A method for solving electromagnetic scattering based on adaptive block-based Krylov subspace basis function

Abstract

The present application relates to the field of electromagnetic numerical calculation, and discloses a kind of method for solving electromagnetic scattering based on adaptive block Krylov subspace base function, method includes the following steps: step one: target region is carried out adaptive region decomposition, and target subdomain is obtained;Step two: target subdomain is expanded, and extended subdomain is formed;Step three: using optimized extended subdomain, the solving calculation of electromagnetic scattering is carried out.The main advantage of the present application is that the efficiency of constructing Krylov subspace base function is higher by using adaptive block technology, which significantly reduces the generation time of Krylov subspace base function based on block, optimizes the block expansion of subdomain, improves the solving calculation time, uses clustering algorithm to carry out region decomposition on the calculation target, and uses the average distance of clustering data points to cluster center to expand each subdomain to ensure the continuity of current, which not only ensures the calculation accuracy, but also improves the construction efficiency of base function, significantly reduces the generation time of Krylov subspace base function based on block.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic numerical calculation technology, specifically a method for solving electromagnetic scattering based on adaptive block Krylov subspace basis functions. Background Technology

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

[0004] Therefore, existing technologies have proposed a block-based KSBFs method for constructing sparse bases to accelerate the generation of sparse bases. This method primarily involves dividing the target into blocks by placing multiple cubes in a grid shape within the analytical space, and then generating subdomains.

[0005] However, for irregular computational objectives, this can lead to subdomains of varying sizes. In subdomains that are too large or too small, different numbers of unknowns can reduce computational accuracy and efficiency. Furthermore, this method is a non-adaptive domain decomposition method that requires human intervention; therefore, accelerating the solution of electromagnetic problems hinges on how to adaptively decompose the computational objective into a domain. Summary of the Invention

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

[0007] The objective of this invention can be achieved through the following technical solutions:

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

[0009] Step 1: Perform adaptive region decomposition on the target region to obtain the target subdomain;

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

[0011] Step 3: Calculate the electromagnetic scattering using the optimized extended subdomain.

[0012] Furthermore, step one performs clustering region decomposition on the target, dividing it into p subdomains, as follows:

[0013]

[0014] In the above formula, p is the number of subdomains, and X i Let μ be the i-th object, S be the number of objects, and μ be the number of objects. i Let i be the i-th cluster center.

[0015] Furthermore, the specific operations for decomposing the target region in step one are as follows:

[0016] The k-means clustering algorithm is used to cluster the given N(X1, X2, ..., X...) clusters. N Given ) unknowns, divide them into p subdomains, satisfying p≤N; first, use the midpoints of the common edges of the triangular pairs as cluster data points to form a dataset, set initial cluster centers, where the number of cluster centers is the same as p, and continuously update the position of the centers through iteration until the region decomposition is completed.

[0017] Furthermore, step two expands the subdomains of the target. In order to ensure the continuity of the target edge current, each subdomain 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 calculate the average distance L from the data points in each subdomain to the cluster center. mean Finally, an extended subdomain larger than the original subdomain is created by multiplying the average distance by a factor of 1.

[0019] Furthermore, data points from other subdomains within the extended subdomain are assigned to this extended subdomain to reduce interference caused by edge current discontinuities.

[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] The beneficial effects of this invention are:

[0023] 1. The present invention provides a method for solving electromagnetic scattering based on adaptive block Krylov subspace basis functions. The main advantages are that the adaptive block technique is more efficient in constructing Krylov subspace basis functions, significantly reduces the generation time of block-based Krylov subspace basis functions, optimizes the block expansion of subdomains, and improves the solution calculation time.

[0024] 2. The present invention provides a method for solving electromagnetic scattering based on adaptive block-based Krylov subspace basis functions. It employs a clustering algorithm to decompose the computational target into regions and uses the average distance from the cluster data points to the cluster center to expand each subdomain to ensure the continuity of the current. This not only ensures the computational accuracy but also improves the construction efficiency of the basis functions, significantly reducing the generation time of block-based Krylov subspace basis functions. Attached Figure Description

[0025] The invention will now be further described with reference to the accompanying drawings.

[0026] Figure 1 This is a basic flowchart of the electromagnetic scattering solution method of this invention;

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

[0028] Figure 3 This is a schematic diagram illustrating the calculation results of the method of the present invention;

[0029] Figure 4 This is a comparison chart of computational results between the method of this invention and other methods in subdomain expansion. Detailed Implementation

[0030] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

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

[0032] Step 1:

[0033] The target is decomposed into p subdomains using clustering, as follows:

[0034]

[0035] In the above formula, p is the number of subdomains, and X i Let μ be the i-th object, S be the number of objects, and μ be the number of objects. i Let i be the i-th cluster center.

[0036] The specific steps are as follows:

[0037] The k-means clustering algorithm is used to cluster the given N(X1, X2, ..., X...) clusters. N Given 10 unknowns, divide them into p subdomains, where p ≤ N. First, use the midpoints of the common edges of the triangular pairs as clustering data points to form a dataset. Set initial cluster centers, where the number of cluster centers is the same as p. Iterate and update the positions of the centers until the region decomposition is completed. During the region decomposition process, iterate and optimize continuously to obtain the distance from each object to the cluster center of its subdomain. Adaptively complete the subdomain partitioning to achieve the purpose of clustering.

[0038] Step Two:

[0039] To ensure the continuity of the target edge current, the subdomains of the target need to be expanded. Each subdomain needs to be expanded and optimized.

[0040] Depend on Figure 2 As shown, the principle of the extension is as follows: calculate the distance from all data points in each subdomain to each cluster center, and then calculate the average distance L from the data points in each subdomain to the cluster center. mean Finally, an extended subdomain larger than the original subdomain is created by multiplying the average distance, and data points from other subdomains within the extended subdomain are assigned to this extended subdomain to reduce interference caused by edge current discontinuities.

[0041] The average distance is calculated as a multiple of 1 to 2; in this embodiment, 1.35L is typically chosen. mean .

[0042] Step 3:

[0043] The extended and optimized subdomains described above are used to perform subsequent calculations for electromagnetic scattering.

[0044] In this embodiment, we will first calculate the bistatic radar cross section (RCS) of a missile model with a length of 1m as an example:

[0045] The incident excitation was a plane wave with a frequency of 3.8 GHz. The electric field integral equation was discretized using the RWG function, which generated a total of 100,497 unknowns. The target was divided into 42 small blocks.

[0046] The method of this invention was then compared with the traditional domain decomposition method. The comparison process and results are as follows:

[0047] Krylov subspace basis functions are used as sparse basis functions, and the solution is obtained using the method of moments based on compressed sensing (CS-Krylov-block) and the traditional method of moments (MoM).

[0048] In the method of this invention, the Krylov subspace basis functions on each block are calculated up to order 150, 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 in good agreement with the traditional MoM, and have high calculation accuracy.

[0050] The method of this invention takes 112.4 s to construct the basis functions, while the method of CS-Krylov-block takes 378.8 s. The method of this invention reduces the time for basis function construction by 70.3% compared with CS-Krylov-block, thereby improving the speed of constructing basis functions and related operations, and improving the speed of solving electromagnetic scattering problems.

[0051] Furthermore, the total computation time of the method of this invention and CS-Krylov-block is 1347.6s and 1639.6s, respectively. The total computation time of the method of this invention for solving electromagnetic scattering is reduced by 17.8% compared with that of CS-Krylov-block. This example verifies that the method of this invention has higher computational efficiency.

[0052] Experimental simulations have shown that expanding the data points according to the average distance from the cluster centers is more accurate and faster than expanding according to the maximum distance from the cluster centers, which is helpful for solving electromagnetic scattering using Krylov subspace basis functions.

[0053] In summary, this invention employs a clustering algorithm to decompose the computational target into regions, and uses the average distance from cluster data points to cluster centers to expand each subdomain to ensure the continuity of the current. This not only guarantees computational accuracy but also improves the efficiency of basis function construction, significantly reducing the generation time of block-based Krylov subspace basis functions.

[0054] The foregoing has shown and described 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. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention.

Claims

1. A method for solving electromagnetic scattering based on adaptive block Krylov subspace basis functions, characterized in that, The method includes the following steps: Step 1: Perform adaptive region decomposition on the target region to obtain the target subdomain; Step 2: Expand the target subdomain to form an extended subdomain; Step 3: Calculate the electromagnetic scattering using the optimized extended subdomain; The specific operations for decomposing the target region in step one are as follows: The k-means clustering algorithm is used to cluster the given N(X1, X2, ..., X...) clusters. N Given ) unknowns, divide them into p subdomains, satisfying p≤N; first, use the midpoints of the common edges of the triangular pairs as cluster data points to form a dataset, set initial cluster centers, where the number of cluster centers is the same as p, and continuously update the position of the centers through iteration until the region decomposition is completed; To ensure the continuity of the target edge current, each subdomain needs to be expanded and optimized. The extended optimization operation is as follows: calculate the distance from all data points in each subdomain to each cluster center, and then calculate the average distance L from the data points in each subdomain to the cluster center. mean Finally, an extended subdomain larger than the original subdomain is created by multiplying the average distance by a factor of 1. Data points from other subdomains within the extended subdomain are assigned to this extended subdomain to reduce interference caused by edge current discontinuities.

2. The method for solving electromagnetic scattering based on adaptive block Krylov subspace basis functions according to claim 1, characterized in that, The first step involves clustering the target into p subdomains, as follows: In the above formula, p is the number of subdomains, and X i Let represent the i-th object, and S represent the number of objects. Let i be the i-th cluster center.

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

4. The method for solving electromagnetic scattering based on adaptive block Krylov subspace basis functions according to claim 1, characterized in that, The size of the extended subdomain is 1.35L. mean .

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