Research On Electromagnetic Simulation Method Based On Low-Rank Direct Solution

With the development of computational electromagnetic theory and the improvement of performance requirements in electromagnetic simulation engineering projects,the research on efficient and accurate numerical analysis methods has increasingly become the focus of research work in the field of computational electromagnetics.In this paper,the research on the application of finite element method,boundary element method and its hybrid algorithm in electromagnetic scattering problem analysis is carried out,and the combination of these three numerical methods with the direct solution is analyzed.The main work includes the following aspects:Firstly,a fast direct solution based on the moment method is studied.The impedance matrix of the moment method is divided into two parts,the near field and the far field,based on the binary tree structure.A multi-layer UV algorithm is used to compress the far-field dense matrix of the moment method into a low-rank decomposition form,and the near-field portion is divided into diagonal full matrices,so that the impedance matrix is constructed to be suitable for the Sherman-Morrison-Woodbury(SMW)identity.The matrix form of inversion.The SMW formula can solve the inverse matrix of the special form matrix through the unique formula,which reduces the complexity of the direct solution inversion and improves the performance of the direct solution.Then,in the finite element-boundary integral hybrid algorithm,the finite element method and the boundary element method are combined to construct the matrix equations of the internal and boundary hybrid systems.The sparse matrix of the finite element part is directly mapped by the near field,and the boundary integral part is used.The dense matrix adopts the low rank compression method,and finally constructs the expression of the H-matrix of the entire finite element-boundary element system matrix.By performing the Lower-Upper(LU)triangulation of the H-matrix format,the finite element can be obtained.The boundary integral system matrix method performs direct solution.By using the data sparse format algorithm,the H-matrix can greatly reduce the computational and storage complexity of the finite element-boundary integral matrix and its inverse matrix,and achieve efficient and direct solution to the finite element-boundary integral system.Different from the moment method,the finite element-boundary integral method is suitable for complex material structure and environmental problems,and the direct solution has the characteristics of controllable precision,good stability and high efficiency.