CN102033985A - High-efficiency time domain electromagnetic simulation method based on H matrix algorithm - Google Patents

High-efficiency time domain electromagnetic simulation method based on H matrix algorithm Download PDF

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CN102033985A
CN102033985A CN 201010556198 CN201010556198A CN102033985A CN 102033985 A CN102033985 A CN 102033985A CN 201010556198 CN201010556198 CN 201010556198 CN 201010556198 A CN201010556198 A CN 201010556198A CN 102033985 A CN102033985 A CN 102033985A
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matrix
time domain
finite element
electromagnetic simulation
seamed edge
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樊振宏
陈如山
丁大志
盛亦军
宛汀
叶晓东
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Nanjing University of Science and Technology
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Nanjing University of Science and Technology
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Abstract

The invention discloses a high-efficiency time domain electromagnetic simulation method based on an H matrix algorithm, which can realize electromagnetic simulation on a large three-dimensional target. In the method, a time domain finite element method (TDFEM) is used as a background, a low-rank compression technique is used as a core, and a tree structure is used as a basis for carrying out logical unit (LU) decomposition on a sparse matrix generated by the TDFEM by a four arithmetic algorithm corresponding to the H matrix. The acquired upper and lower triangular factors have low-rank compressible characteristics, and the compressed matrix equation can realize quick solution of high-efficiency time domain electromagnetic simulation by the H matrix algorithm. The high-efficiency time domain electromagnetic simulation method has the advantages of fast computation speed, low memory consumption, controllable computation accuracy, good stability and the like, can reduce the complexity of computation to O(Nlog<2>N) and reduce the memory consumption to O(NlogN), can be widely applied to the solution of a large sparse linear system of equations during high-efficiency time domain electromagnetic simulation, and can provide important reference for analyzing the electromagnetic property of the large three-dimensional target.

Description

Efficient time domain Electromagnetic Simulation method based on the H-matrix algorithms
Technical field
The present invention relates to a kind of Electromagnetic Simulation technology, particularly a kind of based on
Figure BSA00000356947200012
The efficient time domain Electromagnetic Simulation method of matrix algorithms, the electromagnetic property analysis that it can be in the fields such as communication, radar, microwave integrated circuit provides important reference.
Background technology
Electromagnetic Simulation is to reappear a kind of method that essential process takes place the actual electromagnetic phenomenon on computers.In the practical study process, when the system cost costliness of being studied, experiment is dangerous big or experimental period when long, adopting Electromagnetic Simulation is exactly a kind of substitution studies means especially effectively easily.The core of Electromagnetic Simulation technology is the numerical evaluation of electromagnetic field, and is at present multiple at numerical computation method method of finite difference, finite element method, Finite-Difference Time-Domain Method and the time-domain finite element method etc. of electromagnetic field.Therefore method of finite difference and Finite-Difference Time-Domain Method can only adopt rectangular node, so this method is difficult to the Simulation of Complex border owing to be subject to the grid discrete way; Though finite element method can overcome this problem of method of finite difference and Finite-Difference Time-Domain Method, obtain wide band electromagnetic property, need carry out loaded down with trivial details frequency sweep operation, these factors have also limited simultaneously the Electromagnetic Simulation ability of above-mentioned each method greatly; The proposition of time domain Finite Element Method is less than 20 years so far, it can either accurately be simulated the complex geometry and the medium component characteristic of target easily, can obtain the broadband electromagnetical characteristic of target again very easily, it not only can effectively solve method of finite difference and the Finite-Difference Time-Domain Method limitation problem for complicated research object modeling, can also give full play to finite element method to the labyrinth ability of modeling, have low, the easy advantage such as parallel of no numerical value chromatic dispersion, iteration stability requirement.Therefore, time-domain finite element method has broad application prospects in the Electromagnetic Simulation technical field, also belongs to the research direction in international forward position at the research of its method.
One of gordian technique that the employing time-domain finite element method is carried out the Electromagnetic Simulation analysis is finding the solution the large-scale sparse linear system of equations that is generated.Along with the raising of development in science and technology and engineering application requirements, the scale of time domain Electromagnetic Simulation is increasing, and the scale of the sparse linear system of equations of generation is also increasing.The method of finding the solution large-scale sparse linear system of equations at present has iterative solution method and direct solution usually.Iterative solution method is applicable to the less demanding occasion of solving precision, at sparse matrix, the computation complexity of iterative solution method only is O (N), wherein N represents the number of unknown quantity, its major defect is, when the complex structure of simulation object, the matrix of coefficients condition that forms is relatively poor, the very slow not even convergent of iterative convergence speed situation can appear, though preconditioning technique can be improved this situation, because the limitation of preconditioning technique promptly needs corresponding different preconditioning technique to different problems, therefore be difficult to find a kind of general preconditioning technique efficiently, cause the difficulty of practical application; In addition, finding the solution the vectorial problem in many right, during problem that the constant and the right vector of the matrix of coefficients of promptly waiting to ask equation does not stop to change (problem of spacer step for a long time in the time domain Finite Element Method belongs to this category), all to find the solution one time matrix equation again, waste time and energy for each the right vector.Direct solution can overcome the above-mentioned shortcoming of iterative solution method, has the characteristics of solving precision height and good stability, also has very big advantage for finding the solution of the vectorial problem in many right, but the shortcoming of direct solution is that computation complexity is high and memory consumption is big.As B.He, F.L.Teixeira, " Sparse and Explicit FETD via Approximate Inverse Hodge (Mass) Matrix; " IEEE microwave and wireless components letters, vol.16, no.6, pp.348-350, June 2006. documents disclose a kind of direct solution to inverting based on sparse matrix, it obtains the approximate inverse of matrix rather than accurately contrary by the gating matrix parameter of inverting, can reduce computation complexity to a certain extent and alleviate memory requirements, but it is not high to separate its efficient of system of linear equations by the method for directly inverting.In addition, A.George, " Nested dissection of a regular finite element mesh; " SIAM J.on Numerical Analysis, 10 (2): 345-363, proposed another kind of direct solution of finding the solution the sparse matrix equation in April 1973. documents, it can reduce to computation complexity O (N by sort algorithm 1.5), this is effective and use wider a kind of method in the direct solution of existing sparse matrix equation, but O (N 1.5) computation complexity still belong to nonlinear complexity, it can cause computing time and memory consumption to increase severely along with the growth of unknown quantity number, when simulation scale is big, can cause the active computer hardware configuration to be difficult to bear, therefore, time domain finite element Electromagnetic Simulation presses for a kind of effectively directly solution technique and improves its simulation efficiency.
Summary of the invention
The object of the present invention is to provide that a kind of computing velocity is fast, memory consumption is low, good stability based on The efficient time domain Electromagnetic Simulation method of matrix algorithms.
The technical scheme that realizes the object of the invention is, based on
Figure BSA00000356947200022
The efficient time domain Electromagnetic Simulation method of matrix algorithms be adopt the time domain Finite Element Method with based on The combination of the direct solution of matrix, its concrete operations step is as follows:
The first step, select for use ANSYS software to set up the geometric model of simulation object, adopt tetrahedron element that this model is carried out grid then in ANSYS software and disperse, the required grid discrete message file of simulation analysis is derived in discrete back, comprises cell node message file and node coordinate message file;
Second step, according to the grid discrete message, then, adopt the seamed edge basis function to launch the field of each tetrahedron element inside, utilize the Galerkin method to generate the large-scale sparse linear systems of time domain finite element again, its size is the number of all seamed edge basis functions;
The 3rd step, adopt the simulation object geometric model after two minutes mode of recurrence disperses to grid to divide into groups, construct the binary tree structure of all seamed edge basis function collection;
The 4th step interacted the binary tree structure of test basis function collection in the binary tree structure of seamed edge basis function collection and the Galerkin method, generated the block tree construction of two dimension;
The 5th goes on foot, and the employing admissible condition is theoretical selects far away group of effect between any two groups in the block tree construction, and the matrix of far group effect formation is compressed into two low-rank matrix multiple forms, generation time domain coefficient matrix in finite element method
Figure BSA00000356947200031
Matrix expression wherein only comprises the sub-piece of two classes, promptly allows piece and non-ly allows piece;
In the 6th step, utilize recursive algorithm to reach
Figure BSA00000356947200032
The self-defining arithmetic rule of matrix is to the time domain coefficient matrix in finite element method Matrix carries out the operation that LU decomposes, and obtains
Figure BSA00000356947200034
Three angle factors up and down of matrix form;
In the 7th step, obtaining
Figure BSA00000356947200035
On the basis of three angle factors up and down of matrix form, each time step is carried out afterwards
Figure BSA00000356947200036
Can obtain separating of this time step system of linear equations to back substitution before and after the matrix, finally obtain a simulating area value everywhere;
The 8th step, extract corresponding value as required and obtain the S parameter of microwave circuit, the RCS electromagnetic property parameters such as (RCS) of scatterer by computing, finish the Electromagnetic Simulation process.
The present invention is a core with the low-rank compress technique, based on tree, by The corresponding arithmetic rule of matrix, the sparse matrix that the time domain Finite Element Method is generated carries out the LU decomposition, but three angle factors up and down that obtained have the characteristic of low-rank compression, and the matrix equation after the compression adopts
Figure BSA00000356947200038
Matrix algorithms can be realized the rapid solving of efficient time domain Electromagnetic Simulation.The time domain Finite Element Method belongs to the differential class method, the inverse operator of differentiating operator has the characteristic of integral operator, and the kernel function of integral operator can be write as the form of two separation, show on the matrix to be the form of two low-rank matrix multiples, therefore the parton piece in the time domain finite element inverse of a matrix matrix also can be compressed into the form that low-rank decomposes, promptly time domain finite element inverse of a matrix matrix can with
Figure BSA00000356947200039
The form of matrix is represented.And time domain finite element matrix itself, because the locality of its differentiating operator makes effect far away be zero, therefore, time domain finite element nonzeros is all inserted
Figure BSA000003569472000310
In the full battle array piece of matrix, and the low-rank piece all is zero, like this time domain finite element matrix can with The form of matrix nondestructively shows.Based on
Figure BSA000003569472000312
Matrix format and corresponding arithmetic rule can be implemented under the controlled precision one
Figure BSA000003569472000313
Matrix carries out the operation that LU decomposes, and adds
Figure BSA000003569472000314
Directly finding the solution a system of linear equations just can be finished to back substitution in the front and back of matrix.
The present invention compares with existing time domain numerical simulation technology, and its remarkable advantage is: the discrete match of (1) model is accurate; It is discrete to adopt tetrahedron element that the model of simulation object is carried out grid, and the geometric configuration of the various complexity of match has well guaranteed the accuracy of model; (2) computation complexity and memory consumption are low;
Figure BSA000003569472000315
The matrix direct solution is a core with the low-rank compress technique, based on tree, by The self-defining arithmetic form of matrix can be reduced to computation complexity O (Nlog 2N), memory consumption is reduced to O (NlogN), this complexity that is almost linearity makes it be more suitable for carrying out extensive Electromagnetic Simulation analysis; (3) computational accuracy is controlled; By regulating
Figure BSA000003569472000317
The compression degree of low-rank compression blocks or the power by the control admissible condition can obtain different solving precision in the matrix, computing time and memory consumption that different solving precision needs are different, so computing time and memory consumption are controlled; (4) good stability; Because
Figure BSA000003569472000318
The matrix direct solution has nothing to do in the condition of time domain finite element matrix, therefore still has stronger analysis ability at the relatively poor situation of the matrix of coefficients condition that complex model produced.To in the finding the solution of large-scale sparse linear system of equations, the electromagnetic property analysis that can be the large-scale three dimensional target provided important reference when the present invention can be widely used in adopting time-domain finite element method to carry out efficient time domain Electromagnetic Simulation.
Concrete steps of the present invention are provided by the following drawings and embodiment.
Description of drawings
Fig. 1 is little charged tape crack (EBG) structural representation.
Fig. 2 is for carrying out the synoptic diagram of hierarchical grouping to two dimension target seamed edge basis function.
Fig. 3 carries out the hierarchical grouping synoptic diagram for adopting 8 seamed edge basis function restriction boxes to objective seamed edge basis function.
Fig. 4 is the binary tree structure synoptic diagram of the seamed edge basis function that generated according to Fig. 3 hierarchical grouping mode.
Fig. 5 is the admissible condition synoptic diagram.
Fig. 6 is the organigram of block tree.
Fig. 7 is typical in the reality
Figure BSA00000356947200041
Matrix structure figure.
Fig. 8 is
Figure BSA00000356947200042
Matrix L U decomposing schematic representation.
Fig. 9 is in the EBG structure example
Figure BSA00000356947200043
Consumptions profile computing time of matrix direct solution.
Figure 10 is in the EBG structure example
Figure BSA00000356947200044
The calculating memory consumption curve map of matrix direct solution.
Figure 11 is in the EBG structure example
Figure BSA00000356947200045
The computational accuracy curve map of matrix direct solution.
Embodiment
Below in conjunction with accompanying drawing, be example with the Electromagnetic Simulation analysis of a little charged tape gap structure (EBG), concrete steps of the present invention are described in further detail.
It is as follows according to the present invention little charged tape gap structure (EBG) shown in Figure 1 to be carried out the concrete steps of Electromagnetic Simulation:
The first step, adopt ANSYS software to set up the 3-D geometric model of little charged tape gap structure (EBG), for the whole simulation zone is blocked, cutoff boundary (as complete matching layer) is set at the two ends of little charged tape gap structure, be numbered for then the different materials in the model respectively, the purpose of numbering is in order to give different attributes to the tetrahedron element in the different materials in the time domain Finite Element Method, to be used for extracting the observation point of little charged tape gap structure S parameter when at last aftertreatment being set; After model is built up, adopting ANSYS software that this model is carried out grid again disperses, the grid discrete unit is chosen for tetrahedron element, and with match complex boundary preferably, the tetrahedron element that the tetrahedron element here can be chosen for the high-order curved surface further improves capability of fitting and simulation efficiency.After finishing the grid discrete operations, can from ANSYS software, derive time domain Finite Element Method Electromagnetic Simulation necessary cell node number information file and node coordinate message file.
Second step, cell node number information and node coordinate information according to above-mentioned acquisition, at first adopt the seamed edge basis function to launch to the field of each tetrahedron element inside, utilize the Galerkin method then, according to the mapping relations of the local code of every seamed edge in unit separately to overall situation coding, form the large-scale sparse linear systems of time domain finite element, its size is the number of all seamed edge basis functions.In the process that forms the time domain finite element system, can adopt based on the time domain Finite Element Method of wave equation with based on the unconditional stability technology of the time domain Finite Element Method of Maxwell equation group etc.This example is to adopt the unconditional stability technology based on the time domain Finite Element Method of Maxwell equation group to form the time domain finite element system.All these methods each time step after to time discrete all will be separated a type such as M FETDThe large-scale sparse linear system of equations of x=b, wherein matrix of coefficients M FETDTo each time step is constant, and the right vector b is all different at each time step, and it is the equation solution problem of the vector of the right more than, adopts direct solution to find the solution usually.
The 3rd step constituted a limited index set I={1 with all the seamed edge basis functions in the time domain Finite Element Method, and 2 ... N} is that I is the basis with index set, makes up a binary tree structure T who satisfies following condition I:
(1) I is T IThe top collection;
(2) if set t ∈ is T IBe support, so | t|≤C Leaf
(3) if set t ∈ is T INon-support, t comprises two subclass t so 1, t 2∈ T I, and
Figure BSA00000356947200051
Wherein | t| represents to gather the element number that t comprises, and is the number of the seamed edge basis function that comprises here; C LeafBe pre-set threshold, also be known as the smallest group size, be used for controlling the degree of depth of tree.The concrete construction process of binary tree is as follows: the top layer that at first all basis functions is included into tree, then will be wherein the basis function group that is divided into two, this process stops to segment when repeating down basis function number in each group of the thinnest layer of being got all less than the smallest group size.Value rule of thumb, smallest group size elect 32 or had higher counting yield at 64 o'clock as.Two minutes criterion is chosen as two fens criterions of how much balances here, promptly at first surround objective body with an enough big cube box, balancedly went down in two minutes according to x, y, z change in coordinate axis direction successively then, the process that its seamed edge basis function is gathered concrete hierarchical grouping as shown in Figure 2.This example is the 3 D electromagnetic problem of a complexity, the hierarchical grouping of its seamed edge basis function set adopts three-dimensional restriction box to finish, and for the purpose of clear and intuitive, provides an example that only contains 8 seamed edge basis functions, as shown in Figure 3, the binary tree structure that is generated by Fig. 3 is seen shown in Figure 4.
In the 4th step, on the basis that generates binary tree structure, make up two-dimentional block tree construction.According to the definition of bulk tree, a block tree can be regarded as the two-dimentional tree that two binary trees (row tree and row tree) interact and constitute.In the time domain Finite Element Method, row tree and row tree are made of the test basis function collection in seamed edge basis function collection and the Galerkin method respectively, because their numbers are all identical with expression-form, so T I=I JBlock tree T I * 1Forming process can be described as: recursively segmenting piece t * s is four sub-piece t 1* s 1, t 1* s 2, t 2* s 1And t 2* s 2, this process stops when following condition satisfies:
(1)|t|≤C leaf?or|s|≤C leaf。
(2) set t and s satisfy admissible condition.
Admissible condition is to be used for judging whether a sub-piece can be expressed as the criterion of low-rank form, and its expression formula is as follows:
max{diam(Ω t)，diam(Ω s)}≤ηdist(Ω t，Ω s)
Wherein, diam represents the Euclidean diameter, and dist represents to gather the distance between s and the t, and η＞0 is used for controlling the admissible condition power.Because the present invention adopts the hierarchical grouping mode of three-dimensional restriction box, diam is restriction box circumscribed circle diameter, and dist is distance between the restriction box, and its synoptic diagram as shown in Figure 5.
In the 5th step, the sub-piece of admissible condition will be satisfied
Figure BSA00000356947200061
Write as the form of following low-rank matrix multiple, also claimed Rk-matrix:
M＝AB T
Figure BSA00000356947200062
Wherein A, B are full battle array.In the Rk-matrix A and B block order k much smaller than | t| and | during s|, a large amount of internal memories are saved in full gust of storage Rk-matrix and storage specific energy mutually.The value of k can influence the precision of Rk-approximate matrix, and the degree of the big more expression compression of k is low more, and the corresponding calculated precision is high more.The block tree construction that is generated by the binary tree structure of Fig. 4 is (grey block represents can continue to segment piece among the figure, and white blocks represents to allow piece, and black block is represented the non-piece of allowing) as shown in Figure 6.The matrix of coefficients M of time domain finite element system FETD
Figure BSA00000356947200063
The mathematic(al) representation of matrix is as follows:
Figure BSA00000356947200064
Only contain in the matrix and allow piece and non-ly allow piece, allow that piece expresses with the Rk-matrix form, non-ly allow that piece expresses with full formation formula.Typically
Figure BSA00000356947200066
The matrix synoptic diagram as shown in Figure 7.According to admissible condition, can must leave certain distance with two groups of basis function set of Rk-matrix representation, and time domain finite element seamed edge basis function is the local loop function, the seamed edge that leaves certain distance interacts and must be zero, like this, M FETDIn all nonzero elements all be received in
Figure BSA00000356947200067
The non-of matrix allowed in the piece, and the Rk-matrix is zero, therefore, adopts
Figure BSA00000356947200068
Matrix is expressed M FETDBe accurately harmless.
The 6th step, right
Figure BSA00000356947200069
The M of matrix form FETDCarrying out LU decomposes.As shown in Figure 8, because M FETDBased on the binary tree structure, write as partitioned matrix and be
Figure BSA000003569472000610
For one 2 * 2
Figure BSA000003569472000611
Matrix-block:
Figure BSA000003569472000612
Will Resolve into L and U matrix:
Figure BSA000003569472000614
= L 11 &CircleTimes; U 11 L 11 &CircleTimes; U 12 L 21 &CircleTimes; U 11 L 21 &CircleTimes; U 12 &CirclePlus; L 22 &CircleTimes; U 22
(1) calculates
Figure BSA00000356947200071
Figure BSA00000356947200072
Decompose and obtain L 11, U 11
(2) find the solution trigonometric equation
Figure BSA00000356947200073
Obtain U 12
(3) find the solution trigonometric equation
Figure BSA00000356947200074
Obtain L 21
(4) calculate Obtain L 22U 22, and pass through
Figure BSA00000356947200076
Decompose and obtain L 22, U 22
The aforesaid operations recurrence is carried out and is
Figure BSA00000356947200077
The recursive algorithm that matrix L U decomposes.
Figure BSA00000356947200078
Decompose in the recursive algorithm, relate to finding the solution of trigonometric equation TX=B, wherein T is known triangle (going up triangle or following triangle) Matrix, X are unknown
Figure BSA000003569472000710
Matrix, B are known the right
Figure BSA000003569472000711
Matrix.Press the type of matrix-block X and B, finding the solution of trigonometric equation can be divided into three kinds of situations:
(1) when X and B are the Rk-matrix, is expressed as with the low-rank decomposed form
Figure BSA000003569472000712
Figure BSA000003569472000713
Therefore have: X 2=Y 2, X 1=T -1Y 1Because T is a triangular matrix, X 1Can find the solution acquisition to back substitution by k time preceding (back).
(2) as X and B during for full battle array, X can obtain by finding the solution common triangular matrix: X=T -1B.
(3) when X and B can segment, need find the solution block-tridiagonal matrix.If X and B are 2 * 2 block matrix, T is known triangle down Matrix, trigonometric equation can be written as:
L 11 0 L 21 L 22 X 11 X 12 X 21 X 22 = B 11 B 12 B 21 B 22
L wherein 11, L 22Be following triangle
Figure BSA000003569472000716
Matrix.X 11And X 12Can pass through recursive resolve trigonometric equation L respectively 11X 11=B 11And L 11X 12=B 12Obtain; X 21And X 22Can pass through recursive resolve trigonometric equation L respectively 22X 21=B 21-L 21X 11And L 22X 22=B 22-L 21X 12Obtain.
The false code of the flow process of decomposition algorithm is described below:
Figure BSA000003569472000718
{
If H τ * τCan not segment
Calculate H τ * τLU decompose L τ * τU τ * τ=H τ * τ(full battle array accurately LU is decomposed)
else
S(τ)＝{τ 1，τ 2}，
Find the solution trigonometric equation
Figure BSA000003569472000720
Figure BSA000003569472000721
Y : = - H &tau; 2 &times; &tau; 2 &CirclePlus; L &tau; 2 &times; &tau; 1 U &tau; 1 &times; &tau; 2
Figure BSA000003569472000723
}
Figure BSA000003569472000724
Before three angle factors up and down that decomposition is generated and the decomposition
Figure BSA000003569472000725
Matrix has same tree; Different is, before decomposing
Figure BSA00000356947200081
The pieces of allowing all in the matrix are zero, and
Figure BSA00000356947200082
Part in three angle factors up and down that obtained after decomposing allows that piece has been received in nonzero value.
In the 7th step, carry out The front and back of matrix obtain separating of system of linear equations to back substitution.
Figure BSA00000356947200084
Computation complexity to the back substitution operation before and after the matrix is O (NlogN),
Figure BSA00000356947200085
The front and back of matrix adopt recursive algorithm to finish to back substitution, and when finding the solution trigonometric equation TX=B or XT=B in the 6th step, if B is a vector, the solution procedure of this trigonometric equation is forward direction or back process to back substitution so.
Figure BSA00000356947200086
The operation that matrix L U decomposes is only carried out at first time step, and all time steps afterwards all only need to carry out The front and back of matrix get final product to back substitution operation, execute after the finding the solution of all time step time domain finite element systems, and can obtain a value of whole zoning.
Figure BSA00000356947200088
The front and back of matrix are very fast to the back substitution operating speed, so greatly improved the simulation efficiency of time domain Finite Element Method.Fig. 9 and shown in Figure 10ly be respectively the computing time of EBG structure example and the test of memory consumption has confirmed
Figure BSA00000356947200089
The computation complexity that matrix L U decomposes is O (Nlog 2N), memory consumption is O (NlogN),
Figure BSA000003569472000810
Computation complexity to back substitution before and after the matrix is O (NlogN).Figure 11 shows that fixedly choose the Rk-matrix block order k=10, under the different number unknown quantity situations
Figure BSA000003569472000811
The computational accuracy of matrix direct solution, as can be seen
Figure BSA000003569472000812
The matrix direct solution has good stability.Computational accuracy with choose to block order relevant, the blocking order and can obtain different computational accuracies of different sizes, therefore The matrix direct solution has good precision controllability.
In the 8th step, calculate the electromagnetic property parameter.The required field value of aftertreatment is carried out in extraction, by calculating the S parameter that can obtain the EBG structure.
The present invention adopt based on
Figure BSA000003569472000814
During the efficient time domain Electromagnetic Simulation method emulation three-dimensional electromagnetic scattering problems of matrix algorithms, its operation steps is identical, but because when three-dimensional electromagnetic scattering carried out emulation, need to obtain the radar scattering interface (RCS) of scatterer, therefore, in first step modeling process of the present invention, need to be provided with the closed enveloping surface that is used for calculating RCS; In the 8th step, need carry out nearly far field and change and calculate RCS, can reach ideal effect equally.

Claims (3)

  1. One kind based on
    Figure FSA00000356947100011
    The efficient time domain Electromagnetic Simulation method of matrix algorithms, it be adopt the time domain Finite Element Method with based on
    Figure FSA00000356947100012
    The combination of the direct solution of matrix is characterized in that it is to realize by following operation steps:
    The first step, select for use ANSYS software to set up the geometric model of simulation object, adopt tetrahedron element that this model is carried out grid then in ANSYS software and disperse, the required grid discrete message file of simulation analysis is derived in discrete back, comprises cell node message file and node coordinate message file;
    Second step, according to the grid discrete message, adopt the seamed edge basis function to launch the field of each tetrahedron element inside, utilize the Galerkin method to generate the large-scale sparse linear systems of time domain finite element again, its size is the number of all seamed edge basis functions;
    The 3rd step, adopt the simulation object geometric model after two minutes mode of recurrence disperses to grid to divide into groups, construct the binary tree structure of all seamed edge basis function collection;
    The 4th step interacted the binary tree structure of test basis function collection in the binary tree structure of seamed edge basis function collection and the Galerkin method, generated the block tree construction of two dimension;
    The 5th goes on foot, and the employing admissible condition is theoretical selects far away group of effect between any two groups in the block tree construction, and the matrix of far group effect formation is compressed into two low-rank matrix multiple forms, generation time domain coefficient matrix in finite element method
    Figure FSA00000356947100013
    Matrix expression wherein only comprises the sub-piece of two classes, promptly allows piece and non-ly allows piece;
    In the 6th step, utilize recursive algorithm to reach
    Figure FSA00000356947100014
    The self-defining arithmetic rule of matrix is to the time domain coefficient matrix in finite element method
    Figure FSA00000356947100015
    Matrix carries out the operation that LU decomposes, and obtains
    Figure FSA00000356947100016
    Three angle factors up and down of matrix form;
    In the 7th step, obtaining On the basis of three angle factors up and down of matrix form, each time step is carried out afterwards
    Figure FSA00000356947100018
    Can obtain separating of this time step system of linear equations to back substitution before and after the matrix, finally obtain a simulating area value everywhere;
    The 8th step, extract corresponding value as required and obtain the S parameter of microwave circuit, the RCS electromagnetic property parameters such as (RCS) of scatterer by computing, finish the Electromagnetic Simulation process.
  2. According to claim 1 described based on
    Figure FSA00000356947100019
    The efficient time domain Electromagnetic Simulation method of matrix algorithms is characterized in that: in second step, be to adopt the time domain Finite Element Method of unconditional stability to generate the large-scale sparse linear systems of time domain finite element.
  3. According to claim 1 described based on
    Figure FSA000003569471000110
    The efficient time domain Electromagnetic Simulation method of matrix algorithms, it is characterized in that: in the 3rd step, be to adopt three-dimensional restriction box to finish the hierarchical grouping that the seamed edge basis function is gathered, its method of operating is at first to surround simulation object with the three-dimensional cubic box, finishes the hierarchical grouping that the seamed edge basis function is gathered along two fens this cube boxes of xyz coordinate direction recurrence then.
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CN102508220A (en) * 2011-10-24 2012-06-20 西瑞克斯(北京)通信设备有限公司 Method for obtaining radar cross section (RCS) of homogeneous bi-isotropic medium object
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CN106202595A (en) * 2015-05-07 2016-12-07 南京理工大学 Analyze the time domain non-conformal grid method of dielectric object Transient Em Fields Scattering characteristic
CN106991222A (en) * 2017-03-27 2017-07-28 南京邮电大学 A kind of low frequency electromagnetic characteristic Simulation method based on lamination matrix decomposition
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CN109145483A (en) * 2018-09-04 2019-01-04 宁夏冰核科技有限公司 Fuel cell High-Dimensional Model Real-time Simulation Technology based on triple diagonal matrix algorithm
CN109711044A (en) * 2018-12-26 2019-05-03 山东科技大学 A kind of plane wave Discontinuous Finite Element Method of guinea pig scattering section area
CN110502785A (en) * 2019-07-15 2019-11-26 电子科技大学 A kind of Three-dimensional Time Domain calculates the electromagnetism numerical method of waveguide S parameter
CN111767640A (en) * 2020-05-26 2020-10-13 北京理工大学 Rapid simulation method for target near-field radar echo
CN112270119A (en) * 2020-11-13 2021-01-26 清源智翔(重庆)科技有限公司 Electromagnetic environment cognition method based on finite element
CN112329303A (en) * 2020-11-03 2021-02-05 西安电子科技大学 Array antenna electromagnetic characteristic solving method based on finite element region decomposition
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CN102902841A (en) * 2012-08-28 2013-01-30 同济大学 Method for calculating cross sectional areas of computer-loaded radars with complex structures
CN103279589A (en) * 2013-04-18 2013-09-04 南京理工大学 Rotational symmetric body electromagnetic scattering property simulation method based on matrix nest compression
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CN103309845B (en) * 2013-05-16 2016-08-31 国家电网公司 A kind of system of linear equations sub solving method method for Power System Dynamic Simulation
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CN104951580A (en) * 2014-03-28 2015-09-30 南京理工大学 Unconditional stability and conditional stability mixed time domain spectral element electromagnetic analyzing method
CN104951580B (en) * 2014-03-28 2019-03-29 南京理工大学 The time domain spectral element emi analysis method of unconditional stability and condition stability mixing
CN106202595A (en) * 2015-05-07 2016-12-07 南京理工大学 Analyze the time domain non-conformal grid method of dielectric object Transient Em Fields Scattering characteristic
CN107194088A (en) * 2017-01-03 2017-09-22 金陵科技学院 A kind of high order finite difference time domain electromagnetic-field simulation method based on ICCG
CN106991222B (en) * 2017-03-27 2020-04-21 南京邮电大学 Low-frequency electromagnetic characteristic simulation method based on laminated matrix decomposition
CN106991222A (en) * 2017-03-27 2017-07-28 南京邮电大学 A kind of low frequency electromagnetic characteristic Simulation method based on lamination matrix decomposition
CN107330162A (en) * 2017-06-13 2017-11-07 电子科技大学 For the mesh generation and information acquisition method of non-curved boundary two dimensional model
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CN112905241A (en) * 2019-03-15 2021-06-04 英特尔公司 Sparse optimization for matrix accelerator architecture
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