Method for rapidly and directly solving metal medium composite target based on block sparse row matrix

Abstract

The invention discloses a rapid and direct solving method for a metal medium composite target based on a block sparse row matrix. The method comprises the following steps: approximately representing a low-rank non-diagonal block matrix as multiplication of two decomposition matrixes U and V by adopting a self-adaptive crossover algorithm; cascading the decomposition matrix of each sub-block to obtain an integral decomposition matrix; carrying out compression storage on the decomposition matrixes U and V by adopting a block sparse row matrix, and removing zero blocks generated by matrix cascading; performing inversion on the block diagonal matrix of the finest layer through a conjugate gradient method, and solving an inverse matrix of the block diagonal matrix of the non-finest layer according to an SMW formula; and finally, obtaining a current solving target RCS through vector multiplication of an inverse matrix of a series of block diagonal matrixes and a matrix of a right vector. According to the method, the electromagnetic scattering characteristics of the complex target are solved, and the calculation efficiency of analyzing the electromagnetic single-station scattering characteristics of the complex target can be improved.

Description

Technical Field

[0001] The invention belongs to the technical field of numerical calculation of electromagnetic characteristics of complex targets, and in particular relates to a fast and direct solution method for metal dielectric composite targets based on block sparse row matrices. Background Art

[0002] With the rapid development of science and technology, dielectric materials have been widely used in the field of electromagnetic engineering, such as antenna cover structures, stealth materials coated on aircraft, etc. Therefore, electromagnetic modeling and analysis of complex targets containing dielectric materials has important engineering application value and academic research significance.

[0003] Traditional iterative methods have problems such as slow convergence, low precision or even no convergence when solving ill-conditioned matrices, which affects the accuracy of the solution. In addition, in actual application scenarios, the single-station electromagnetic scattering characteristics of the target are often analyzed, that is, the right-hand side term problem. The iterative solution method must restart the iteration for each right-hand side excitation vector, which seriously affects the calculation efficiency. Summary of the invention

[0004] The purpose of the present invention is to provide a fast and direct solution method for metal medium composite targets based on block sparse row matrix, so as to realize electromagnetic scattering characteristic analysis of complex targets.

[0005] The technical solution to achieve the purpose of the present invention is as follows: In the first aspect, the present invention provides a method for quickly and directly solving a metal-medium composite target based on a block sparse row matrix, the steps of which are as follows:

[0006] Step 1: The low-rank non-diagonal block matrix is ​​approximately expressed as the multiplication of two decomposition matrices U and V using an adaptive crossover algorithm; the decomposition matrix of each sub-block is cascaded to obtain the overall decomposition matrix;

[0007] Step 2: Use block sparse row matrix to compress and store the decomposed matrices U and V, and remove zero blocks generated by matrix cascading;

[0008] Step 3: Invert the block diagonal matrix of the finest layer by the conjugate gradient method, and solve the inverse matrix of the block diagonal matrix of the non-finest layer according to the SMW formula; finally, the current is obtained by matrix-vector multiplication of a series of inverse matrices of block diagonal matrices with the vector on the right side to solve RCS.

[0009] In a second aspect, the present invention provides a computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the method described in the first aspect when executing the program.

[0010] In a third aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in the first aspect.

[0011] In a fourth aspect, the present invention provides a computer program product, comprising a computer program, which implements the steps of the method described in the first aspect when executed by a processor.

[0012] Compared with the prior art, the present invention has the following significant advantages: (1) When calculating the target RCS, the present invention requires less storage memory than the traditional storage method, which greatly improves the calculation efficiency; (2) Compared with the traditional iterative method, the present invention adopts a direct solution method, which only needs to calculate the required right-hand side terms once and has no special requirements on the matrix properties. It can process more diverse models and saves calculation time. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 It is a schematic diagram of binary tree grouping technology.

[0014] Figure 2 This is a schematic diagram of BSR technology.

[0015] Figure 3 It is a diagram of the metal-dielectric composite model.

[0016] Figure 4 This is a comparison chart of RCS results of the metal-medium composite model. DETAILED DESCRIPTION

[0017] The present invention proposes a method for fast and direct solution of metal dielectric composite targets based on block sparse row matrices, and the steps are as follows: an adaptive crossover algorithm is used to approximate the low-rank non-diagonal block matrix as the multiplication of two decomposition matrices U and V. The decomposition matrix of each sub-block is cascaded to obtain the overall decomposition matrix. The decomposition matrices U and V are compressed and stored using a block sparse row matrix to remove zero blocks generated by matrix cascading. The finest layer block diagonal matrix is ​​inverted by the conjugate gradient method, and the inverse matrix of the non-finest layer block diagonal matrix is ​​solved according to the SMW formula; finally, the current solution RCS is obtained by matrix-vector multiplication of a series of inverse matrices of block diagonal matrices with the right-hand vector.

[0018] The present invention is further described in detail below in conjunction with the accompanying drawings.

[0019] Step 1: The low-rank non-diagonal block matrix is ​​approximately expressed as the multiplication of two decomposition matrices U and V using an adaptive crossover algorithm. The decomposition matrix of each sub-block is cascaded to obtain the overall decomposition matrix.

[0020] Step 2: Use block sparse row matrices to compress and store the decomposed matrices U and V, and remove zero blocks generated by matrix concatenation.

[0021] Step 3: Invert the block diagonal matrix of the finest layer by the conjugate gradient method, and solve the inverse matrix of the block diagonal matrix of the non-finest layer according to the SMW formula; finally, the current is obtained by matrix-vector multiplication of a series of inverse matrices of block diagonal matrices with the vector on the right side to solve RCS.

[0022] Furthermore, in step 1, the low-rank non-diagonal block matrix is ​​approximately expressed as the multiplication of two decomposition matrices U and V using an adaptive crossover algorithm. The decomposition matrix of each sub-block is cascaded to obtain the overall decomposition matrix, as follows:

[0023] The binary tree grouping technique is used to hierarchically group the target geometry, such as Figure 1 As shown, in each layer, the parent group block of the previous layer is divided into two sub-blocks. For three-dimensional structures, the method of alternating equal division in the x, y, and z directions is adopted to make the grouping balanced in all directions. Through the binary tree grouping technology, the impedance matrix is ​​transformed into a stacked matrix:

[0024] (1)

[0025] Where Z represents the impedance matrix, the superscript represents the layer number, and the subscript represents the group number of the interaction group in the corresponding layer;

[0026] In the stacked matrix shown in equation (1), the interaction matrix between non-overlapping sub-blocks is The adaptive crossover algorithm is approximated as two small matrix multiplications, resulting in:

[0027] (2)

[0028] Where U and V are low-rank approximations of the matrix Z, i and j represent the group numbers of the two interacting groups;

[0029] Therefore, the impedance matrix Z can be sparsely represented as

[0030] (3)

[0031] Impedance matrix for metal-dielectric composite targets have

[0032] (4)

[0033] Where m represents metal material, d represents dielectric material, and the digital subscript represents the material number;

[0034] Any matrix block Can be expressed as

[0035] (5)

[0036] Where J represents the equivalent current, M represents the equivalent magnetic current, and represents the matrix element obtained by self-coupling, and represents the matrix element obtained by mutual coupling between J and M; i and j represent the material numbers;

[0037] For each matrix block , , , The items are compressed individually using the adaptive crossover algorithm, and the resulting decomposition matrices are concatenated in the following way:

[0038] (6)

[0039] (7)

[0040] In the formula, m and n represent the two interacting materials, and the numerical subscripts represent the group numbers of the two interacting groups.

[0041] Furthermore, in step 2, a block sparse row matrix is ​​used to compress and store the decomposed matrices U and V, and remove zero blocks generated by matrix concatenation, as follows:

[0042] like Figure 2 As shown in the figure, the block sparse row matrix stores the matrix in the form of sub-blocks, where Block row represents the row coordinates of the matrix sub-block and Block col represents the column coordinates of the matrix sub-block. The Blcok_row_ptr array represents the offset of each row of the matrix sub-block, the values ​​array represents the value of each non-zero sub-block, and the columns array represents the column coordinates of the matrix sub-block. Since the matrix sub-blocks generated by block compression are of different sizes, the improved block sparse row matrix is ​​used for storage. On the basis of establishing the row index and column index, a new array is created to store the row dimension and column dimension of each matrix sub-block.

[0043] Furthermore, in step 3, the conjugate gradient method is used to invert the block diagonal matrix of the finest layer, and the inverse matrix of the block diagonal matrix of the non-finest layer is solved according to the SMW formula; finally, the current is solved by multiplying the inverse matrix of a series of block diagonal matrices with the matrix-vector of the right vector, as follows:

[0044] For the matrix with a stacked structure in equation (3), the diagonal matrix is ​​extracted from the coarse layer to the fine layer and converted into a unit matrix. Finally, the impedance matrix is ​​converted into the form of multiplication of multiple block diagonal matrices, as shown below:

[0045] (8)

[0046] (9)

[0047] In the formula represents a diagonal matrix, l is the number of layers, I represents the identity matrix, represents the updated U matrix;

[0048] According to the grouping situation, Continuing to decompose and generalize to multi-layer form, we can get the expression of impedance matrix:

[0049] (10)

[0050] Any expression in formula (10) Diagonal Block Matrix in Matrix It can be expressed as:

[0051] (11)

[0052] Where k represents the group number, l represents the number of layers, , Indicates the finest layer, express The dimensions of the matrix, Representation Matrix The rank of the off-diagonal block matrix after matrix compression decomposition.

[0053] According to the Sherman-Morrison-Woodbury formula, in formula (11) The inverse matrix can be expressed as:

[0054] (12)

[0055] (13)

[0056] Get the matrix The inverse of , which can then be expressed as a block diagonal matrix The inverse of . Therefore, the solution to the matrix equation can be obtained by multiplying the inverse matrices of several block diagonal matrices with the matrix-vector multiplication of the right-hand vector g, as shown in the following formula:

[0057] (14)

[0058] From this, the total current can be solved, and then the RCS of this model can be obtained based on the current.

[0059] Traditional iterative methods need to solve the right-hand side terms multiple times and have a slow convergence speed for ill-conditioned matrices. However, this method only needs to calculate the required right-hand side terms once and has no special requirements on the matrix properties. It also uses sparse row matrix storage, which saves computational memory and improves efficiency.

[0060] The beneficial effects of the present invention are described below in conjunction with the embodiments and drawings.

[0061] This example calculates electromagnetic scattering of a metal-medium composite target. This example is implemented on a computing platform with an 11th Gen Intel(R) Core(TM) i5-11320H @ 3.20GHz 3.19 GHz and 16GB of memory. The target model is as follows: Figure 3 As shown, there are three cuboids with dimensions of 0.06×0.02×0.02m. The dielectric constant of the first part is , the second part is metal, and the dielectric constant of the third part is The plane wave incident frequency is 3GHz and the direction is ,in is the pitch angle, The RCS of a single station under VV polarization is calculated using the same incident wave setting. The method of the present invention is compared with other methods. The curve fitting of RCS is shown in the figure below. Figure 4 As shown in Table 1, the three curves are well matched. The comparison of the computation time and memory of the two methods is shown in Table 1.

[0062] Table 1

[0063]

[0064] It can be seen from Table 1 that the memory required by the method of the present invention is smaller than that required by the traditional storage method; and the direct solution method of the present invention only needs to calculate the right-hand side term once, and the calculation time is much shorter than the fast multipole method, which reflects the effectiveness of the method of the present invention.

[0065] The above are only preferred embodiments of the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications should also be considered as the protection scope of the present invention. All components not specified in this embodiment can be implemented using existing technologies.

Claims

1. A fast and direct solution method for metal-medium composite targets based on block sparse row matrix, characterized in that: Here are the steps: Step 1: The low-rank non-diagonal block matrix is ​​approximately expressed as the multiplication of two decomposition matrices U and V using an adaptive crossover algorithm; the decomposition matrix of each sub-block is cascaded to obtain the overall decomposition matrix; Step 2: Use block sparse row matrix to compress and store the decomposed matrices U and V, and remove zero blocks generated by matrix cascading; Step 3: Invert the block diagonal matrix of the finest layer by the conjugate gradient method, and solve the inverse matrix of the block diagonal matrix of the non-finest layer according to the SMW formula; finally, obtain the current RCS by matrix-vector multiplication of the inverse matrix of the block diagonal matrix and the vector on the right.

2. The method for fast and direct solution of metal-medium composite targets based on block sparse row matrix according to claim 1 is characterized in that: In step 1, the low-rank non-diagonal block matrix is ​​approximately expressed as the multiplication of two decomposition matrices U and V using an adaptive crossover algorithm. The decomposition matrix of each sub-block is cascaded to obtain the overall decomposition matrix, as follows: The target geometric structure is hierarchically grouped using the binary tree grouping technique. In each layer, the parent block of the previous layer is divided into two sub-blocks. Through the binary tree grouping technique, the impedance matrix is ​​transformed into a stacked matrix: (1) Where Z represents the impedance matrix, the superscript represents the layer number, and the subscript represents the group number of the interaction group in the corresponding layer; In the stacked matrix shown in equation (1), the interaction matrix between non-overlapping sub-blocks is The adaptive crossover algorithm is approximated as two small matrix multiplications, resulting in: (2) Where U and V are low-rank approximations of the matrix Z, i and j represent the group numbers of the two interacting groups; Therefore, the impedance matrix Z is sparsely represented as (3) Impedance matrix for metal-dielectric composite targets have (4) Where m represents metal material, d represents dielectric material, and the digital subscript represents the material number; Any matrix block Expressed as (5) Where J represents the equivalent current, M represents the equivalent magnetic current, and represents the matrix element obtained by self-coupling, and represents the matrix element obtained by mutual coupling between J and M; i and j represent the material numbers; For each matrix block , , , The items are compressed individually using the adaptive crossover algorithm, and the resulting decomposition matrices are concatenated in the following way: (6) (7) In the formula, m and n represent the two interacting materials, and the numerical subscripts represent the group numbers of the two interacting groups.

3. The method for fast and direct solution of metal-medium composite targets based on block sparse row matrix according to claim 2 is characterized in that: In step 2, a block sparse row matrix is ​​used to compress and store the decomposed matrices U and V, and the zero blocks generated by matrix concatenation are removed, as follows: The block sparse row matrix stores the matrix in the form of sub-blocks and establishes the row index and column index of the matrix block; based on the establishment of the row index and column index, a new array is created to store the row dimension and column dimension of each matrix sub-block.

4. The method for fast and direct solution of metal-medium composite targets based on block sparse row matrix according to claim 2 is characterized in that: In step 3, the conjugate gradient method is used to invert the block diagonal matrix of the finest layer, and the inverse matrix of the block diagonal matrix of the non-finest layer is solved according to the SMW formula; finally, the current is solved by multiplying the inverse matrix of the block diagonal matrix with the matrix-vector of the right vector, as follows: For the matrix with a stacked structure in equation (3), the diagonal matrix is ​​extracted from the coarse layer to the fine layer and converted into a unit matrix. Finally, the impedance matrix is ​​converted into the form of multiplication of multiple block diagonal matrices, as shown below: (8) (9) In the formula represents a diagonal matrix, l is the number of layers, I represents the identity matrix, represents the updated U matrix; In formula (8), Continuing to decompose and generalize to the multi-layer form, we can get the expression of the impedance matrix: (10) Any Diagonal Block Matrix in Matrix It is expressed as: (11) Where k represents the group number, l represents the number of layers, , express The dimensions of the matrix, Representation Matrix The rank of the non-diagonal block matrix after matrix compression decomposition; According to the Sherman-Morrison-Woodbury formula, in formula (11) The inverse of is: (12) (13) Get the matrix The inverse of The inverse of ; therefore, the solution to the matrix equation is obtained by multiplying the inverse matrices of several block diagonal matrices with the matrix-vector multiplication of the right-hand vector g, as shown in the following formula: (14) The total current is thus solved, and the RCS of this model can be obtained based on the current.

5. A computer device comprising a memory, a processor and a computer program in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps of the method according to any one of claims 1 to 4 are implemented.

6. 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 described in any one of claims 1 to 4 are implemented.

7. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method described in any one of claims 1 to 4 are implemented.

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