Fast Algorithm Research Based On E-H Finite-element Time-domain Method

In recent decades,computational electromagnetics have been seen a considerable surge in research on efficient accurate numerical methods,which have been stimulated by the demands for electromagnetic targets simulations.The finite element time-domain(FETD)method has attracted the attention of researchers in the field of computational electromagnetics due to the fact that it can model complex geometry structures and inhomogeneous materials.High order hierarchical vector basis functions method is a very useful way to satisfy the development of higher accuration of the analysis of the electromagnetic engineering.The numerical results of several examples show that using the high order basis functions can reduce unknowns by larger discretization size to obtain the same accuracy with the low order basis functions.The matrix inversion of the conventional FETD leads to the heavy cost of solution time while calculating the problems of electrically large size.Discontinuous galerkin finite element time-domain(DG-FETD)method will process the system matrix for each subdomain separately before time marching,which can greatly reduce the simulation time.Discontinuous galerkin finite element time-domain method divides the computation domain into several non-overlapping subdomains and computes both the electric and magnetic fields in each subdomain,and only the fields on the interfaces of adjacent subdomains are directly related to each other.The method allows that the basis functions are discontinuous across boundaries between subdomains,so the central flux is introduced at the interfaces between adjacent subdomains to impose the tangential continuity of the electrical and magnetic fields.A mathematical framework called the ‘Hierarchical(H-)matrix' framework can also be introduced to accelerate the direct solution of finite-element linear equations.The concept of H-matrix and the operations defined in H-matrix arithmetic are introduced.The detailed numerical procedure of the H-matrix-based direct solver is given,and the complexity of the H-matrix-based direct solver is analyzed.