CN-119203756-B - Method for solving electromagnetic scattering based on Krylov subspace basis function of adaptive partitioning

CN119203756BCN 119203756 BCN119203756 BCN 119203756BCN-119203756-B

Abstract

The invention relates to the field of electromagnetic numerical computation and discloses a method for solving electromagnetic scattering based on a Krylov subspace basis function of self-adaptive partitioning, which comprises the following steps of carrying out self-adaptive region decomposition on a target region to obtain a target subdomain; and step three, utilizing the optimized extended subdomain to carry out solving calculation of electromagnetic scattering. The method has the main advantages that the self-adaptive blocking technology is adopted to construct the Krylov subspace basis function, so that the generation time of the Krylov subspace basis function based on blocking is remarkably reduced, the blocking expansion of the subdomains is optimized, the solving calculation time is improved, the clustering algorithm is adopted to carry out regional decomposition on a calculation target, and the average distance from a clustering data point to a clustering center is adopted to expand each subdomain to ensure the continuity of current, so that the calculation precision is ensured, the construction efficiency of the basis function is improved, and the generation time of the Krylov subspace basis function based on blocking is remarkably reduced.

Inventors

WANG ZHONGGEN
YUAN HAORAN
NIE WENYAN
SUN YUFA
LI CHENLU
LIN HAN
WU JUAN
ZHANG XUEJUN

Assignees

安徽理工大学

Dates

Publication Date: 20260508
Application Date: 20240918

Claims (4)

1. A method for solving electromagnetic scattering based on a Krylov subspace basis function of self-adaptive partitioning is characterized in that, The method comprises the following steps: performing self-adaptive region decomposition on a target region to obtain a target subdomain; Expanding the target subdomain to form an expanded subdomain; thirdly, utilizing the optimized extended subdomain to carry out solving calculation of electromagnetic scattering; the specific operation of decomposing the target area in the step is as follows: Dividing given N (X 1 ,X 2 ,……,X N ) unknowns into p sub-domains by adopting a k-means clustering algorithm, and meeting the requirement that p is less than or equal to N; firstly, taking the middle points of the public sides of the triangular pairs as clustering data points to form a data set, and setting initialization clustering centers, wherein the number of the clustering centers is the same as p, and continuously updating the positions of the centers through iteration until the area decomposition is completed; in order to ensure the continuity of the target edge current, expansion optimization is required to be carried out on each sub-domain; Calculating the distance from all data points in each sub-field to each clustering center, then solving the average distance L mean from the data points in each sub-field to the clustering center, and finally expanding an expanded sub-field larger than the sub-field according to the multiple of the average distance; Data points of other subfields within the extended subfield are assigned to the extended subfield for reducing disturbances caused by edge current discontinuities.
2. The method for solving electromagnetic scattering according to claim 1, wherein the method comprises the steps of, The first step is to perform cluster region decomposition on the target and divide the target into p subdomains, and the method comprises the following steps: In the above formula, p is the number of subfields, X i is the i-th object, S is the number of objects, Denoted as the i-th cluster center.
3. The method for solving electromagnetic scattering according to claim 1, wherein the method comprises the steps of, The extended subdomain is 1-2 times of the average distance from the data point in each subdomain to the clustering center.
4. The method for solving electromagnetic scattering based on the Krylov subspace basis function of the adaptive partitioning according to claim 1, wherein the extended subdomain size is 1.35L mean .

Description

Method for solving electromagnetic scattering based on Krylov subspace basis function of adaptive partitioning Technical Field The invention relates to the technical field of electromagnetic numerical computation, in particular to a method for solving electromagnetic scattering based on a Krylov subspace basis function of self-adaptive partitioning. Background Moment methods (MoM) are powerful techniques to solve the problems of electromagnetic field scattering and radiation. In recent years, the combination of compressed sensing technology (CS) and MoM (CS-MoM) greatly reduces the computational complexity of solving the electromagnetic scattering problem. The main principle of the CS-MoM method is to construct an underdetermined system meeting the CS structure by utilizing partial impedance matrix equation in MoM, and for the sparse basis structure in CS-MoM, there are mainly a characteristic basis function method (CBFs), a characteristic modulus function method (CMs) and a Krylov subspace basis function method (KSBFs), however, due to high computational complexity of the sparse basis structure, it is difficult to solve the scattering problem of relatively large objects by using KSBFs. Thus, a method for constructing a sparse base based on the KSBFs blocks is proposed in the prior art to accelerate the generation of the sparse base. The method mainly comprises the steps of dividing a target into blocks by placing a plurality of cubes in a grid shape in an analysis space, and generating subdomains. But for irregular calculation targets this may lead to different sub-fields sizes, while in too large and too small sub-fields different numbers of unknowns may reduce the accuracy and efficiency of the calculation. In addition, the method is a non-adaptive region decomposition method requiring human participation, so that how to adaptively decompose the region of the calculation target is to accelerate solving of the electromagnetic problem. Disclosure of Invention The invention aims to provide a method for solving electromagnetic scattering based on a Krylov subspace basis function of self-adaptive partitioning, which aims to solve the problems in the prior art. The aim of the invention can be achieved by the following technical scheme: a method for solving electromagnetic scattering based on an adaptive blocking Krylov subspace basis function, the method comprising the steps of: performing self-adaptive region decomposition on a target region to obtain a target subdomain; Expanding the target subdomain to form an expanded subdomain; and thirdly, carrying out solving calculation of electromagnetic scattering by utilizing the optimized extended subdomain. Further, the step of performing cluster region decomposition on the target, dividing the target into p subfields, and the steps are as follows: In the above formula, p is the number of subfields, X i is the i-th object, S is the number of objects, and μ i is the i-th cluster center. Further, the specific operation of decomposing the target area in the step is as follows: Dividing given N (X 1,X2,……,XN) unknowns into p sub-domains by adopting a k-means clustering algorithm, and meeting the requirement that p is less than or equal to N, firstly taking the middle points of the public sides of the triangular pairs as clustering data points to form a data set, setting an initialization clustering center, wherein the number of the clustering centers is the same as p, and continuously updating the positions of the centers through iteration until the region decomposition is completed. Further, the second step expands the sub-fields of the target, and in order to ensure the continuity of the edge current of the target, expansion optimization needs to be performed on each sub-field. Further, the expansion optimization operation is as follows, the distances from all data points in all subfields to each clustering center are calculated, then the average distance L mean from the data points in all subfields to the clustering center is calculated, and finally an expansion subfield larger than the subfields is expanded according to the multiple of the average distance. Further, data points of other subfields within the extended subfield are assigned to the extended subfield for reducing disturbances caused by edge current discontinuities. Further, the extended subdomain is 1-2 times the average distance from the data point in each subdomain to the cluster center. Further, the extended subfield size is 1.35L mean. The invention has the beneficial effects that: 1. The method for solving the electromagnetic scattering based on the Krylov subspace basis function of the self-adaptive partitioning has the main advantages that the efficiency of constructing the Krylov subspace basis function by adopting the self-adaptive partitioning technology is higher, the generation time of the Krylov subspace basis function based on the partitioning is obviously reduced, the partitioning expans