CN115577603A - Simulation method and system for reducing unit matrix dimension and related equipment - Google Patents

Simulation method and system for reducing unit matrix dimension and related equipment Download PDF

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CN115577603A
CN115577603A CN202211557508.2A CN202211557508A CN115577603A CN 115577603 A CN115577603 A CN 115577603A CN 202211557508 A CN202211557508 A CN 202211557508A CN 115577603 A CN115577603 A CN 115577603A
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朱玉泉
关鹏
杨睿智
胡锦钊
常林森
郭嘉帅
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Shenzhen Volans Technology Co Ltd
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Abstract

The invention is suitable for the technical field of piezoelectric material force-electricity coupling, and provides a simulation method, a system and related equipment for reducing the dimension of a unit matrix, wherein the simulation method comprises the following steps: acquiring a geometric structure of the surface acoustic wave device, and dividing the surface acoustic wave device into a plurality of basic structures according to the geometric structure; constructing a weight function and a gradient function for a finite element method, and constructing a six-node quadrilateral element according to the weight function and the gradient function; carrying out grid division on the basic structure according to a finite element method, and calculating a simulation element matrix corresponding to the basic structure by utilizing a six-node quadrilateral element; and splicing and cascading the simulation unit matrixes obtained by different basic structures to obtain a simulation overall matrix, and calculating the frequency point frequency response of the simulation overall matrix under the preset simulation frequency to obtain the simulation frequency response curve of the surface acoustic wave device. According to the invention, the six-node quadrilateral unit is used in the calculation of the unit matrix, so that the dimensionality of the unit matrix is reduced, and the simulation calculation efficiency is improved.

Description

Simulation method and system for reducing unit matrix dimension and related equipment
Technical Field
The invention belongs to the technical field of piezoelectric material force-electricity coupling, and particularly relates to a simulation method and system for reducing unit matrix dimension and related equipment.
Background
With the development of smart phones, the demand of surface acoustic wave devices is increasing. A saw device is an acoustic member, such as a resonator, that is electrically coupled, typically by a finite element method for accurate simulation. The finite element method (ISBN: 7-80159-853-9, 2015) was proposed in the 50 th century and is a mathematical calculation method for converting a complex structure calculation problem into an analysis and aggregation problem of simple elements, but because the finite element method consumes huge calculation resources, in an actual environment, a complete simulation of a surface acoustic wave device in a full size is not performed, and a two-dimensional simulation is performed after a plane strain assumption is generally adopted. However, when there are more finger insertion structures or the requirement for model accuracy is high in the surface acoustic wave device, the two-dimensional model also has large computational resource and time consumption. According to the characteristic that the insertion finger structure of the surface acoustic wave device changes periodically, the hierarchical cascade technology is widely applied.
The hierarchical cascade technology eliminates the operation of internal freedom degree through Schur complement (Schur complement) operation, greatly reduces the requirement on computing resources, and enables full-scale simulation of the surface acoustic wave device to be possible. The problem is that the hierarchical cascading technology needs to carry out Schur complement operation on basic structures in the surface acoustic wave device, such as a single insertion finger, a GAP (GAP), a left PML layer and a right PML layer for multiple times in the application process, and in the actual simulation process, because the basic structures are formed by splicing unit matrixes calculated by a finite unit method, the whole matrix of the basic structure is still large, and huge performance consumption is generated in the Schur complement operation. In the simulation of the conventional finite element method, the calculation efficiency is generally improved by reducing the number of grids and the order of the elements, but on one hand, the reduction of the number of grids affects the simulation result, and on the other hand, the second-order elements are also needed for the simulation of the electromagnetic field to ensure the calculation accuracy.
Therefore, the overall matrix size of the basic structure in the simulation is difficult to reduce. In the prior art, generally, schur complement operation of a basic structure is accelerated by methods such as a parallel technology and GPU acceleration, but serial calculation is still mainly performed by a CPU on a personal computer and a cluster without a GPU, so that an optimization space still exists in the technology.
Disclosure of Invention
The embodiment of the invention provides a simulation method, a simulation system and related equipment for reducing the dimension of a unit matrix, and aims to solve the problems of large dimension and low simulation efficiency of the unit matrix obtained by using a hierarchical cascade technology in the simulation process of the conventional surface acoustic wave device.
In a first aspect, an embodiment of the present invention provides a simulation method for reducing a dimension of a cell matrix, where the simulation method is used to simulate a surface acoustic wave device, and the simulation method includes the following steps:
acquiring a geometric structure of the surface acoustic wave device, and dividing the surface acoustic wave device into a plurality of basic structures according to the geometric structure;
constructing a weight function and a gradient function for a finite element method, and constructing a six-node quadrilateral element according to the weight function and the gradient function;
carrying out grid division on the basic structure according to the finite element method, and calculating a simulation element matrix corresponding to the basic structure by using the six-node quadrilateral element;
and splicing and cascading the simulation unit matrixes obtained by different basic structures to obtain a simulation overall matrix, and calculating the frequency point frequency response of the simulation overall matrix under a preset simulation frequency to obtain a simulation frequency response curve of the surface acoustic wave device.
Further, defining the weight function as
Figure 904474DEST_PATH_IMAGE001
The gradient function is
Figure 865477DEST_PATH_IMAGE002
The weight function
Figure 841523DEST_PATH_IMAGE001
Satisfies the following conditions:
Figure 287286DEST_PATH_IMAGE003
；
Figure 665178DEST_PATH_IMAGE004
Figure 797082DEST_PATH_IMAGE005
Figure 932528DEST_PATH_IMAGE006
Figure 745763DEST_PATH_IMAGE007
Figure 40478DEST_PATH_IMAGE008
Figure 546546DEST_PATH_IMAGE009
；
wherein, the first and the second end of the pipe are connected with each other,s、trespectively an abscissa and an ordinate in a local coordinate system;
the gradient function
Figure 903709DEST_PATH_IMAGE002
Satisfies the following conditions:
Figure 582952DEST_PATH_IMAGE010
。
furthermore, the six-node quadrilateral unit is subjected to second-order interpolation in the horizontal direction and first-order interpolation in the vertical direction.
Still further, the infrastructure includes a finger structure and a GAP structure.
Further, the step of splicing and cascading the simulation unit matrices obtained by the different infrastructure structures to obtain a simulation overall matrix further includes:
and eliminating the common matrix node generated when the simulation unit matrix is spliced and cascaded by using Schur complement operation.
In a second aspect, an embodiment of the present invention further provides a simulation system for reducing a dimension of a cell matrix, where the simulation system is used to simulate a surface acoustic wave device, and includes:
the simulation parameter acquisition module is used for acquiring the geometric structure of the surface acoustic wave device and dividing the surface acoustic wave device into a plurality of basic structures according to the geometric structure;
the node unit construction module is used for constructing a weight function and a gradient function of a finite element method and constructing a six-node quadrilateral unit according to the weight function and the gradient function;
the finite element modeling module is used for carrying out grid division on the basic structure according to the finite element method and calculating a simulation element matrix corresponding to the basic structure by utilizing the six-node quadrilateral element;
and the cascade simulation module is used for splicing and cascading the simulation unit matrixes obtained by different basic structures to obtain a simulation overall matrix, and calculating the frequency point frequency response of the simulation overall matrix under the preset simulation frequency to obtain the simulation frequency response curve of the surface acoustic wave device.
In a third aspect, an embodiment of the present invention further provides a computer device, including: a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the simulation method for reducing the dimension of the cell matrix as described in any one of the above embodiments.
In a fourth aspect, an embodiment of the present invention further provides a computer-readable storage medium, where a computer program is stored on the computer-readable storage medium, and when the computer program is executed by a processor, the computer program implements the steps in the simulation method for reducing the dimension of the cell matrix as described in any one of the above embodiments.
Compared with the method for calculating the unit matrix by using the nine-node Lagrange unit in the finite element theory for simulating the surface acoustic wave device in the prior art, the method has the advantages that the novel six-node quadrilateral unit is constructed and used in the calculation of the unit matrix by utilizing the characteristics that the surface acoustic wave device mainly presents nonlinear change in a displacement field and an electric potential field in a propagation direction, and nearly linear change and rapid attenuation are realized in the displacement field and the electric potential field which are vertical to the propagation direction, so that the dimensionality of the unit matrix is reduced, the calculation requirement of the surface acoustic wave device simulation using a finite element method is reduced, and the calculation efficiency is improved.
Drawings
FIG. 1 is a flow chart of simulation steps of a surface acoustic wave device using a finite element method according to the prior art;
FIG. 2 is a schematic diagram of the basic structure division of a surface acoustic wave device provided by the present invention;
fig. 3 is a schematic diagram of a second-order lagrangian unit commonly used in the finite element method according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of a process for splicing a unit matrix into an overall matrix according to an embodiment of the present invention;
FIG. 5 is a block diagram of a flow chart illustrating steps of a simulation method for reducing dimensions of a cell matrix according to an embodiment of the present invention;
FIG. 6 is a schematic diagram of a six-node quadrilateral unit constructed according to an embodiment of the invention;
FIG. 7 is a schematic diagram illustrating a comparison of units with different node numbers according to an embodiment of the present invention;
FIG. 8 is a diagram illustrating comparison results between a simulation method for reducing the dimension of a cell matrix according to an embodiment of the present invention and a simulation of the prior art;
FIG. 9 is a diagram illustrating comparison results between simulation of another simulation method for reducing cell matrix dimensions according to an embodiment of the present invention and simulation of the prior art;
FIG. 10 is a schematic structural diagram of a simulation system 200 for reducing the dimension of a cell matrix according to an embodiment of the present invention;
fig. 11 is a schematic structural diagram of a computer device according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
For convenience of understanding, the present invention first describes a simulation process of a surface acoustic wave device using a finite element method in the prior art, where the simulation process described in the present invention takes geometric parameters of the surface acoustic wave device as initial parameters, and a final purpose of the simulation is to obtain a simulated frequency response curve of the surface acoustic wave device at a certain frequency.
Specifically, a flow chart of simulation steps of a surface acoustic wave device using a finite element method in the prior art is shown in fig. 1, and the simulation steps include the following steps:
s1, acquiring the geometric structure of the surface acoustic wave device to be simulated.
In general, the geometric information of the surface acoustic wave device includes information such as a film thickness, metallization ratio, and pitch of the interdigital structure.
And S2, dividing the basic structure according to the geometric structure.
As shown in fig. 2, the upper part of fig. 2 is the acquired geometric structure information, and the basic structure after dividing the geometric structure information is shown in the lower part of fig. 2, wherein the structure with the electrode structure is the finger insertion structure, and the structure without the electrode structure is the GAP structure.
And S3, modeling the basic structure according to a finite element method.
The basic structure is subjected to grid division by using a finite element method, and an overall matrix a of the basic structure under a specific frequency is constructed, generally, the step S3 includes the following substeps:
and S31, grid division.
And S32, determining the weight function and the gradient function type.
The function of the weight function can be understood as fitting to a range of degrees of freedom, a more common interpolation method in the prior art is lagrangian interpolation, provided that a known curve is used
Figure 669857DEST_PATH_IMAGE011
Three known points in
Figure 284509DEST_PATH_IMAGE012
Then the curve of the segment
Figure 456864DEST_PATH_IMAGE011
The representation can be performed by interpolation, and the interpolation result is:
Figure 674219DEST_PATH_IMAGE013
；
the above formula can be optimally expressed as
Figure 54778DEST_PATH_IMAGE014
Wherein:
Figure 902648DEST_PATH_IMAGE015
；
Figure 359037DEST_PATH_IMAGE016
；
for a multi-dimensional problem
Figure 255449DEST_PATH_IMAGE017
By two orthogonal interpolation functionsNumber of
Figure 51367DEST_PATH_IMAGE018
And
Figure 132455DEST_PATH_IMAGE019
the orthogonality is obtained, namely:
Figure 279403DEST_PATH_IMAGE020
。
in summary, it can be concluded that: for the lagrange interpolation function, the order of the fitted curve depends on the number of known points.
For a complex physical model, the variation trend of the degree of freedom is often non-linear, so an at least second-order interpolation function is generally required to perform fitting, and the second-order interpolation function can be represented as a second-order lagrange unit commonly used in the finite element method shown in fig. 3.
Generally, the finite element method is used to perform the simulation process of the surface acoustic wave device, and a weight function of a conventional second-order lagrangian element needs to be derived, and the process is as follows:
the degrees of freedom defined in a grid vary spatially as
Figure 979506DEST_PATH_IMAGE021
And the degree of freedom value of each node can be expressed as
Figure 895509DEST_PATH_IMAGE022
A weight function can be constructed based on the degrees of freedom of each node
Figure 616341DEST_PATH_IMAGE001
Matrix, thereby pair
Figure 188267DEST_PATH_IMAGE021
Carry out interpolation, i.e.
Figure 488799DEST_PATH_IMAGE023
；
In a limited receiptIn the meta method, the weight function is derived in the local coordinate system
Figure 321625DEST_PATH_IMAGE024
The coordinates of the nine nodes are respectively expressed as:
Figure 852839DEST_PATH_IMAGE025
；
according to the coordinates, the interpolation function of each node is obtained by the Lagrange interpolation form and is respectively expressed as:
Figure 974378DEST_PATH_IMAGE026
；
Figure 140918DEST_PATH_IMAGE027
；
Figure 765934DEST_PATH_IMAGE028
；
Figure 235093DEST_PATH_IMAGE029
；
Figure 375087DEST_PATH_IMAGE030
；
Figure 283000DEST_PATH_IMAGE031
；
Figure 965785DEST_PATH_IMAGE032
；
Figure 668162DEST_PATH_IMAGE033
；
Figure 295452DEST_PATH_IMAGE034
；
according to the above interpolation function, the weight function matrix is represented as:
Figure 679160DEST_PATH_IMAGE035
；
gradient function required in finite element method
Figure 278769DEST_PATH_IMAGE002
Then the matrix is formed by partial derivatives of the weight function in different directions in the local coordinate system, i.e. the matrix is formed by partial derivatives of the weight function in different directions in the local coordinate system
Figure 214364DEST_PATH_IMAGE036
The matrix can be formed
Figure 532213DEST_PATH_IMAGE002
The complete unfolding is as follows:
Figure 689918DEST_PATH_IMAGE037
。
and S33, calculating a unit matrix.
The numerical solution of the surface acoustic wave device is to solve an equation set coupling a kinetic equation and Maxwell equations, wherein the kinetic equation and the Maxwell equations have the expression formula as follows:
Figure 471929DEST_PATH_IMAGE038
；
the finite element method is realized by multiplying both sides of the equation by a test function
Figure 516109DEST_PATH_IMAGE039
And solving for an integral equal to 0 in a small area, namely:
Figure 258937DEST_PATH_IMAGE040
；
stress therein
Figure 46764DEST_PATH_IMAGE041
And electrical displacement
Figure 683282DEST_PATH_IMAGE042
Are intermediate variables, and the degree of freedom of the actual solution is displacement
Figure 898363DEST_PATH_IMAGE043
And electric potential
Figure 597328DEST_PATH_IMAGE044
Therefore, there is a relationship between stress and electric displacement relative displacement and electric potential
Figure 251163DEST_PATH_IMAGE045
、
Figure 679871DEST_PATH_IMAGE046
Wherein, in the step (A),
Figure 3536DEST_PATH_IMAGE047
which is indicative of the strain of the fiber,
Figure 783273DEST_PATH_IMAGE048
is a constant of elasticity of the magnetic particles,
Figure 709641DEST_PATH_IMAGE049
is a piezoelectric constant of the piezoelectric element,
Figure 429073DEST_PATH_IMAGE050
is the dielectric constant;
the above system of equations uses degree of freedom displacement
Figure 251535DEST_PATH_IMAGE043
And electric potential
Figure 315306DEST_PATH_IMAGE044
When the method is used for expression, the second-order derivation needs to be carried out on displacement and potential, the requirement on continuity of the solution is high, and divergence is usedThe theorem transforms the equation set to obtain:
Figure 248627DEST_PATH_IMAGE051
；
at this time, the degree of freedom displacement is still required
Figure 324031DEST_PATH_IMAGE043
And electric potential
Figure 114132DEST_PATH_IMAGE044
Is a continuous solution, while in the finite element method, the goal is to compute the degrees of freedom of each node, and therefore, the use of a weight function is required
Figure 602882DEST_PATH_IMAGE052
And
Figure 11998DEST_PATH_IMAGE001
by displacement of nodes
Figure 66542DEST_PATH_IMAGE053
And electric potential
Figure 230807DEST_PATH_IMAGE054
To displacement of
Figure 878957DEST_PATH_IMAGE043
And electric potential
Figure 154080DEST_PATH_IMAGE044
Carry out interpolation, i.e.
Figure 594289DEST_PATH_IMAGE055
And
Figure 663876DEST_PATH_IMAGE056
；
to strain
Figure 312506DEST_PATH_IMAGE057
And electrical displacement
Figure 188058DEST_PATH_IMAGE042
Which is a displacement
Figure 420456DEST_PATH_IMAGE043
And electric potential
Figure 598628DEST_PATH_IMAGE044
Can be derived from the weight function to obtain a gradient function
Figure 549266DEST_PATH_IMAGE058
And with
Figure 228509DEST_PATH_IMAGE059
And using a gradient function
Figure 987518DEST_PATH_IMAGE060
And
Figure 664487DEST_PATH_IMAGE002
by displacement of nodes
Figure 899159DEST_PATH_IMAGE053
And electric potential
Figure 54197DEST_PATH_IMAGE054
To strain
Figure 198871DEST_PATH_IMAGE057
And electrical displacement
Figure 577899DEST_PATH_IMAGE042
Carry out interpolation, i.e.
Figure 237551DEST_PATH_IMAGE061
And
Figure 632498DEST_PATH_IMAGE062
；
at this time, the system of the original dynamics equation and maxwell equation can be expressed as:
Figure 693995DEST_PATH_IMAGE063
；
then using Galerkin method to select and weight function
Figure 775083DEST_PATH_IMAGE052
And
Figure 922031DEST_PATH_IMAGE001
same trial function
Figure 356554DEST_PATH_IMAGE064
The original dynamics equation and the Maxwell equation system are further converted into:
Figure 69295DEST_PATH_IMAGE065
；
the above equation set is expressed by matrix as:
Figure 258968DEST_PATH_IMAGE066
；
although the kinetic equation and the Maxwell equation set can be expressed by a matrix, the kinetic equation and the Maxwell equation set are still in an integral form instead of an algebraic form in the traditional numerical method, so that the Gaussian integration method is used for processing the integral converted into a local coordinate system in the finite element method, and the integral in a global coordinate system is processed
Figure 830895DEST_PATH_IMAGE067
Conversion to integral in local coordinate system
Figure 131426DEST_PATH_IMAGE068
Namely:
Figure 964253DEST_PATH_IMAGE069
；
in the above formula
Figure 996931DEST_PATH_IMAGE070
Namely a unit matrix, the specific expression of which is as follows:
Figure 118471DEST_PATH_IMAGE071
；
Figure 19431DEST_PATH_IMAGE072
；
Figure 910026DEST_PATH_IMAGE073
。
and S34, splicing the unit matrixes into an integral matrix.
Taking two basic structures as an example, their respective cell matrices are simplified and represented as 4 × 4 matrices, k respectively 1 And k is 2 As shown below, wherein k 1 3, 4 degree of freedom (four bottom right) and k 2 The 1 st and 2 nd degrees of freedom (four upper left) of (c) represent the same node.
Figure 615071DEST_PATH_IMAGE074
；
Therefore, when the two units are spliced, the information of the two degrees of freedom needs to be added to obtain an overall matrix a of the two units, as shown below:
Figure 20644DEST_PATH_IMAGE075
；
exemplary, the process of stitching the unit matrix into the overall matrix is schematically illustrated in fig. 4.
And S4, eliminating the internal degree of freedom of the basic structure.
Utilizing Schur complement operation to eliminate the intermediate degree of freedom of the basic structure, only retaining the degree of freedom of the left and right boundaries of the structure and the degree of freedom of the electric potential at the junction of the electrode and the substrate, thereby obtaining the integrated matrix A after Schur complement Schur And using Schur BuThe overall matrix A thereafter Schur Replacing its original overall matrix a.
And S5, cascading the basic structures.
The overall matrix A of the base structure after Schur complement operation Schur And performing splicing cascade, wherein the cascade principle is similar to integral matrix splicing in a finite element method, and the integral matrixes A1 and A2 of two adjacent basic structures in the surface acoustic wave device are combined.
The principle of combination in the finite element method is for an overall matrix A of dimension M 1 (M), an integral matrix A with N dimensions 2 (N x N), when two basic structures have K degrees of freedom which are shared, a new overall matrix A with M + N-K dimensions can be constructed 3 (M + N-K) ((M + N-K)), wherein the matrix information corresponding to the unshared degrees of freedom is used directly in the matrix after the concatenation, and the matrix information corresponding to the shared degrees of freedom is used after the addition.
And S6, obtaining the frequency response of the surface acoustic wave device.
And processing the finally cascaded matrix by combining preset electrical conditions with a mathematical formula, and obtaining the frequency response of the surface acoustic wave device under the frequency.
For example, after two cell matrices of the basic structure are cascaded, a matrix M describing the whole saw device can be obtained, where the matrix M describes the left and right boundaries and the degrees of freedom at the boundary between the electrode and the substrate, and can be partitioned into a generalized block matrix 2*2, which respectively describes the electrical degree of freedom E and other degrees of freedom B to be analyzed, as shown below:
Figure 928557DEST_PATH_IMAGE076
；
for the frequency response, such as the admittance parameter, to be calculated by the simulation target, the admittance parameter can be obtained by processing using the following formula:
Figure 611343DEST_PATH_IMAGE077
；
so far, the process of performing simulation of the saw device by using the finite element method and obtaining a simulation frequency response curve at a certain frequency in the prior art is finished.
In the prior art, a hierarchical cascade technology is used, a surface acoustic wave device is divided into a plurality of insertion finger structures, schur complement operation is carried out on each insertion finger structure to eliminate internal freedom degree, then the insertion finger structures after Schur complement are cascaded in sequence, and therefore the size of an integral matrix of the surface acoustic wave device is reduced 3 ) That is, when the overall matrix A is large, the Schur complement result A is obtained Schur The time of Schur complement also increases significantly, so that the Schur complement occupies more computation time and slows down the computation efficiency, and finally becomes the bottleneck of the computation efficiency of the prior art.
In an embodiment of the present invention, step S3 in the prior art is specifically improved, specifically, referring to fig. 5, fig. 5 is a block diagram illustrating a step flow of a simulation method for reducing a dimension of a cell matrix according to an embodiment of the present invention, where the simulation method is used for simulating a surface acoustic wave device, and specifically includes the following steps:
s101, acquiring a geometric structure of the surface acoustic wave device, and dividing the surface acoustic wave device into a plurality of basic structures according to the geometric structure.
Still further, the infrastructure includes a finger structure and a GAP structure.
S102, constructing a weight function and a gradient function for a finite element method, and constructing a six-node quadrilateral element according to the weight function and the gradient function.
Furthermore, the six-node quadrilateral unit is subjected to second-order interpolation in the horizontal direction and first-order interpolation in the vertical direction.
Specifically, the six-node quadrilateral unit provided by the embodiment of the invention utilizes the characteristics that the surface acoustic wave device mainly has nonlinear change in the displacement field and the potential field in the propagation direction, and nearly linearly changes and rapidly attenuates in the displacement field and the potential field perpendicular to the propagation direction, compared with the original nine-node lagrangian unit, the six-node quadrilateral unit has second-order interpolation in the horizontal direction and first-order interpolation in the vertical direction, and a schematic diagram of the six-node quadrilateral unit constructed by the embodiment of the invention is shown in fig. 6.
And then, according to a Lagrange interpolation method, similar to the traditional nine-node Lagrange unit, constructing a weight function and a gradient function of the six-node unit.
Further, defining the weight function as
Figure 313719DEST_PATH_IMAGE001
The gradient function is
Figure 941010DEST_PATH_IMAGE002
Said weight function
Figure 59139DEST_PATH_IMAGE001
Satisfies the following conditions:
Figure 924326DEST_PATH_IMAGE003
；
Figure 859921DEST_PATH_IMAGE004
Figure 177770DEST_PATH_IMAGE005
Figure 99590DEST_PATH_IMAGE006
Figure 819284DEST_PATH_IMAGE007
Figure 660201DEST_PATH_IMAGE008
Figure 901564DEST_PATH_IMAGE009
；
wherein the content of the first and second substances,s、trespectively an abscissa and an ordinate in a local coordinate system;
the gradient function
Figure 486130DEST_PATH_IMAGE002
Satisfies the following conditions:
Figure 60330DEST_PATH_IMAGE010
。
based on the relationship of inverse derivation, in the actual process, the weight function and the gradient function of the six-node quadrilateral unit need to be determined in advance, and then unit construction is carried out based on the weight function and the gradient function.
And S103, carrying out grid division on the basic structure according to the finite element method, and calculating a simulation element matrix corresponding to the basic structure by using the six-node quadrilateral element.
The invention also provides another implementation mode, in the application of hierarchical cascade, a COMSOL-Matlab joint simulation hierarchical cascade algorithm is often adopted, namely steps S102 and S103 call COMSOL finite element method software and specify the geometric parameters of the basic structure in the COMSOL software, so that modeling, automatic network division and overall matrix output are realized;
at this time, since the weight function and the gradient function of the six-node quadrilateral unit cannot be determined in the COMSOL software, but only the second-order lagrangian unit or the edge-padding point element built in the COMSOL software can be called, the whole matrix derived from the COMSOL software needs to be processed by a certain method, so that the whole matrix of the six-node quadrilateral unit in the embodiment of the present invention is obtained.
Specifically, referring to fig. 7, fig. 7 is a schematic diagram illustrating comparison of units with different node numbers according to an embodiment of the present invention, for an overall matrix formed by second-order lagrangian units (9-nodes) derived from COMSOL software, weight functions of the overall matrix are N1 to N9, and shape functions numbered as 8, 9, and 6 can be equally superimposed on units 1, 5, and 2 and units 4, 7, and 3 to obtain the weight function of the six-node quadrilateral unit according to the embodiment of the present invention, that is:
Figure 947515DEST_PATH_IMAGE078
；
for the skillful edge point elements (8-nodes) constructed in the COMSOL software, the weight functions are respectively N 1 To N 8 The shape functions numbered 8 and 6 may be equally superimposed on the 1 and 2 units and the 4 and 3 units to obtain the weight function of the six-node quadrilateral unit in the embodiment of the present invention, that is:
Figure 36694DEST_PATH_IMAGE079
。
s104, splicing and cascading the simulation unit matrixes obtained from different basic structures to obtain a simulation overall matrix, and calculating the frequency point frequency response of the simulation overall matrix under a preset simulation frequency to obtain a simulation frequency response curve of the surface acoustic wave device.
Further, the step of splicing and cascading the simulation unit matrices obtained by the different infrastructure structures to obtain a simulation overall matrix further includes:
and eliminating the common matrix node generated when the simulation unit matrix is spliced and cascaded by using Schur complement operation.
For example, the simulation method for reducing the dimension of the cell matrix provided by the embodiment of the present invention is compared with the simulation of the prior art as follows:
under the frequency of a single resonator, the width pitch of a single interpolation finger is 0.9635 micrometer, the height of a metal electrode is 0.146 micrometer, the metallization rate is 0.6, the thickness of a model is 32.759 micrometer, the interpolation is used on two sides of the model to respectively construct reflection grids of 100 interpolation fingers, 50 pairs of 100 interpolation fingers are used in the model as IDTs, the number of calculated frequency points is 400 frequency points, each frequency point is 1Mhz, meanwhile, for simulation comparison, the depth of a substrate of 6 times pitch is set in an experiment, a PML layer of 2 times pitch is arranged at the bottom of the substrate to prevent boundary reflection, and a PML layer of 2 times pitch width is also arranged on the outer side of the reflection grids to prevent boundary reflection; then, the electrode was divided into 174 grids, where the number of the electrode grids was 3 × 3=9, the number of the substrate grids was 30 × 5=150, and the number of the pml grids was 5 × 3= 15.
As a theoretical comparison, when a conventional second-order lagrangian unit is used, the dimension of the generated overall matrix is (3292 × 9292), and the time spent in calculating the unit matrix and the overall matrix is about 700ms in total; the dimension of the generated overall matrix of the six-node quadrilateral unit used in the embodiment of the invention is (1688 × 1688), and the total time spent in calculating the unit matrix and calculating the overall matrix is about 330ms.
The simulation comparison results of the simulation method for reducing the unit matrix dimension provided by the embodiment of the invention and the simulation in the prior art are shown in fig. 8 and fig. 9, and it can be seen that the calculation time consumption of the six-node quadrilateral unit adopted by the embodiment of the invention is far less than that of the nine-node unit and that of the eight-node unit, the calculation time consumption of the six-node quadrilateral unit is 20% of that of the nine-node unit, and the frequency response is relatively close, so that the simulation method for reducing the unit matrix dimension provided by the embodiment of the invention has better performance in calculation accuracy and calculation efficiency.
Compared with the simulation method of using the nine-node Lagrange unit to calculate the unit matrix in the finite element theory for the simulation of the surface acoustic wave device in the prior art, the simulation method has the advantages that a new six-node quadrilateral unit is constructed and used in the calculation of the unit matrix by utilizing the characteristics that the surface acoustic wave device mainly shows nonlinear change in a displacement field and an electric potential field in a propagation direction, and almost linearly changes and quickly attenuates the displacement field and the electric potential field in the direction perpendicular to the propagation direction, so that the dimension of the unit matrix is reduced, the calculation requirement of the simulation of the surface acoustic wave device using the finite element method is reduced, and the calculation efficiency is improved.
An embodiment of the present invention further provides a simulation system for reducing a unit matrix dimension, where the simulation system is used to simulate a surface acoustic wave device, please refer to fig. 10, and fig. 10 is a schematic structural diagram of a simulation system 200 for reducing a unit matrix dimension, which includes:
the simulation parameter acquisition module 201 is configured to acquire a geometric structure of the surface acoustic wave device, and divide the surface acoustic wave device into a plurality of basic structures according to the geometric structure;
a node unit constructing module 202, configured to construct a weight function and a gradient function of the finite unit method, and construct a six-node quadrilateral unit according to the weight function and the gradient function;
the finite element modeling module 203 is used for carrying out grid division on the basic structure according to the finite element method and calculating a simulation element matrix corresponding to the basic structure by using the six-node quadrilateral element;
the cascade simulation module 204 is configured to splice and cascade the simulation unit matrices obtained by the different base structures to obtain a simulation overall matrix, and calculate a frequency point frequency response of the simulation overall matrix at a preset simulation frequency to obtain a simulation frequency response curve of the surface acoustic wave device.
The simulation system 200 for reducing the dimension of the cell matrix can implement the steps in the simulation method for reducing the dimension of the cell matrix in the above embodiment, and can implement the same technical effects, and the description in the above embodiment is referred to, and is not repeated herein.
Referring to fig. 11, fig. 11 is a schematic structural diagram of a computer device provided in an embodiment of the present invention, where the computer device 300 includes: a memory 302, a processor 301, and a computer program stored on the memory 302 and executable on the processor 301.
The processor 301 calls the computer program stored in the memory 302 to execute the steps in the simulation method for reducing the dimension of the cell matrix according to the embodiment of the present invention, and with reference to fig. 5, the method specifically includes:
s101, acquiring a geometric structure of the surface acoustic wave device, and dividing the surface acoustic wave device into a plurality of basic structures according to the geometric structure;
s102, constructing a weight function and a gradient function used for the finite element method, and constructing a six-node quadrilateral element according to the weight function and the gradient function;
s103, carrying out grid division on the basic structure according to the finite element method, and calculating a simulation element matrix corresponding to the basic structure by using the six-node quadrilateral element;
s104, splicing and cascading the simulation unit matrixes obtained by different basic structures to obtain a simulation overall matrix, and calculating frequency point frequency response of the simulation overall matrix under a preset simulation frequency to obtain a simulation frequency response curve of the surface acoustic wave device.
Further, defining the weight function as
Figure 628212DEST_PATH_IMAGE001
The gradient function is
Figure 994602DEST_PATH_IMAGE002
Said weight function
Figure 380584DEST_PATH_IMAGE001
Satisfies the following conditions:
Figure 957059DEST_PATH_IMAGE003
；
Figure 24372DEST_PATH_IMAGE004
Figure 307586DEST_PATH_IMAGE005
Figure 192366DEST_PATH_IMAGE006
Figure 193820DEST_PATH_IMAGE007
Figure 300709DEST_PATH_IMAGE008
Figure 500746DEST_PATH_IMAGE009
；
wherein the content of the first and second substances,s、trespectively an abscissa and an ordinate in a local coordinate system;
the gradient function
Figure 494110DEST_PATH_IMAGE002
Satisfies the following conditions:
Figure 654964DEST_PATH_IMAGE010
。
furthermore, the six-node quadrilateral unit is subjected to second-order interpolation in the horizontal direction and first-order interpolation in the vertical direction.
Still further, the infrastructure includes a finger structure and a GAP structure.
Further, the step of splicing and cascading the simulation unit matrices obtained by the different infrastructure structures to obtain a simulation overall matrix further includes:
and eliminating the common matrix node generated when the simulation unit matrix is spliced and cascaded by using Schur complement operation.
The computer device 300 provided in the embodiment of the present invention can implement the steps in the simulation method for reducing the dimension of the cell matrix in the above embodiment, and can implement the same technical effects, and details are not repeated herein with reference to the description in the above embodiment.
The embodiment of the present invention further provides a computer-readable storage medium, where a computer program is stored on the computer-readable storage medium, and when the computer program is executed by a processor, the computer program implements each process and step in the simulation method for reducing the dimension of the cell matrix provided in the embodiment of the present invention, and can implement the same technical effect, and in order to avoid repetition, details are not repeated here.
It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by a computer program, which can be stored in a computer-readable storage medium, and when executed, can include the processes of the embodiments of the methods described above. The storage medium may be a magnetic disk, an optical disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), or the like.
It should be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising a … …" does not exclude the presence of another identical element in a process, method, article, or apparatus that comprises the element.
Through the above description of the embodiments, those skilled in the art will clearly understand that the method of the above embodiments can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware, but in many cases, the former is a better implementation manner. Based on such understanding, the technical solutions of the present invention may be embodied in the form of a software product, which is stored in a storage medium (such as ROM/RAM, magnetic disk, optical disk) and includes instructions for enabling a terminal (such as a mobile phone, a computer, a server, an air conditioner, or a network device) to execute the method according to the embodiments of the present invention.
While the present invention has been described with reference to the preferred embodiments, it is to be understood that the invention is not limited to the disclosed embodiments, which are illustrative, but not restrictive, and that various changes may be made therein by those skilled in the art without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (8)

1. A simulation method for reducing unit matrix dimension is used for simulating a surface acoustic wave device, and is characterized by comprising the following steps:
acquiring a geometric structure of the surface acoustic wave device, and dividing the surface acoustic wave device into a plurality of basic structures according to the geometric structure;
constructing a weight function and a gradient function for a finite element method, and constructing a six-node quadrilateral element according to the weight function and the gradient function;
carrying out grid division on the basic structure according to the finite element method, and calculating a simulation element matrix corresponding to the basic structure by using the six-node quadrilateral element;
and splicing and cascading the simulation unit matrixes obtained by different basic structures to obtain a simulation integral matrix, and calculating the frequency point frequency response of the simulation integral matrix under a preset simulation frequency to obtain a simulation frequency response curve of the surface acoustic wave device.
2. The simulation method for reducing the dimensionality of a cell matrix of claim 1, wherein the weight function is defined as
Figure 992336DEST_PATH_IMAGE001
The gradient function is
Figure 316002DEST_PATH_IMAGE002
Said weight function
Figure 830159DEST_PATH_IMAGE001
Satisfies the following conditions:
Figure 22106DEST_PATH_IMAGE003
；
Figure 741538DEST_PATH_IMAGE004
Figure 298422DEST_PATH_IMAGE005
Figure 362193DEST_PATH_IMAGE006
Figure 295514DEST_PATH_IMAGE007
Figure 636496DEST_PATH_IMAGE008
Figure 364281DEST_PATH_IMAGE009
；
wherein the content of the first and second substances,s、trespectively an abscissa and an ordinate in a local coordinate system;
the gradient function
Figure 915348DEST_PATH_IMAGE002
Satisfies the following conditions:
Figure 58884DEST_PATH_IMAGE010
。
3. the simulation method for reducing the dimension of a cell matrix according to claim 1, wherein the six-node quadrilateral cells are interpolated horizontally by a second order and vertically by a first order.
4. The simulation method for reducing the dimension of a cell matrix according to claim 1, wherein the infrastructure comprises an interpolation structure and a GAP structure.
5. The simulation method for reducing the dimension of the cell matrix according to claim 1, wherein the step of splicing and cascading the simulation cell matrices obtained from different infrastructure to obtain a simulation overall matrix further comprises:
and eliminating the common matrix node generated when the simulation unit matrix is spliced and cascaded by using Schur complement operation.
6. A simulation system for reducing the dimension of a cell matrix, the simulation system being configured to simulate a surface acoustic wave device, comprising:
the simulation parameter acquisition module is used for acquiring the geometric structure of the surface acoustic wave device and dividing the surface acoustic wave device into a plurality of basic structures according to the geometric structure;
the node unit construction module is used for constructing a weight function and a gradient function of a finite element method and constructing a six-node quadrilateral unit according to the weight function and the gradient function;
the finite element modeling module is used for carrying out grid division on the basic structure according to the finite element method and calculating a simulation element matrix corresponding to the basic structure by utilizing the six-node quadrilateral element;
and the cascade simulation module is used for splicing and cascading the simulation unit matrixes obtained by different basic structures to obtain a simulation overall matrix, and calculating the frequency point frequency response of the simulation overall matrix under the preset simulation frequency to obtain the simulation frequency response curve of the surface acoustic wave device.
7. A computer device, comprising: memory, processor and computer program stored on the memory and executable on the processor, the processor implementing the steps in the simulation method for reducing cell matrix dimensions according to any one of claims 1 to 5 when executing the computer program.
8. A computer-readable storage medium, having stored thereon a computer program which, when being executed by a processor, carries out the steps of the simulation method for reducing a dimension of a cell matrix according to any one of claims 1 to 5.
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