Method for solving electromagnetic scattering based on Krylov subspace basis function of adaptive partitioning

Abstract

The invention relates to the field of electromagnetic numerical calculation, and discloses a method for solving electromagnetic scattering based on a Krylov subspace basis function of adaptive partitioning, and the method comprises the steps: 1, carrying out the adaptive region decomposition of a target region, and obtaining a target subdomain; 2, expanding the target sub-domain to form an expanded sub-domain; and step 3, solving and calculating electromagnetic scattering by using the optimized extended sub-domain. The method has the main advantages that the efficiency of constructing the Krylov subspace primary function by adopting the adaptive partitioning technology is higher, the generation time of the Krylov subspace primary function based on partitioning is remarkably shortened, the partitioning extension of the subdomain is optimized, the time for solving calculation is shortened, region decomposition is carried out on the calculation target by adopting the clustering algorithm, and the calculation efficiency is improved. And each sub-domain is expanded by adopting the average distance from a clustering data point to a clustering center to ensure the continuity of the current, so that the calculation precision is ensured, the construction efficiency of the primary function is improved, and the generation time of the primary function based on the block Krylov subspace is remarkably shortened.

Description

Technical Field

[0001] The invention relates to the technical field of electromagnetic numerical calculation, in particular to a method for solving electromagnetic scattering based on adaptive block-based Krylov subspace basis functions. Background Art

[0002] The method of moments (MoM) is a powerful technique for solving electromagnetic field scattering and radiation problems. In recent years, the combination of compressed sensing (CS) and MoM (CS-MoM) has greatly reduced the computational complexity of solving electromagnetic scattering problems.

[0003] The main principle of the CS-MoM method is to use the partial impedance matrix equations in MoM to construct an underdetermined system that satisfies the CS structure. For the sparse basis construction in CS-MoM, there are mainly characteristic basis functions (CBFs), characteristic mode functions (CMs) and Krylov subspace basis functions (KSBFs). However, due to the high computational complexity of the sparse basis construction, it is difficult to use KSBFs to solve the scattering problem of relatively large objects.

[0004] Therefore, a method for constructing a sparse basis based on block-based KSBFs is proposed in the prior art to accelerate the generation of sparse basis, which is mainly to divide the target into blocks and generate subdomains by placing multiple cubes in a grid shape in the analytical space.

[0005] However, for irregular computational targets, this may result in different sizes of subdomains, and in overly large and underly-sized subdomains, different numbers of unknowns may reduce the accuracy and efficiency of the computation. In addition, this method is a non-adaptive regional decomposition method that requires human intervention, so speeding up the solution of electromagnetic problems is how to adaptively decompose the computational target. Summary of the invention

[0006] The object of the present invention is to provide a method for solving electromagnetic scattering based on Krylov subspace basis functions of adaptive blocks, so as to solve the problems in the prior art.

[0007] The purpose of the present invention can be achieved through the following technical solutions:

[0008] A method for solving electromagnetic scattering based on adaptive block-based Krylov subspace basis functions, the method comprising the following steps:

[0009] Step 1: Adaptively decompose the target area to obtain the target subdomain;

[0010] Step 2: Expand the target subdomain to form an extended subdomain;

[0011] Step 3: Use the optimized extended subdomain to solve the electromagnetic scattering calculation.

[0012] Furthermore, in step 1, the target is clustered and decomposed into p sub-domains, as follows:

[0013]

[0014] In the above formula, p is the number of subdomains, X i is represented by the i-th object, S is the number of objects, μ i Represented as the i-th cluster center.

[0015] Furthermore, the specific operation of decomposing the target area in step 1 is as follows:

[0016] Use k-means clustering algorithm to cluster the given N (X1, X2, ..., X N ) unknown numbers are divided into p subdomains, and p≤N is satisfied; first, the midpoints of the common edges of the triangle pairs are used as clustering data points to form a data set, and the initial cluster centers are set. The number of cluster centers is the same as p, and the positions of the centers are continuously updated through iteration until the regional decomposition is completed.

[0017] Furthermore, the step 2 expands the sub-domain of the target. In order to ensure the continuity of the target edge current, each sub-domain needs to be expanded and optimized.

[0018] Furthermore, the extended optimization operation is as follows: calculate the distance from all data points in each subdomain to each cluster center, and then find the average distance L from the data points in each subdomain to the cluster center mean , and finally expand an extended subdomain that is larger than the subdomain according to the multiple of the average distance.

[0019] Furthermore, data points of other sub-domains within the extended sub-domain are assigned to the extended sub-domain to reduce interference caused by edge current discontinuity.

[0020] Furthermore, the extended subdomain is 1-2 times the average distance from the data points in each subdomain to the cluster center.

[0021] Furthermore, the size of the extended subdomain is 1.35L mean .

[0022] Beneficial effects of the present invention:

[0023] 1. The method for solving electromagnetic scattering based on the Krylov subspace basis function of the present invention has the main advantages of using the adaptive block technology to construct the Krylov subspace basis function with higher efficiency, significantly reducing the generation time of the Krylov subspace basis function based on the block, optimizing the block expansion of the subdomain, and improving the solution calculation time;

[0024] 2. The method for solving electromagnetic scattering based on adaptive block Krylov subspace basis function of the present invention adopts clustering algorithm to perform regional decomposition of the calculation target, and uses the average distance from cluster data points to the cluster center to expand each subdomain to ensure the continuity of the current, which not only ensures the calculation accuracy, but also improves the construction efficiency of the basis function, and significantly reduces the generation time based on the block Krylov subspace basis function. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The present invention will be further described below in conjunction with the accompanying drawings.

[0026] Figure 1 It is a basic flow chart of the method for solving electromagnetic scattering of the present invention;

[0027] Figure 2 It is a schematic diagram of subdomain expansion of the method of the present invention;

[0028] Figure 3 It is a schematic diagram of the calculation result of the method of the present invention;

[0029] Figure 4 It is a comparison chart of the calculation results of the method of the present invention and other methods on subdomain expansion. DETAILED DESCRIPTION

[0030] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0031] A method for solving electromagnetic scattering based on adaptive block Krylov subspace basis function, such as Figure 1-4 As shown, the method comprises the following steps:

[0032] Step 1:

[0033] The target is clustered and decomposed into p subdomains as follows:

[0034]

[0035] In the above formula, p is the number of subdomains, X i is represented by the i-th object, S is the number of objects, μ i Represented as the i-th cluster center.

[0036] The specific operations are as follows:

[0037] Use k-means clustering algorithm to cluster the given N (X1, X2, ..., X N ) unknown numbers are divided into p subdomains, and p≤N is satisfied; first, the midpoints of the common edges of the triangle pairs are used as clustering data points to form a data set, and the initial cluster centers are set, where the number of cluster centers is the same as p. The positions of the centers are continuously updated through iteration until the regional decomposition is completed. During the regional decomposition process, continuous iterative optimization is performed to obtain the cluster center distance from each object to its subdomain, and the subdomain partitioning is completed adaptively, thereby achieving the purpose of clustering.

[0038] Step 2:

[0039] The subdomains of the target are expanded. In order to ensure the continuity of the target edge current, each subdomain needs to be expanded and optimized.

[0040] Depend on Figure 2 As shown in Figure 2, the principle of the expansion is to calculate the distance from all data points in each subdomain to each cluster center, and then find the average distance L from the data points in each subdomain to the cluster center. mean ,Finally, an extended subdomain larger than the subdomain is expanded according to the multiple of the average distance, and the data points of other subdomains in the extended subdomain are assigned to the extended subdomain to reduce the ,interference caused by the edge current discontinuity.

[0041] The multiple of the average distance is 1-2 times. In this embodiment, 1.35L is usually selected. mean .

[0042] Step 3:

[0043] The above-mentioned extended and optimized subdomain is used to perform subsequent electromagnetic scattering solution calculations.

[0044] In this embodiment, the dual-station radar cross section (RCS) of a missile model with a length of 1 m is calculated as an example:

[0045] The incident excitation is a plane wave with a frequency of 3.8 GHz. The RWG function is used to discretize the electric field integral equation, which generates a total of 100,497 unknowns. The target is divided into 42 small blocks.

[0046] Then, the method of the present invention is compared with the traditional regional decomposition method, and the comparison process and results are as follows:

[0047] The Krylov subspace basis function is used as the sparse basis, and the method of moments based on compressed sensing (CS-Krylov-block) and the traditional method of moments (MoM) are used to solve the problem.

[0048] In the method of the present invention, the Krylov subspace basis function on each block is calculated up to the 150th order, and the number of rows extracted is M=0.3N.

[0049] Depend on Figure 3 It can be seen that the results of the method of the present invention are highly similar to those of the traditional MoM, and the calculation results of the method of the present invention are well consistent with the traditional MoM, and have higher calculation accuracy;

[0050] The time for constructing the basis function in the method of the present invention is 112.4 seconds, while the time for constructing the basis function in the CS-Krylov-block is 378.8 seconds. The method of the present invention reduces the time for constructing the basis function by 70.3% compared with the CS-Krylov-block, improves the speed of constructing the basis function and related operations, and improves the speed of solving and calculating electromagnetic scattering.

[0051] In addition, the total calculation time of the method of the present invention and CS-Krylov-block is 1347.6s and 1639.6s respectively, and the total time of solving electromagnetic scattering by the present invention is reduced by 17.8% compared with the total calculation time of CS-Krylov-block. This example verifies that the present invention has higher calculation efficiency.

[0052] Experimental simulations have shown that the calculation accuracy and speed of expanding according to the average distance from the data point to the cluster center are higher than those of expanding according to the maximum distance from the data point to the cluster center, which is helpful for solving electromagnetic scattering using Krylov subspace basis functions.

[0053] In summary, the present invention adopts a clustering algorithm to perform regional decomposition of the calculation target, and uses the average distance from the cluster data point to the cluster center to expand each subdomain to ensure the continuity of the current, which not only ensures the calculation accuracy, but also improves the construction efficiency of the basis function, and significantly reduces the generation time of the block Krylov subspace basis function.

[0054] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, and these changes and improvements all fall within the scope of the present invention to be protected.

Claims

1. A method for solving electromagnetic scattering based on adaptive block-based Krylov subspace basis functions, characterized in that: The method comprises the following steps: Step 1: Adaptively decompose the target area to obtain the target subdomain; Step 2: Expand the target subdomain to form an extended subdomain; Step 3: Use the optimized extended subdomain to solve the electromagnetic scattering calculation.

2. The method for solving electromagnetic scattering based on adaptive block-based Krylov subspace basis function according to claim 1, characterized in that: The first step performs clustering region decomposition on the target and divides it into p sub-domains as follows: In the above formula, p is the number of subdomains, X i is represented by the i-th object, S is the number of objects, μ i Represented as the i-th cluster center.

3. The method for solving electromagnetic scattering based on adaptive block-based Krylov subspace basis function according to claim 1, characterized in that: The specific operation of step 1 to decompose the target area is as follows: Use k-means clustering algorithm to cluster the given N (X1, X2, ..., X N ) unknown numbers are divided into p subdomains, and p≤N is satisfied; first, the midpoints of the common edges of the triangle pairs are used as clustering data points to form a data set, and the initial cluster centers are set. The number of cluster centers is the same as p, and the positions of the centers are continuously updated through iteration until the regional decomposition is completed.

4. The method for solving electromagnetic scattering based on adaptive block-based Krylov subspace basis function according to claim 1, characterized in that: The step 2 expands the sub-domain of the target. In order to ensure the continuity of the target edge current, each sub-domain needs to be expanded and optimized.

5. The method for solving electromagnetic scattering based on adaptive block-based Krylov subspace basis function according to claim 1, characterized in that: The extended optimization operation is as follows: calculate the distance from all data points in each subdomain to each cluster center, and then find the average distance L from the data points in each subdomain to the cluster center. mean , and finally expand an extended subdomain that is larger than the subdomain according to the multiple of the average distance.

6. The method for solving electromagnetic scattering based on adaptive block-based Krylov subspace basis function according to claim 5, characterized in that: Data points of other sub-domains within the extended sub-domain are assigned to the extended sub-domain to reduce interference caused by edge current discontinuity.

7. The method for solving electromagnetic scattering based on adaptive block-based Krylov subspace basis function according to claim 5, characterized in that: The extended subdomain is 1-2 times the average distance from the data points in each subdomain to the cluster center.

8. The method for solving electromagnetic scattering based on adaptive block-based Krylov subspace basis function according to claim 5, characterized in that: The extended subdomain size is 1.35L mean .

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