Metal target electromagnetic scattering characteristic analysis method and system based on hybrid nested equivalent source direct solver

Abstract

The invention discloses a metal target electromagnetic scattering characteristic analysis method and system based on a hybrid nested equivalent source direct solver, and the method specifically comprises the steps: building a target equivalent surface current to-be-solved model, and dividing a global to-be-solved basis function corresponding to the model into a plurality of groups in different space regions; for each group, constructing an elimination matrix for the far-field coupling matrix blocks to realize compression elimination of allowable blocks; the Schel complement of the remaining inadmissible matrix blocks is calculated, so that elimination of the inadmissible blocks is realized; compressing a fill-in matrix block added on the allowable block, extracting a column vector of the fill-in matrix block, adding the column vector to the orthogonalization receiving matrix of the next group, and skipping the residual decomposition process of the group according to an overflow condition generated by matrix addition and translation from a sub-layer to a parent layer; and traversing each layer and each group in sequence, solving a system matrix equation, and finally obtaining electromagnetic scattering characteristics such as radar sectional area of the target. The method is high in calculation efficiency and lower in memory requirement.

Description

Technical Field

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

[0002] The method of moments (MoM), which is widely used in electromagnetic calculations, discretizes the integral equation to form a matrix equation and expands the solution as a linear combination of a series of basis functions. For the analysis of the electromagnetic scattering characteristics of metal objects, the key lies in how to solve the matrix equation to obtain the current coefficients of the discrete surface of the metal target. The solution method of the matrix equation often uses an iterative method or a direct method.

[0003] For iterative solutions, various fast algorithms are usually combined to accelerate and reduce memory requirements, such as the fast multipole algorithm (FMM) and its multilevel form, the multilevel fast multipole algorithm (MLFMA), the FFT-based method, ACA, the multilevel matrix decomposition algorithm (MLMDA), etc. However, in the case of a ill-conditioned system matrix, there are essentially convergence problems in iterative solutions. In addition, iterative solution algorithms are inefficient for multi-right-hand vector problems.

[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 in the above problems. Since the inverse of the system matrix in the direct solution framework is explicitly represented, for multi-right-hand vector problems, the solution is obtained through matrix-matrix multiplication, rather than restarting the solution required in iterative solutions. Therefore, the efficiency in 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 the hierarchical semi-separable matrix (HSS-matrix), the butterfly structure matrix, the hierarchical matrix ( matrix) and its improved forms matrix.

[0005] Reference 1 (M. Ma and D. Jiao, “Accuracy Directly Controlled Fast DirectSolution of General -Matrices and Its Application to Solving Electrodynamic Volume Integral Equations,” IEEE Trans. Microw. Theory Techn. , vol. 66, no. 1, pp. 35 - 48, Jan. 2018) proposed a direct solution algorithm based on matrices. This algorithm expands the kernel function into the sum of a series of Lagrangian polynomial products to achieve a compressed representation of the admissible blocks of the system matrix. Subsequently, Reference 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) proposed a kernel - independent fast direct solver based on skeleton decomposition. Among them, the dominant basis functions (i.e., skeletons) are selected through interpolation decomposition to represent the interactions between the original complete set of basis functions. However, for the method of simply using skeletons, a corresponding radiation and reception matrix needs to be constructed for each layer and each group, and the direct solver is a one - way traversal method from the bottom layer to the top layer. The skeletons are combined and regrouped into higher levels to form a complete set of basis functions for the parent group. The skeleton basis functions at each layer are selected from the basis functions of the bottom layer, which cannot guarantee optimal sampling. Therefore, it is urgent to study a strategy that combines skeletons and equivalent points to solve the problems of low computational efficiency and large memory requirements. Summary of the Invention

[0006] The object 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, so as to improve the computational efficiency and reduce the memory requirements.

[0007] The technical solution for achieving the object of the present invention is as follows: A method for analyzing the electromagnetic scattering characteristics of metal targets based on a hybrid nested equivalent source direct solver includes the following steps:

[0008] Step 1: Establish an equivalent surface current model to be solved for the metal target. Divide the global basis functions to be solved 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 numbers to ensure that the basis functions in the same group are in the same spatial region of the system matrix. Start the calculation from the bottom layer and initialize the group numbers. ;

[0009] Step 2: Use the hybrid nested equivalent source algorithm to characterize the far-field coupling of each part of the metal target, construct the low-rank compressed form of the far-field impedance matrix block of the th group and orthogonalize it to obtain the orthogonalized receiving matrix of the th group;

[0010] Step 3: For the orthogonalized receiving matrix of the th group:

[0011] If there is an overflow when translating from the sub-layer to the parent layer, let and return to Step 2 to execute each step in sequence;

[0012] If there is no overflow, compress and extract the column vectors of the fill-in matrix block associated with the th group, construct an elimination matrix for the far-field coupling matrix block, and perform corresponding processing according to the following conditions: If and there is an overflow when adding the matrix, let and return to Step 2 to execute each step in sequence; otherwise, multiply the elimination matrix by the admissible matrix block to achieve the compression and elimination of the admissible matrix block;

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

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

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

[0016] Step 6: If all layers have been traversed, solve the system matrix equation and enter Step 7;

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

[0018] Step 7: In the scenario of multi-directional electromagnetic wave incidence, solve for the surface current distribution of the metal target in different directions according to the inverse of the system matrix, and finally obtain the electromagnetic scattering characteristics such as the RCS of the target.

[0019] A metal target electromagnetic scattering characteristic analysis system based on a hybrid nested equivalent source direct solver, which is used to implement the metal target electromagnetic scattering characteristic analysis method based on the 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:

[0020] The first module establishes an equivalent surface current to-be-solved model of the metal target, divides the global to-be-solved basis functions corresponding to the model into multiple groups in different spatial regions according to the hierarchical structure of the octree, rearranges the system matrix according to the group numbers, ensures that the basis functions in the same group are in the same spatial region of the system matrix, starts the calculation from the bottom layer, and initializes the group numbers ;

[0021] The second module uses the hybrid nested equivalent source algorithm to characterize the far-field coupling of each part of the metal target, constructs the low-rank compressed form of the far-field impedance matrix block of the th group and orthogonalizes it to obtain the orthogonalized receiving matrix of the th group;

[0022] The third module is for the th group of orthogonalized receiving matrices:

[0023] If overflow occurs when the sub-layer is translated to the parent layer, let and return to the second module;

[0024] If no overflow occurs, compress and extract the column vectors of the fill-in matrix block associated with the th group, construct an elimination matrix for the far-field coupling matrix block, and perform corresponding processing according to the following conditions: If and matrix addition causes overflow, let and return to the second module; otherwise, compress and eliminate the admissible matrix block through the product of the elimination matrix;

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

[0026] The fifth module, if all groups in the current layer have been traversed, enters the sixth module;

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

[0028] The sixth module, if all layers have been traversed, solves the system matrix equation and enters the seventh module;

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

[0030] The seventh module, in the scenario of multi-directional electromagnetic wave incidence, solves the surface current distribution of the metal target in different directions according to 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 on the memory and executable on the processor. When the processor executes the program, it implements the electromagnetic scattering characteristic analysis method of the metal target based on the hybrid nested equivalent source direct solver.

[0032] A computer-readable storage medium stores a computer program thereon. When the program is executed by a processor, it implements the steps in the electromagnetic scattering characteristic analysis method of the metal target based on the hybrid nested equivalent source direct solver.

[0033] Compared with the prior art, the significant advantages of the present invention are:

[0034] (1) Combining two types of basis functions, the skeleton and the equivalent source, to compress the low-rank matrix, which has higher computational efficiency in analyzing the multi-incident field application scenarios of metal targets;

[0035] (2) Combining the method of the skeleton and the equivalent point, which has lower memory requirements compared with the method of simply using the 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. Description of the Drawings

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

[0038] Figure 1b It 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 for Figure 2 A schematic diagram of the system matrix after the admissible block elimination of the first group of the original matrix.

[0041] Figure 3b It is for Figure 2 A schematic diagram of the system matrix after the non-admissible block elimination of the first group of the original matrix.

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

[0043] Figure 5aYes Figure 2 The corresponding matrix factorization process diagram of the first group of admissible blocks in

[0044] Figure 5b Yes Figure 2 The corresponding matrix factorization process diagram of the first group of inadmissible blocks in

[0045] Figure 5c Yes Figure 2 The corresponding matrix factorization process diagram of the second group of admissible blocks in

[0046] Figure 5d Yes Figure 2 The corresponding matrix factorization process diagram of the second group of inadmissible blocks in

[0047] Figure 5e Yes Figure 2 The corresponding matrix factorization process diagram of the third group of admissible blocks in

[0048] Figure 5f Yes Figure 2 The corresponding matrix factorization process diagram of the third group of inadmissible blocks in

[0049] Figure 5g Yes Figure 2 The corresponding matrix factorization process diagram of the fourth group of admissible blocks in

[0050] Figure 5h Yes Figure 2 The corresponding matrix factorization process diagram of the fourth group of inadmissible blocks in

[0051] Figure 6 It is the comparison diagram of the RCS of the metal sphere and the analytical solution result.

[0052] Figure 7 Yes Figure 6 The curve graph of the change of the two - norm error between the calculated current of the metal sphere and the reference value with the algorithm accuracy under different skeleton selection accuracy conditions.

[0053] Figure 8 It is the calculation result diagram of the bistatic RCS of the aircraft model. Specific implementation method

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

[0055] Step 1: Establish a model for the equivalent surface current to be solved of the metal target, divide the global basis functions to be solved 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 numbers, ensure that the basis functions in the same group are in the same block spatial region of the system matrix, start the calculation from the bottom layer, and initialize the group numbers ;

[0056] Step 2: Use the hybrid nested equivalent source algorithm to characterize the far-field coupling of each part of the metal target, construct the low-rank compressed form of the group of far-field impedance matrix blocks and orthogonalize them to obtain the group of orthogonalized receiving matrices;

[0057] Step 3: For the group of orthogonalized receiving matrices:

[0058] If there is an overflow when the sub-layer is translated to the parent layer, then let and return to Step 2 to execute each step in sequence;

[0059] If there is no overflow, compress and extract the column vectors of the fill-in matrix blocks associated with the group, construct an elimination matrix for the far-field coupling matrix blocks, and perform corresponding processing according to the following conditions: If and there is an overflow when the matrix is augmented, then let and return to Step 2 to execute each step in sequence; otherwise, multiply the elimination matrix by the admissible matrix blocks to achieve the compression and elimination of the admissible matrix blocks;

[0060] Step 4: Calculate the Schur complement of the inadmissible matrix blocks to achieve the elimination of the inadmissible blocks, and at the same time generate the fill-in matrix blocks added to the admissible blocks;

[0061] Step 5: If all groups in the current layer have been traversed, then enter Step 6;

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

[0063] Step 6: If all layers have been traversed, then solve the system matrix equation, enter Step 7;

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

[0065] Step 7: In the scenario of multi-directional electromagnetic wave incidence, solve for the surface current distribution of the metal target in different directions according to the inverse of the system matrix, and finally obtain the electromagnetic scattering characteristics such as the RCS of the target.

[0066] As a specific example, in Step 1, an equivalent surface current to-be-solved model of the metal target is established as follows:

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

[0068] Then, the surface of the metal target is discretized by the method of surface meshing, 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 numbered by group to form a system matrix, so as to obtain the model to be solved for the equivalent surface current of the metal target.

[0069] Since direct solution requires explicit representation of the matrix, it is first necessary to rearrange the system matrix according to the group sequence number to ensure that the basis functions of the same group are in the same block area of the system matrix.

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

[0071] The electromagnetic scattering field of the metal target becomes flat as the distance increases. First, the 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 number of basis functions in each group at the lowest layer is less than that at the higher layer. Therefore, the skeletonization compression method is used at the lowest layer to select the skeleton basis functions that play a dominant role in the radiation field, and the compressed representation of the far-field low-rank matrix is realized. At non-lowest layers, the radiation field of the original basis functions is represented by uniformly distributed equivalent sources to realize the compressed representation of the far-field matrix at higher layers. The approximation process is as Figure 1a 、 Figure 1b shown.

[0073] The compressed representation forms of the far-field matrices at different layers are

[0074] (1)

[0075] where, 、 represent the far-acting field group and source group; and are the outer test surfaces of the source group and the field group respectively; and are the skeleton basis functions selected for the source group and the field group respectively at the lowest layer, and are the equivalent source point basis functions constructed for the source group and the equivalent field point basis functions constructed for the field group at higher layers respectively; 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, represents the impedance matrix from the equivalent source point outside the field group to the basis functions inside the field group, represents the pseudo-inverse matrix of the impedance matrix from the equivalent source point outside the field group to the equivalent field points inside the field group, represents the impedance matrix from the equivalent source points inside the source group to the equivalent field points inside the field group, Denotes the pseudo-inverse matrix of the impedance matrix from the equivalent source points within the source group to the test field points outside the source group, Denotes the impedance matrix from the basis functions within the source group to the test field points outside the source group, Denotes the inner equivalent surface of the source group and the field group, Denotes the skeleton basis functions at the bottom layer, Denotes the equivalent points at non-bottom layers, Denotes the current layer number, Denotes the total number of layers;

[0076] The physical meaning of this step in practical applications is that at the bottom layer, among the basis functions constructed after discretizing the metal target, the dominant skeleton basis functions for electromagnetic scattering are selected to characterize the scattering field generated by this group of the metal target, while at higher layers, equivalent scattering points uniformly distributed on a spherical shell are constructed to characterize the scattering field.

[0077] For the group, after constructing the compressed representation form of the far-field matrix, for the group, the radiation and reception matrices are orthogonalized through Singular Value Decomposition (SVD). The group reception matrix is

[0078] (2)

[0079] Wherein, is the matrix composed of the truncated left singular vectors of the group, and is the orthogonalized reception matrix; is the remaining part after singular value decomposition;

[0080] After the orthogonalization of the group is completed, the transfer matrix between the group and the group is updated to , thus ensuring the correctness of the compressed representation:

[0081] (3)

[0082] Wherein, , the superscript represents matrix transpose.

[0083] As a specific example, in step 3, the fill-in matrix block column vectors associated with the group are compressed and extracted, and an elimination matrix for the far-field coupling matrix block is constructed as follows:

[0084] When extracting the column vectors of the fill-in matrix blocks associated with the nd group, first calculate and sum the Gram matrices of the fill-in matrix blocks generated by the association with the th group on the admissible blocks, and then perform SVD decomposition on the sum of the matrices to extract the column vectors:

[0085] (4)

[0086] where is the matrix complementary to obtained during the orthogonalization process of the SVD decomposition of , and together form a unitary matrix, is the local serial number of the admissible block of the fill-in block associated with the th group, is the global serial number of the admissible block of the fill-in block associated with the th group, is the fill-in matrix block added to the admissible block , is the number of admissible blocks of the fill-in block associated with the th group; is all the column vectors of the fill-in matrix blocks associated with the th group extracted, represents the diagonal matrix generated by the SVD decomposition, and the superscript represents the conjugate transpose of the matrix;

[0087] Supplement the extracted column vectors into the orthogonalization receiving matrix of the th group. The updated receiving matrix can represent both the original admissible blocks and the subsequently added fill-in matrix blocks:

[0088] (5)

[0089] where is the updated receiving matrix of the th group; By changing the truncation threshold of the SVD decomposition, the error control of the system matrix inversion algorithm is realized; Combine the column vectors orthogonal to to construct the cancellation matrix for the far-field coupling matrix block:

[0090] (6)

[0091] where is the updated receiving matrix of the The complementary matrix of

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

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

[0094] During the matrix decomposition process, after the elimination of the admissible matrix block, the remaining uneliminated matrix is the inadmissible matrix block; by using the part of the self-coupling matrix to be decomposed in each group, for the elimination of the inadmissible matrix block, the Schur complements of the inadmissible matrix block at different positions in the entire system matrix are calculated to achieve the further decomposition of the system matrix, which is realized through the following matrix equation:

[0095] (7)

[0096] where

[0097] (8)

[0098] In the formula is the part of the self-coupling matrix to be decomposed, , , , , , , , are the matrix blocks located at the right, bottom, bottom-right, top-left, top, top-right, left, and bottom-left positions respectively; is the identity matrix, and are the elimination matrices for the inadmissible block, and are the upper and lower triangular matrices after the matrix is decomposed, , are respectively , inverse matrices;

[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] In equations (9) to (12), the second term on the right side 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 respectively, so that

[0108] (14)

[0109] Realize the elimination of the inadmissible matrix block. After this step, the system matrix after the first group of eliminations is as Figure 3b shown.

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

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

[0112] (15)

[0113] where is the transfer matrix between the updated th group and the th group in equation (3), is the updated radiation matrix of the th group, is the final transfer matrix between the th group and the th group after elimination of each layer, is the fill-in matrix block added to the admissible block ; The dimensional expansion is to keep consistent with the dimension of the augmented receiving matrix, so that

[0114] (16)

[0115] Among them 。

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

[0117] The final system matrix is decomposed into a form of a series of matrix products, and the inverse of the matrix can also be expressed as a series of matrix products, so as to solve the system matrix equation:

[0118] (17)

[0119] Among them is the number of groups in the th layer, , , 、 is the product of the elimination matrices for admissible and inadmissible blocks in the th layer and the th group, and are the elimination matrices for inadmissible blocks in the th layer and the th group, is the elimination matrix for admissible blocks in the th layer and the th group of the system; is the permutation matrix of the entire system matrix after the decomposition of the th layer, and the purpose is to aggregate all the remaining matrix blocks together for the decomposition of the next layer; is the inverse of the system matrix, is the inverse of the diagonal matrix block remaining in the highest layer after the last decomposition;

[0120] In the scenario of multi-directional electromagnetic wave incidence, the surface current distribution of the metal target in different directions is solved according to the inverse of the system matrix, and finally the electromagnetic scattering characteristics such as the RCS of the target are obtained. Taking the Figure 2 given system matrix as an example, after all the eliminations of the current layer, the system matrix is as shown in Figure 4 , and the complete elimination process of the current layer of the matrix is as shown in Figure 5a to Figure 5h .

[0121] The present invention also provides an electromagnetic scattering characteristic analysis system of a metal target based on a hybrid nested equivalent source direct solver, which is used to implement the electromagnetic scattering characteristic analysis method of the metal target based on the 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] The first module is to establish an equivalent surface current model to be solved for a metal target, divide the global basis functions to be solved 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 numbers, ensure that the basis functions in the same group are in the same spatial region of the system matrix, and start the calculation from the bottom layer and initialize the group numbers ;

[0123] The second module is to use the hybrid nested equivalent source algorithm to characterize the far-field coupling of each part of the metal target, construct the low-rank compression form of the far-field impedance matrix block of the th group and orthogonalize it to obtain the orthogonalized receiving matrix of the th group;

[0124] The third module is for the orthogonalized receiving matrix of the th group:

[0125] If there is an overflow when the sub-layer is translated to the parent layer, then let and return to the second module;

[0126] If there is no overflow, compress and extract the column vectors of the fill-in matrix block associated with the th group, construct an elimination matrix for the far-field coupling matrix block, and perform corresponding processing according to the following conditions: If and there is an overflow when the matrix is augmented, then let and return to the second module; otherwise, perform compression elimination on the admissible matrix block through the product of the elimination matrix;

[0127] The fourth module is to calculate the Schur complement of the inadmissible matrix block, achieve the elimination of the inadmissible block, and at the same time generate the fill-in matrix block added to the admissible block;

[0128] The fifth module, if all groups in the current layer have been traversed, then enter the sixth module;

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

[0130] The sixth module, if all layers have been traversed, then solve the system matrix equation and enter the seventh module;

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

[0132] The seventh module, in the scenario of multi-directional electromagnetic wave incidence, solve for the surface current distribution of the metal target in different directions according to the inverse of the system matrix, and finally obtain 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 on the memory and executable on the processor. When the processor executes the program, the electromagnetic scattering characteristic analysis method of a metal target based on a hybrid nested equivalent source direct solver as described above is implemented.

[0134] The present invention also provides a computer-readable storage medium, on which a computer program is stored. When the program is executed by a processor, the steps in the electromagnetic scattering characteristic analysis method of a metal target based on a hybrid nested equivalent source direct solver are implemented.

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

[0136] Embodiment

[0137] In this embodiment, according to the direct solution algorithm of the present invention, the bistatic RCS result of a metal spherical shell with a radius of 1.8 m is calculated and compared with the analytical solution, as Figure 6 shown.

[0138] Furthermore, in order to illustrate the characteristic that the algorithm error is controllable, the variation curve of the two-norm error between the calculated current of the metal sphere and the reference value with the algorithm accuracy under different skeleton selection accuracies is given, as Figure 7 shown.

[0139] The two-norm error of the current is defined as

[0140] (18)

[0141] where and are the current coefficients calculated by the algorithm and the reference current coefficients respectively. The current coefficients obtained by LU decomposition and inversion are applicable to this example.

[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 800 MHz, and the size of the aircraft is approximately , is the electromagnetic wave wavelength. The calculation results are compared when the algorithm accuracies set in step 4 are set to and respectively, and compared with the pure MoM calculation results, as Figure 8 shown.

[0143] In summary, the present invention eliminates the admissible matrix blocks and inadmissible matrix blocks respectively to achieve the decomposition and inversion of the system matrix. Moreover, the error of the inversion algorithm is controllable. From the above simulation of calculation examples and result analysis, the current solution error gradually decreases with the improvement of the algorithm accuracy. Under the condition that the algorithm accuracy is set to , and the skeleton extraction accuracy is , the two-norm error between the solved current and the reference value can be controlled within or less, verifying the correctness of the algorithm.

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 the 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 various parts of the metal target and construct the The low-rank compressed form of the far-field impedance matrix block is obtained by orthogonalizing it. The orthogonalized receiving matrix of the group; Step 3: Group orthogonalized receiving matrix: If the child layer overflows when it is translated to the parent layer, then 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: If the matrix addition produces overflow, 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 according to the inverse of the system matrix, and finally the electromagnetic scattering characteristics such as RCS 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 is characterized in that: In step 1, the equivalent surface current model of the metal target is established as follows: Firstly, the metal target to be analyzed is modeled to obtain the 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 form a system matrix according to the group number, 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 is characterized in that: The step 2 is specifically 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 uniformly distributed equivalent source is used to represent the radiation field of the original basis function to achieve the compressed representation of the high-level far-field matrix; The compressed representation of the far-field matrix at 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 At the lowest level, they are the skeleton basis functions selected for the source group and the field group, and at the higher level, they 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, The impedance matrix representing 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 in 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 the field group, represents the skeleton basis function at the bottom layer, Indicates the equivalent point at the 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 orthogonalized receiving matrix; 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.

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: 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 elimination matrix for the far-field coupling matrix block, as follows: Extraction and When filling-in matrix block column vectors associated with a group, first calculate the Group association generates the Gram matrices of the fill-in matrix blocks on the admissible blocks and adds them together, then performs SVD decomposition on the sum of the matrices to extract the column vectors: (4) in For The obtained value in the process of SVD decomposition orthogonalization is The 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 block 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 a matrix; Append the extracted column vector to the The updated receiving matrix can represent both the original admissible blocks and the fill-in matrix blocks 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 elimination matrix for the far-field coupling matrix block : (6) in, For the Group updated receiving matrix The complement matrix of .

5. The method for analyzing electromagnetic scattering characteristics of metal targets based on a hybrid nested equivalent source direct solver according to claim 4 is characterized in that: The step 4 is specifically as follows: In the matrix decomposition process, after the elimination of the admissible matrix blocks, the remaining uneliminated matrices are inadmissible matrix blocks; using the to-be-decomposed part of each group of self-coupling matrices, for the elimination of the inadmissible matrix blocks, the Schur complement of the inadmissible matrix blocks at different positions of 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, , , , , , , , They are 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 For the 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 in 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.

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: 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 .

7. The method for analyzing electromagnetic scattering characteristics of metal targets based on a hybrid nested equivalent source direct solver according to claim 6, 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 at the last 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 according to the inverse of the system matrix, and finally the electromagnetic scattering characteristics such as RCS of the target are obtained.

8. 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 feature analysis method based on a hybrid nested equivalent source direct solver as described in any one of claims 1 to 7. The system includes a first module to a 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 orthogonalizing it. The orthogonalized receiving matrix of the group; The third module is for Group orthogonalized receiving matrix: If the child layer overflows when it is translated to the parent layer, then 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: If the matrix addition produces overflow, 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, eliminates 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; In the seventh module, 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.

9. A mobile terminal comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: 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 7 is implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps in 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 7.

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