Electromagnetic scattering characteristic analysis method and system for metal targets based on hybrid nested equivalent source direct solver

Abstract

The present invention discloses a method and system for analyzing electromagnetic scattering characteristics of metal targets based on a hybrid nested equivalent source direct solver. Specifically, the method comprises the following steps: establishing a target equivalent surface current model to be solved, and dividing the global basis functions to be solved corresponding to the model into multiple groups in different spatial regions; constructing an elimination matrix for the far-field coupling matrix blocks for each group to compress and eliminate the admissible blocks; eliminating the inadmissible blocks by calculating the Schur complement of the remaining inadmissible matrix blocks; compressing the fill-in matrix blocks added to the admissible blocks, extracting their column vectors and adding them to the orthogonalized receiving matrix of the next group; skipping the remaining decomposition process of the group in the event of overflow caused by matrix addition or translation from a sublayer to a parent layer; and sequentially traversing each layer and group to solve the system matrix equation, ultimately obtaining the electromagnetic scattering characteristics of the target, such as the radar cross-section. The method has high computational efficiency and lower memory requirements.

Description

Technical Field

[0001] The present invention belongs to the field of electromagnetic computing technology, and in particular to a method and system for analyzing electromagnetic scattering characteristics of metal targets based on a hybrid nested equivalent source direct solver. Background Art

[0002] The method of moments (MoM), widely used in electromagnetic calculations, discretizes integral equations into matrix equations and expands the solution into a linear combination of basis functions. The key to analyzing the electromagnetic scattering characteristics of metal objects lies in solving the matrix equation to obtain the current coefficients of the metal target's discrete surfaces. These matrix equations are often solved using iterative or direct methods.

[0003] Iterative solutions are often accelerated by combining various fast algorithms to reduce memory requirements, such as the fast multipole method (FMM) and its multilevel form, the multilevel fast multipole algorithm (MLFMA), FFT-based methods, ACA, and the multilevel matrix decomposition algorithm (MLMDA). However, in the case of ill-conditioned system matrices, iterative solutions inherently suffer from convergence issues. Furthermore, iterative solutions are inefficient for problems with multiple right-handed vectors.

[0004] Different from iterative solutions, fast direct solution algorithms have become a research hotspot in recent years due to their significant advantages over iterative solutions for the above problems. Since the inverse of the system matrix is ​​explicitly represented in the direct solution framework, for multi-right-hand vector problems, the solution is obtained through matrix-matrix multiplication, rather than restarting the solution as required in iterative solutions. Therefore, the efficiency of analyzing such problems is much higher than that of iterative solutions. Many direct solvers with different matrix structures have been reported in the open literature, such as stacked semi-separated matrix (HSS-matrix), butterfly structure matrix, layered matrix ( matrix) and its improved form matrix.

[0005] Document 1 (M. Ma and D. Jiao, “Accuracy Directly Controlled Fast DirectSolution of General -Matrices and Its Application to Solving ElectrodynamicVolume Integral Equations," IEEE Trans. Microw. Theory Techn. , vol. 66, no. 1,pp. 35-48, Jan. 2018) proposed a A direct matrix solution algorithm. This algorithm expands the kernel function into a sum of products of a series of Lagrange polynomials to achieve a compressed representation of the admissible blocks of the system matrix. Later, the paper 2 (Z. Rong, M. Jiang, Y. Chen, L. Lei, X. Yang, and J. Hu, “Strong admissibility skeletonization factorization for fast direct solution of electromagnetic scattering from conducting objects,” IEEE Trans. Antennas Propag., vol. 69, no. 10, pp. 6607-6617, Oct. 2021) proposes a kernel-independent fast direct solver based on skeleton decomposition. The dominant basis functions (i.e., skeletons) are selected through interpolation decomposition to represent the interactions between the original full set of basis functions. However, using only skeletons requires constructing a corresponding radiation reception matrix for each layer and each group. Furthermore, the direct solver is a one-way traversal method from the bottom layer to the top layer, combining and regrouping skeletons into higher layers to form the full set of basis functions for the parent group. The skeleton basis functions for each layer are selected from the basis functions at the bottom layer, which does not guarantee optimal sampling. Therefore, a strategy combining skeletons with equivalent points is urgently needed to address the issues of low computational efficiency and high memory requirements. Summary of the Invention

[0006] The purpose of the present invention is to provide a method and system for analyzing the electromagnetic scattering characteristics of metal targets based on a hybrid nested equivalent source direct solver, thereby improving computational efficiency and reducing memory requirements.

[0007] The technical solution to achieve the purpose of the present invention is: a method for analyzing electromagnetic scattering characteristics of metal targets based on a hybrid nested equivalent source direct solver, comprising the following steps:

[0008] Step 1: Establish the equivalent surface current model of the metal target, divide the global basis functions corresponding to the model into multiple groups in different spatial regions according to the hierarchical structure of the octree, rearrange the system matrix according to the group number, ensure that the basis functions of the same group are in the same spatial region of the system matrix, start calculation from the bottom layer, and initialize the group number. ;

[0009] Step 2: Use the hybrid nested equivalent source algorithm to characterize the far-field coupling of each part of the metal target and construct the The low-rank compressed form of the far-field impedance matrix block is obtained by orthogonalization. The orthogonalized receiving matrix of the group;

[0010] Step 3: Group orthogonalized receiving matrix:

[0011] If the child layer overflows when it moves to the parent layer, let And return to step 2 to execute each step in sequence;

[0012] If no overflow occurs, the compressed extraction is the same as the first The fill-in matrix block column vector of the group association is constructed to construct the elimination matrix for the far-field coupling matrix block, and the corresponding processing is performed according to the following conditions: And the matrix addition produces overflow, then let And return to step 2 to execute each step in sequence; otherwise, the admissible matrix block is compressed and eliminated by multiplying the elimination matrix with the admissible matrix block;

[0013] Step 4: Calculate the Schur complement of the inadmissible matrix block to eliminate the inadmissible block and generate a fill-in matrix block added to the admissible block;

[0014] Step 5: If all groups in the current layer have been traversed, proceed to step 6;

[0015] Otherwise, let , and return to step 2 to execute each step in sequence;

[0016] Step 6: If all layers are traversed, the system matrix equation is solved and the process goes to step 7.

[0017] Otherwise, update the current layer transfer matrix, enter the next layer calculation, and initialize the next layer number , return to step 2 and execute each step in sequence;

[0018] Step 7: In the scenario of electromagnetic waves incident from multiple directions, the surface current distribution of the metal target in different directions is solved based on the inverse of the system matrix, and finally the electromagnetic scattering characteristics such as the RCS of the target are obtained.

[0019] A metal target electromagnetic scattering feature analysis system based on a hybrid nested equivalent source direct solver is provided. The system is used to implement the metal target electromagnetic scattering feature analysis method based on a hybrid nested equivalent source direct solver. The system includes a first module to a seventh module arranged in sequence. The functions of each module are as follows:

[0020] In the first module, the equivalent surface current model of the metal target is established, and the global basis functions corresponding to the model are divided into multiple groups in different spatial regions according to the hierarchical structure of the octree. The system matrix is ​​rearranged according to the group number to ensure that the basis functions of the same group are in the same spatial area of ​​the system matrix. The calculation starts from the bottom layer and the group number is initialized. ;

[0021] The second module uses the hybrid nested equivalent source algorithm to characterize the far-field coupling of various parts of the metal target and construct the The low-rank compressed form of the far-field impedance matrix block is obtained by orthogonalization. The orthogonalized receiving matrix of the group;

[0022] The third module is for Group orthogonalized receiving matrix:

[0023] If the child layer overflows when it moves to the parent layer, let and returns to the second module;

[0024] If no overflow occurs, the compressed extraction is the same as the first The fill-in matrix block column vector of the group association is constructed to construct the elimination matrix for the far-field coupling matrix block, and the corresponding processing is performed according to the following conditions: And the matrix addition produces overflow, then let and returns to the second module; otherwise, the compression elimination of the admissible matrix blocks is achieved by eliminating the matrix product;

[0025] The fourth module calculates the Schur complement of the inadmissible matrix block to eliminate the inadmissible block and generates a fill-in matrix block added to the admissible block;

[0026] In the fifth module, if all groups in the current layer are traversed, the sixth module is entered;

[0027] Otherwise, let , and return to the second module;

[0028] In the sixth module, if all layers are traversed, the system matrix equation is solved and the seventh module is entered;

[0029] Otherwise, update the current layer transfer matrix, enter the next layer calculation, and initialize the next layer number , return to the second module;

[0030] The seventh module, in the scenario of electromagnetic waves incident from multiple directions, solves the surface current distribution of the metal target in different directions based on the inverse of the system matrix, and finally obtains the electromagnetic scattering characteristics such as the RCS of the target.

[0031] A mobile terminal includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the method for analyzing electromagnetic scattering characteristics of metal targets based on a hybrid nested equivalent source direct solver is implemented.

[0032] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the method for analyzing electromagnetic scattering characteristics of metal targets based on a hybrid nested equivalent source direct solver.

[0033] Compared with the prior art, the present invention has the following significant advantages:

[0034] (1) Combining skeleton and equivalent source basis functions to compress low-rank matrices has higher computational efficiency in the application scenario of analyzing multiple incident fields of metal targets;

[0035] (2) The method combining skeleton and equivalent points has lower memory requirements than the method using only skeleton;

[0036] (3) The direct solution framework is independent of the integral kernel and can be widely applied to other types of integral equation problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1a This is a schematic diagram of the low-rank compression process of the lowest-level skeletonization method.

[0038] Figure 1b This is a schematic diagram of the low-rank compression process of the high-level equivalent source method.

[0039] Figure 2 It is a schematic diagram of the original system matrix divided into four groups.

[0040] Figure 3a It is aimed at Figure 2 Schematic diagram of the system matrix after the first set of admissible blocks of the original matrix are eliminated.

[0041] Figure 3b It is aimed at Figure 2 Schematic diagram of the system matrix after the first group of inadmissible blocks of the original matrix are eliminated.

[0042] Figure 4 This is a schematic diagram of the system matrix after the decomposition of the four groups is completed.

[0043] Figure 5ayes Figure 2 The first set of admissible blocks in corresponds to the matrix decomposition process diagram.

[0044] Figure 5b yes Figure 2 The first group of inadmissible blocks corresponds to the matrix decomposition process diagram.

[0045] Figure 5c yes Figure 2 The second set of admissible blocks in corresponds to the matrix decomposition process diagram.

[0046] Figure 5d yes Figure 2 The second group of inadmissible blocks corresponds to the matrix decomposition process diagram.

[0047] Figure 5e yes Figure 2 The third group of admissible blocks in corresponds to the matrix decomposition process diagram.

[0048] Figure 5f yes Figure 2 The third group of inadmissible blocks corresponds to the matrix decomposition process diagram.

[0049] Figure 5g yes Figure 2 The fourth group of admissible blocks in the figure corresponds to the matrix decomposition process diagram.

[0050] Figure 5h yes Figure 2 The fourth group of inadmissible blocks corresponds to the matrix decomposition process diagram.

[0051] Figure 6 This is a comparison chart of the metal sphere RCS and analytical solution results.

[0052] Figure 7 yes Figure 6 The second norm error between the calculated current of the metal ball and the reference value changes with the algorithm accuracy under different skeleton selection accuracy conditions.

[0053] Figure 8 This is the result diagram of the dual-station RCS calculation of the aircraft model. DETAILED DESCRIPTION

[0054] The present invention provides a method for analyzing electromagnetic scattering characteristics of metal targets based on a hybrid nested equivalent source direct solver, comprising the following steps:

[0055] Step 1: Establish the equivalent surface current model of the metal target, divide the global basis functions corresponding to the model into multiple groups in different spatial regions according to the hierarchical structure of the octree, rearrange the system matrix according to the group number, ensure that the basis functions of the same group are in the same spatial region of the system matrix, start calculation from the bottom layer, and initialize the group number. ;

[0056] Step 2: Use the hybrid nested equivalent source algorithm to characterize the far-field coupling of each part of the metal target and construct the The low-rank compressed form of the far-field impedance matrix block is obtained by orthogonalization. The orthogonalized receiving matrix of the group;

[0057] Step 3: Group orthogonalized receiving matrix:

[0058] If the child layer overflows when it moves to the parent layer, let And return to step 2 to execute each step in sequence;

[0059] If no overflow occurs, the compressed extraction is the same as the first The fill-in matrix block column vector of the group association is constructed to construct the elimination matrix for the far-field coupling matrix block, and the corresponding processing is performed according to the following conditions: And the matrix addition produces overflow, then let And return to step 2 to execute each step in sequence; otherwise, the admissible matrix block is compressed and eliminated by multiplying the elimination matrix with the admissible matrix block;

[0060] Step 4: Calculate the Schur complement of the inadmissible matrix block to eliminate the inadmissible block and generate a fill-in matrix block added to the admissible block;

[0061] Step 5: If all groups in the current layer have been traversed, proceed to step 6;

[0062] Otherwise, let , and return to step 2 to execute each step in sequence;

[0063] Step 6: If all layers are traversed, the system matrix equation is solved and the process goes to step 7.

[0064] Otherwise, update the current layer transfer matrix, enter the next layer calculation, and initialize the next layer number , return to step 2 and execute each step in sequence;

[0065] Step 7: In the scenario of electromagnetic waves incident from multiple directions, the surface current distribution of the metal target in different directions is solved based on the inverse of the system matrix, and finally the electromagnetic scattering characteristics such as the RCS of the target are obtained.

[0066] As a specific example, in step 1, the equivalent surface current model of the metal target is established as follows:

[0067] First, the metal target to be analyzed is modeled to obtain a physical model of the metal target;

[0068] Then, the surface of the metal target is discretized by the surface segmentation method, and the electromagnetic field matrix equation corresponding to the discretized metal target is constructed based on the electric field integral equation. The electromagnetic field matrix equations corresponding to each discrete block are group-numbered to form a system matrix, thereby obtaining the equivalent surface current model of the metal target.

[0069] Since direct solution requires the display of the matrix, the system matrix must first be rearranged according to the group number to ensure that the basis functions of the same group are in the same area of ​​the system matrix.

[0070] As a specific example, step 2 is as follows:

[0071] The electromagnetic scattering field of metal targets tends to be flat as the distance increases. Firstly, a hybrid nested equivalent source method is introduced to compress the far-field coupling, thereby reducing the computational complexity.

[0072] For the matrix low-rank compression process, the average basis function of each group in the lowest layer is less than that in the higher layers. Therefore, the skeleton compression method is used in the lowest layer to select the skeleton basis function that plays a dominant role in the radiation field to achieve the compression representation of the far-field low-rank matrix. In the non-lowest layer, the radiation field of the original basis function is represented by a uniformly distributed equivalent source to achieve the compression representation of the high-level far-field matrix. The approximate process is as follows: Figure 1a 、 Figure 1b shown.

[0073] The compressed representation of the far-field matrix of different layers is:

[0074] (1)

[0075] Among them, among them, 、 Indicates the far-acting field group and source group; and They are the external test surfaces of the source group and the field group respectively; and The lowest level is the skeleton basis functions selected for the source group and the field group, and the higher levels are the equivalent source point basis functions constructed for the source group and the equivalent field point basis functions constructed for the field group; is the radiation matrix of the source group; is the receiving matrix of the field group. In the electric field integral equation, the radiation and receiving matrices of the same group are transposed to each other. is the transfer matrix; represents the impedance matrix between the source group and the field group, The impedance matrix representing the equivalent source point outside the field group to the basis function inside the field group, The pseudo-inverse matrix represents the impedance matrix from the equivalent source point outside the field group to the equivalent field point inside the field group, It represents the impedance matrix from the equivalent source point in the source group to the equivalent field point in the field group. The pseudo-inverse matrix represents the impedance matrix from the equivalent source point within the source group to the test field point outside the source group, Represents the impedance matrix from the basis function within the source group to the test field point outside the source group, represents the internal equivalent surface of the source group and field group, Represents the skeleton basis function at the bottom layer, Indicates an equivalent point at a non-bottommost level, Indicates the current layer number. Indicates the total number of layers;

[0076] The physical meaning of this step in practical applications is that at the lowest level, the skeleton basis function that plays a dominant role in electromagnetic scattering is selected from the basis functions constructed after the metal target is discretized to characterize the scattering field generated by the group of metal targets, while at the higher level, equivalent scattering points uniformly distributed on a spherical shell are constructed to characterize the scattering field.

[0077] For the After constructing the far-field matrix compression representation, The radiation and reception matrices of the group are orthogonalized by singular value decomposition (SVD). Group receiving matrix for

[0078] (2)

[0079] in, For the The matrix composed of the left singular vectors after group truncation is the receiving matrix after orthogonalization; It is the remaining part after singular value decomposition;

[0080] In the After the group orthogonalization is completed, Group and Transfer matrix between groups Updated to , thus ensuring the correctness of the compressed representation:

[0081] (3)

[0082] in, , superscript Represents matrix transpose.

[0083] As a specific example, in step 3, the compression extraction is The column vectors of the fill-in matrix blocks associated with each group are used to construct the cancellation matrix for the far-field coupling matrix blocks, as follows:

[0084] Extraction and When filling-in matrix block column vectors associated with the group, first calculate Group association generates the Gram matrix of the fill-in matrix block on the admissible block and adds them together, then performs SVD decomposition on the sum of the matrices to extract the column vector:

[0085] (4)

[0086] in For The obtained value during the SVD decomposition orthogonalization process is complementary matrix, and Together they form a unitary matrix, For The local sequence number of the allowed blocks of the fill-in block associated with the group, For The global sequence number of the allowed blocks of the fill-in block associated with the group, To add to the admissible block fill-in matrix blocks on , For The allowed number of fill-in blocks associated with a group; For all the extracted The column vector of the group-associated fill-in matrix block, Denotes the diagonal matrix produced by SVD decomposition, with the superscript represents the conjugate transpose of the matrix;

[0087] Append the extracted column vector to the The updated receiving matrix can represent both the original admissible block and the fill-in matrix block added later:

[0088] (5)

[0089] in, For the The updated receiving matrix of the group is obtained; by changing the truncation threshold of SVD decomposition, the error of the system matrix inversion algorithm is controlled; combined with The orthogonal column vectors are used to construct the cancellation matrix for the far-field coupling matrix block :

[0090] (6)

[0091] in, For the Group updated receiving matrix The complement matrix of .

[0092] By multiplying the elimination matrix with the admissible block, the orthogonality between the elimination column vector and the admissible block is used to achieve compression elimination of the admissible block associated with the group. Next, we proceed to the direct solution process. Taking a matrix structure divided into four groups as an example, the system matrix is ​​as follows: Figure 2 For each group, firstly, the elimination matrix of the far-field coupling matrix block is constructed by combining the column vector orthogonal to the new radiation matrix to achieve the admissible block compression elimination of the group. After this step, the system matrix of the first group is as follows: Figure 3a shown.

[0093] As a specific example, step 4 is as follows:

[0094] In the matrix decomposition process, after the admissible matrix blocks are eliminated, the remaining uneliminated matrices are inadmissible matrix blocks. By using the to-be-decomposed part of each group of self-coupling matrices and eliminating the inadmissible matrix blocks, the Schur complement of the inadmissible matrix blocks at different positions in the entire system matrix is ​​calculated to achieve further decomposition of the system matrix, which is achieved through the following matrix equation:

[0095] (7)

[0096] in,

[0097] (8)

[0098] In the formula is the part of the self-coupling matrix to be decomposed, 、 、 、 、 、 、 、 Located in Matrix blocks at right, bottom, bottom-right, top-left, top, top-right, left, and bottom-left positions; is the unit matrix, and To eliminate the matrix for inadmissible blocks, and is a matrix conduct The decomposed upper and lower triangular matrices are: 、 They are 、 The inverse matrix of

[0099] 、 、 and is the Schur complement at different positions of the system matrix, and the expression is

[0100] (9)

[0101] (10)

[0102] (11)

[0103] (12)

[0104] The second term on the right side of equations (9) to (12) is called the fill-in matrix block;

[0105] Define two elimination matrices and :

[0106] (13)

[0107] Left-multiply and right-multiply the inadmissible matrix block to be decomposed, so that

[0108] (14)

[0109] To achieve the elimination of inadmissible matrix blocks, the first group of elimination after this step system matrix is ​​as follows Figure 3b shown.

[0110] As a specific example, the current layer transfer matrix is ​​updated in step 6 as follows:

[0111] After eliminating all matrices in the current layer, the admissible block The transfer matrix is ​​expanded and updated:

[0112] (15)

[0113] in is the updated first Group and The transfer matrix between groups, For the The updated radiation matrix of the group, After each layer is eliminated Group and The final transfer matrix between groups, To add to the admissible block The fill-in matrix block is expanded to keep consistent with the augmented receiving matrix dimension, so that

[0114] (16)

[0115] in .

[0116] As a specific example, step 7 is as follows:

[0117] Finally, the system matrix is ​​decomposed into a series of matrix products, and the inverse of the matrix can also be expressed as a series of matrix products, thereby solving the system matrix equation:

[0118] (17)

[0119] in For the The number of layers, , , 、 For the Tier The product of the elimination matrices for admissible and inadmissible blocks, and For the Tier Form an elimination matrix for inadmissible blocks, For the system Tier Group the elimination matrix for admissible blocks; For the The permutation matrix of the entire system matrix after the layer decomposition is completed, the purpose is to aggregate all the remaining matrix blocks together for the next layer of decomposition; is the inverse of the system matrix, The inverse of the diagonal matrix block remaining in the final highest level of decomposition;

[0120] In the scenario of electromagnetic waves incident from multiple directions, the surface current distribution of the metal target in different directions is solved by the inverse of the system matrix, and finally the electromagnetic scattering characteristics such as the RCS of the target are obtained. Figure 2 As an example of the given system matrix, after all the current layers are eliminated, the system matrix is ​​as follows Figure 4 As shown, the complete elimination process of the current layer of the matrix is ​​as follows Figure 5a to Figure 5h shown.

[0121] The present invention also provides a metal target electromagnetic scattering feature analysis system based on a hybrid nested equivalent source direct solver, which is used to implement the metal target electromagnetic scattering feature analysis method based on a hybrid nested equivalent source direct solver. The system includes a first module to a seventh module arranged in sequence, and the functions of each module are as follows:

[0122] In the first module, the equivalent surface current model of the metal target is established, and the global basis functions corresponding to the model are divided into multiple groups in different spatial regions according to the hierarchical structure of the octree. The system matrix is ​​rearranged according to the group number to ensure that the basis functions of the same group are in the same spatial area of ​​the system matrix. The calculation starts from the bottom layer and the group number is initialized. ;

[0123] The second module uses the hybrid nested equivalent source algorithm to characterize the far-field coupling of various parts of the metal target and construct the The low-rank compressed form of the far-field impedance matrix block is obtained by orthogonalization. The orthogonalized receiving matrix of the group;

[0124] The third module is for Group orthogonalized receiving matrix:

[0125] If the child layer overflows when it moves to the parent layer, let and returns to the second module;

[0126] If no overflow occurs, the compressed extraction is the same as the first The fill-in matrix block column vector of the group association is constructed to construct the elimination matrix for the far-field coupling matrix block, and the corresponding processing is performed according to the following conditions: And the matrix addition produces overflow, then let and returns to the second module; otherwise, the compression elimination of the admissible matrix blocks is achieved by eliminating the matrix product;

[0127] The fourth module calculates the Schur complement of the inadmissible matrix block to eliminate the inadmissible block and generates a fill-in matrix block added to the admissible block;

[0128] In the fifth module, if all groups in the current layer are traversed, the sixth module is entered;

[0129] Otherwise, let , and return to the second module;

[0130] In the sixth module, if all layers are traversed, the system matrix equation is solved and the seventh module is entered;

[0131] Otherwise, update the current layer transfer matrix, enter the next layer calculation, and initialize the next layer number , return to the second module;

[0132] The seventh module, in the scenario of electromagnetic waves incident from multiple directions, solves the surface current distribution of the metal target in different directions based on the inverse of the system matrix, and finally obtains the electromagnetic scattering characteristics such as the RCS of the target.

[0133] The present invention also provides a mobile terminal, including a memory, a processor, and a computer program stored in the memory and runnable on the processor. When the processor executes the program, the method for analyzing the electromagnetic scattering characteristics of metal targets based on a hybrid nested equivalent source direct solver is implemented.

[0134] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the method for analyzing electromagnetic scattering characteristics of metal targets based on a hybrid nested equivalent source direct solver.

[0135] The present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments.

[0136] Example

[0137] This embodiment uses the direct solution algorithm of the present invention to calculate the bistatic RCS results of a metal spherical shell with a radius of 1.8m and compare them with the analytical solution, as shown in Figure 2. Figure 6 shown.

[0138] Furthermore, in order to illustrate the controllable characteristics of the algorithm error, the curve of the second norm error between the calculated current of the metal ball and the reference value is given as the algorithm accuracy changes under different skeleton selection accuracy conditions, such as Figure 7 shown.

[0139] The current second norm error is defined as

[0140] (18)

[0141] in and These are the current coefficient and reference current coefficient calculated by the algorithm, respectively. This example applies to the current coefficient obtained by inverting the LU decomposition.

[0142] In addition, based on the method of the present invention, the bistatic RCS of an aircraft is calculated. The incident wave direction is , , the RCS range is , , the operating frequency is set to 800MHz, and the size of the aircraft is approximately , is the wavelength of the electromagnetic wave. For comparison, the algorithm accuracy set in step 4 is set to and The calculation results are compared with those of pure MoM calculations, such as Figure 8 shown.

[0143] In summary, the present invention eliminates the admissible matrix blocks and the inadmissible matrix blocks respectively, thereby achieving the decomposition and inversion of the system matrix. Moreover, the error of the inversion algorithm is controllable. From the above simulation and result analysis, the current solution error gradually decreases with the improvement of the algorithm accuracy. When the algorithm accuracy is set to , the skeleton extraction accuracy is Under the condition of The correctness of the algorithm is verified below.

Claims

1. A method for analyzing electromagnetic scattering characteristics of metal targets based on a hybrid nested equivalent source direct solver, characterized in that: The following steps are involved: Step 1: Establish the equivalent surface current model of the metal target, divide the global basis functions corresponding to the model into multiple groups in different spatial regions according to the hierarchical structure of the octree, rearrange the system matrix according to the group number, ensure that the basis functions of the same group are in the same spatial region of the system matrix, start calculation from the bottom layer, and initialize the group number. ; Step 2: Use the hybrid nested equivalent source algorithm to characterize the far-field coupling of each part of the metal target and construct the The low-rank compressed form of the far-field impedance matrix block is obtained by orthogonalization. The orthogonalized receiving matrix of the group is as follows: For the matrix low-rank compression process, the average basis function of each group in the lowest layer is less than that in the higher layers. The skeleton compression method is used in the lowest layer to select the skeleton basis function that plays a dominant role in the radiation field to achieve the compressed representation of the far-field low-rank matrix. In the non-lowest layer, the radiation field of the original basis function is represented by a uniformly distributed equivalent source to achieve the compressed representation of the higher-level far-field matrix. The compressed representation of the far-field matrix of different layers is: (1) in, 、 Indicates the far-acting field group and source group; and They are the external test surfaces of the source group and the field group respectively; and The lowest level is the skeleton basis functions selected for the source group and the field group, and the higher levels are the equivalent source point basis functions constructed for the source group and the equivalent field point basis functions constructed for the field group; is the radiation matrix of the source group; is the receiving matrix of the field group. In the electric field integral equation, the radiation and receiving matrices of the same group are transposed to each other. is the transfer matrix; represents the impedance matrix between the source group and the field group, The impedance matrix representing the equivalent source point outside the field group to the basis function inside the field group, The pseudo-inverse matrix represents the impedance matrix from the equivalent source point outside the field group to the equivalent field point inside the field group, It represents the impedance matrix from the equivalent source point in the source group to the equivalent field point in the field group. The pseudo-inverse matrix represents the impedance matrix from the equivalent source point within the source group to the test field point outside the source group, Represents the impedance matrix from the basis function within the source group to the test field point outside the source group, represents the internal equivalent surface of the source group and field group, Represents the skeleton basis function at the bottom layer, Indicates an equivalent point at a non-bottommost level, Indicates the current layer number. Indicates the total number of layers; For the After constructing the far-field matrix compression representation, The radiation and reception matrices of the group are orthogonalized by singular value decomposition. Group receiving matrix for (2) in, For the The matrix composed of the left singular vectors after group truncation is the receiving matrix after orthogonalization; It is the remaining part after singular value decomposition; In the After the group orthogonalization is completed, Group and Transfer matrix between groups Updated to : (3) in, , superscript Represents matrix transpose; Step 3: Group orthogonalized receiving matrix: If the child layer overflows when it moves to the parent layer, let And return to step 2 to execute each step in sequence; If no overflow occurs, the compressed extraction is the same as the first The fill-in matrix block column vector of the group association is constructed to construct the elimination matrix for the far-field coupling matrix block, and the corresponding processing is performed according to the following conditions: And the matrix addition produces overflow, then let And return to step 2 to execute each step in sequence; otherwise, the admissible matrix block is compressed and eliminated by multiplying the elimination matrix with the admissible matrix block; Step 4: Calculate the Schur complement of the inadmissible matrix block to eliminate the inadmissible block and generate a fill-in matrix block added to the admissible block; Step 5: If all groups in the current layer have been traversed, proceed to step 6; Otherwise, let , and return to step 2 to execute each step in sequence; Step 6: If all layers are traversed, the system matrix equation is solved and the process goes to step 7. Otherwise, update the current layer transfer matrix, enter the next layer calculation, and initialize the next layer number , return to step 2 and execute each step in sequence; Step 7: In the scenario of electromagnetic waves incident from multiple directions, the surface current distribution of the metal target in different directions is solved based on the inverse of the system matrix, and finally the RCS electromagnetic scattering characteristics of the target are obtained.

2. The method for analyzing electromagnetic scattering characteristics of metal targets based on a hybrid nested equivalent source direct solver according to claim 1, characterized in that: In step 1, the equivalent surface current model of the metal target is established as follows: First, the metal target to be analyzed is modeled to obtain a physical model of the metal target; Then, the surface of the metal target is discretized by the surface segmentation method, and the electromagnetic field matrix equation corresponding to the discretized metal target is constructed based on the electric field integral equation. The electromagnetic field matrix equations corresponding to each discrete block are group-numbered to form a system matrix, thereby obtaining the equivalent surface current model of the metal target.

3. The method for analyzing electromagnetic scattering characteristics of metal targets based on a hybrid nested equivalent source direct solver according to claim 2, characterized in that: In step 3, the compression extraction is The column vectors of the fill-in matrix blocks associated with each group are used to construct the cancellation matrix for the far-field coupling matrix blocks, as follows: Extraction and When filling-in matrix block column vectors associated with the group, first calculate Group association generates the Gram matrix of the fill-in matrix block on the admissible block and adds them together, then performs SVD decomposition on the sum of the matrices to extract the column vector: (4) in For The obtained value during the SVD decomposition orthogonalization process is complementary matrix, and Together they form a unitary matrix, For The local sequence number of the allowed blocks of the fill-in block associated with the group, For The global sequence number of the allowed blocks of the fill-in block associated with the group, To add to the admissible block fill-in matrix blocks on , For The allowed number of fill-in blocks associated with a group; For all the extracted The column vector of the fill-in matrix blocks for group association, Denotes the diagonal matrix produced by SVD decomposition, with the superscript represents the conjugate transpose of the matrix; Append the extracted column vector to the The updated receiving matrix can represent both the original admissible block and the fill-in matrix block added later: (5) in, For the The updated receiving matrix of the group is obtained; by changing the truncation threshold of SVD decomposition, the error of the system matrix inversion algorithm is controlled; combined with The orthogonal column vectors are used to construct the cancellation matrix for the far-field coupling matrix block : (6) in, For the Group updated receiving matrix The complement matrix of .

4. The method for analyzing electromagnetic scattering characteristics of metal targets based on a hybrid nested equivalent source direct solver according to claim 3 is characterized in that: The step 4 is specifically as follows: In the matrix decomposition process, after the admissible matrix blocks are eliminated, the remaining uneliminated matrices are inadmissible matrix blocks. By using the to-be-decomposed part of each group of self-coupling matrices and eliminating the inadmissible matrix blocks, the Schur complement of the inadmissible matrix blocks at different positions in the entire system matrix is ​​calculated to achieve further decomposition of the system matrix, which is achieved through the following matrix equation: (7) in, (8) In the formula is the part of the self-coupling matrix to be decomposed, 、 、 、 、 、 、 、 Located in Matrix blocks at right, bottom, bottom-right, top-left, top, top-right, left, and bottom-left positions; is the unit matrix, and To eliminate the matrix for inadmissible blocks, and is a matrix conduct The decomposed upper and lower triangular matrices are: 、 They are 、 The inverse matrix of 、 、 and is the Schur complement at different positions of the system matrix, and the expression is (9) (10) (11) (12) The second term on the right side of equations (9) to (12) is called the fill-in matrix block; Define two elimination matrices and : (13) Left-multiply and right-multiply the inadmissible matrix block to be decomposed, so that (14) Achieve the elimination of inadmissible matrix blocks.

5. The method for analyzing electromagnetic scattering characteristics of metal targets based on a hybrid nested equivalent source direct solver according to claim 4, characterized in that: Update the current layer transfer matrix as described in step 6 as follows: After eliminating all matrices in the current layer, the admissible block The transfer matrix is ​​expanded and updated: (15) in is the updated first Group and The transfer matrix between groups, For the The updated radiation matrix of the group, After each layer is eliminated Group and The final transfer matrix between groups, To add to the admissible block The fill-in matrix block is expanded to keep consistent with the augmented receiving matrix dimension, so that (16) in .

6. The method for analyzing electromagnetic scattering characteristics of metal targets based on a hybrid nested equivalent source direct solver according to claim 5, characterized in that: The step 7 is specifically as follows: Finally, the system matrix is ​​decomposed into a series of matrix products, and the inverse of the matrix can also be expressed as a series of matrix products, thereby solving the system matrix equation: (17) in For the The number of layers, , , 、 For the Tier The product of the elimination matrices for admissible and inadmissible blocks, and For the Tier Form an elimination matrix for inadmissible blocks, For the system Tier Group the elimination matrix for admissible blocks; For the The permutation matrix of the entire system matrix after the layer decomposition is completed, the purpose is to aggregate all the remaining matrix blocks together for the next layer of decomposition; is the inverse of the system matrix, The inverse of the diagonal matrix block remaining in the final highest level of decomposition; In the scenario of electromagnetic waves incident from multiple directions, the surface current distribution of the metal target in different directions is solved based on the inverse of the system matrix, and finally the RCS electromagnetic scattering characteristics of the target are obtained.

7. A metal target electromagnetic scattering feature analysis system based on a hybrid nested equivalent source direct solver, characterized in that: The system is used to implement the metal target electromagnetic scattering characteristic analysis method based on the hybrid nested equivalent source direct solver according to any one of claims 1 to 6. The system includes the first module to the seventh module arranged in sequence, and the functions of each module are as follows: In the first module, the equivalent surface current model of the metal target is established, and the global basis functions corresponding to the model are divided into multiple groups in different spatial regions according to the hierarchical structure of the octree. The system matrix is ​​rearranged according to the group number to ensure that the basis functions of the same group are in the same spatial area of ​​the system matrix. The calculation starts from the bottom layer and the group number is initialized. ; The second module uses the hybrid nested equivalent source algorithm to characterize the far-field coupling of various parts of the metal target and construct the The low-rank compressed form of the far-field impedance matrix block is obtained by orthogonalization. The orthogonalized receiving matrix of the group; The third module is for Group orthogonalized receiving matrix: If the child layer overflows when it moves to the parent layer, let and returns to the second module; If no overflow occurs, the compressed extraction is the same as the first The fill-in matrix block column vector of the group association is constructed to construct the elimination matrix for the far-field coupling matrix block, and the corresponding processing is performed according to the following conditions: And the matrix addition produces overflow, then let and returns to the second module; otherwise, the compression elimination of the admissible matrix blocks is achieved by eliminating the matrix product; The fourth module calculates the Schur complement of the inadmissible matrix block to eliminate the inadmissible block and generates a fill-in matrix block added to the admissible block; In the fifth module, if all groups in the current layer are traversed, the sixth module is entered; Otherwise, let , and return to the second module; In the sixth module, if all layers are traversed, the system matrix equation is solved and the seventh module is entered; Otherwise, update the current layer transfer matrix, enter the next layer calculation, and initialize the next layer number , return to the second module; The seventh module, in the scenario of electromagnetic waves incident from multiple directions, solves the surface current distribution of the metal target in different directions based on the inverse of the system matrix, and finally obtains the RCS electromagnetic scattering characteristics of the target.

8. A mobile terminal comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the method for analyzing electromagnetic scattering characteristics of metal targets based on a hybrid nested equivalent source direct solver according to any one of claims 1 to 6 is implemented.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method for analyzing electromagnetic scattering characteristics of metal targets based on a hybrid nested equivalent source direct solver are implemented as described in any one of claims 1 to 6.

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