated circuit, and the current sources of the multilayer integrated circuit are layered, that is, the current density distributed on each metal layer of the integrated circuit layout with the complex shape is only equal to that of each metal layer of the integrated circuit layout with the complex shapexAndyis related tozIndependently, the current density distribution is onlyx, yA function of (a);
step S312, taking an electric field expression generated by the point current source at the field point as an integrand of two-dimensional gaussian integration, and calculating a field generated by the surface current source of the simple-shaped polygon at the same position based on a field linear superposition principle, including: the field generated by the current source in the two-dimensional plane S at any point in space can be calculated by the two-dimensional gaussian integral:
Figure 91194DEST_PATH_IMAGE023
；
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE024
at any point in space for the current source within the two-dimensional plane S (x,y,z) The field that is generated is,
Figure 317907DEST_PATH_IMAGE025
is an arbitrary position within the two-dimensional surface S: (u,v) At any point in space (a)x,y,z) The expression of the field that is generated,
Figure DEST_PATH_IMAGE026
representing a gaussian integration point corresponding to a two-dimensional gaussian integration in the two-dimensional plane S,p,qrespectively representu,vIn the first directionpA first, aqThe number of the Gaussian integration points is equal to the total number of the points,
Figure 280178DEST_PATH_IMAGE027
is the weight factor corresponding to the gaussian integral point;
step S313, calculating fields generated by the current on the simple-shaped polygon at different positions of other layers of the integrated circuit, and determining the fields generated by the current on the simple-shaped polygon divided on the layout of other layers of the integrated circuit based on the linear superposition principle of the fields;
step S314, determining the second step based on the linear superposition principle of the fieldlIs layered onmThe electric field generated by the source layer.
6. The method of claim 1, wherein the iterative process is based on the influence of a dyadic Green's functionGDetermines a layer that can be ignored, adaptively adjustsmExtent of influence of source layer by other layers adjacent thereto
Figure DEST_PATH_IMAGE028
。
7. A coarse grain parallel iteration device for coupling dynamic application between integrated circuit layers is characterized by comprising a parallel calculation grain division module, a parallel calculation coarse grain division module and a parallel calculation coarse grain operation module;
the parallel computing particle dividing module is used for dividing iterative computing of interlayer coupling of the integrated circuit into parallel computing particles;
the parallel computing coarse grain dividing module is used for acquiring weighted CPU time of each parallel computing grain and total CPU time of an iteration method for coupling real-time updating between layers of an integrated circuit based on one-time complete serial iterative computation, and combining the parallel computing grains into two-stage parallel computing coarse grains according to the ratio of the weighted CPU time to the total CPU time; the first stage of parallel coarse grain calculation is to calculate the electromagnetic field and current distribution of each source layer, and the first stage of parallel coarse grain calculation comprises the steps of calculating the influence of other layers on the source layer to update source items acting on the source layer in a coupling mode and calculating the electromagnetic field and current distribution of the source layer by utilizing two-dimensional finite elements; the second level of parallel computing coarse grains is used for computing the layer-layer mutual influence of the integrated circuit;
the parallel computing coarse grain operation module is used for randomly disordering the sequences of all computing tasks executed by the parallel computing coarse grains at the same level in the process of executing the parallel computing coarse grains to form a new computing task sequence, and dynamically distributing the new computing task sequence to different computing processes to complete the parallel computing of the computing tasks.
8. The integrated circuit interlayer coupling dynamic applied coarse grain parallel iteration device according to claim 7, wherein the first-stage parallel computation coarse grains and the second-stage parallel computation coarse grains are a set of computation tasks in different ranges, the first-stage parallel computation coarse grains comprise a plurality of second-stage parallel computation coarse grains and a computation task for computing electromagnetic fields and current distributions of the integrated circuit layer by using two-dimensional finite elements, parallel computation grains belonging to the same stage can be computed in parallel, the first-stage parallel computation grains can be allocated with a plurality of computation processes, and the second-stage parallel computation grains can be allocated with only one computation process.
9. The integrated circuit interlayer coupling dynamic applied coarse grain parallel iteration device of claim 7, wherein the specific step of the second stage parallel computation coarse grain comprises:
step 1, calculating an electric field generated by a point current source at a field point, wherein an electric field expression generated by the point current source at the field point is a special analytical expression formed according to a layered special structure of an integrated circuit, and the current sources of the multilayer integrated circuit are distributed in a layered manner, namely the current density distributed on each metal layer of the integrated circuit layout with the complex shape is only equal to that of each metal layer of the integrated circuit layout with the complex shapexAndyis related tozIndependently, the current density distribution is onlyx, yA function of (a);
step 2, taking an electric field expression generated by the point current source at the field point as an integrand function of two-dimensional Gaussian integration, and calculating fields generated by the surface current source of the simple-shaped polygon at the same position based on a linear superposition principle of the fields, wherein the field expression comprises the following steps: the field generated by the current source in the two-dimensional plane S at any point in space can be calculated by the two-dimensional gaussian integral:
Figure 691568DEST_PATH_IMAGE023
；
wherein the content of the first and second substances,
Figure 67185DEST_PATH_IMAGE024
at any point in space for the current source within the two-dimensional plane S (x,y,z) The field that is generated is,
Figure 159906DEST_PATH_IMAGE025
is an arbitrary position within the two-dimensional surface S: (u,v) At any point in space (a)x,y,z) The expression of the field that is generated,
Figure 304580DEST_PATH_IMAGE026
representing a gaussian integration point corresponding to a two-dimensional gaussian integration in the two-dimensional plane S,p,qrespectively representu,vIn the first directionpA first, aqThe number of the Gaussian integration points is equal to the total number of the points,
Figure 214767DEST_PATH_IMAGE027
is the weight factor corresponding to the gaussian integral point;
step 3, calculating fields generated by the current on the simple-shaped polygon at different positions of other layers of the integrated circuit, and determining the fields generated by the current on the simple-shaped polygon divided on the layout of other layers of the integrated circuit based on the linear superposition principle of the fields;
step 4, determining the first step based on the linear superposition principle of the fieldlIs layered onmThe electric field generated by the source layer.
10. The apparatus of claim 7, wherein the formula for computing the weighted CPU time of the parallel computation grain is:
Figure 77681DEST_PATH_IMAGE017
in the formula:
Figure 974092DEST_PATH_IMAGE018
is as followsiThe weighted CPU times of the particles are calculated in parallel,
Figure 707693DEST_PATH_IMAGE019
is as followsiThe CPU time of a single calculation of a grain is calculated in parallel,
Figure 664148DEST_PATH_IMAGE020
is as followsiThe number of particle executions is calculated in parallel.
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