3-D Electromagnetic Scattering Computation in Free-Space With the FETI-FDP2 Method

Abstract

International audienceThe electromagnetic dual-primal finite element tearing and interconnecting (FETI-DPEM) method is a nonoverlapping domain decomposition method developed for the finite element analysis of large-scale electromagnetic problems, where the corner edges are globally numbered. This paper presents an extension of the FETI-DPEM2 method, named FETI-full dual primal (FETI-FDP2), where more flexible Robin-type boundary conditions are imposed, on the inner interfaces between subdomains as well as on the corner edges, leading to a new interface problem. Its capacities are tested in the framework of a three-dimensional (3-D) free-space scattering problem, with a scattered field formulation and a computational domain truncated by perfectly mathed layers (PML). First, we compare its accuracy with respect to other FETI-DPEM2 methods and to a complete resolution of the FEM problem, thanks to a direct sparse solver. We show that the convergence of iterative solvers is affected by the presence of the PML and can be accelerated by means of a more accurate approximation, between adjacent subdomains, of the Dirichlet-to-Neumann (DtN) operator. The effectiveness of the iterative solvers are also considered for different test cases. The advantages of the proposed FETI-FDP2 method combined with the associated DtN approximation is numerically demonstrated, regardless the chosen working frequency or the iterative solvers

Review on Computational Electromagnetics

“…Ivan Vo znyuk [25] discussed Finite -Element Tearing and interconnecting Full-Dual-Primal (FETI-FDP2) (FETI-FDP2) method an extended version of FETI-DPEM 2 is used in analysis of 3D large-scale electro magnetic problems using robin type boundary condition at corners and interface. Electrically s mall problems are solved by using Krylov solver and ASP/AM G(Au xiallary Space Preconditioners / Algebraic Mu ltigrid) preconditioners as they facilitate convergence with lesser iterations.…”

“…However the implementation could be extended not only to geometry that is tedious to solve but also to electrically large problems using DDM [26]. The incapability of iterative solver to converge due to presence of PM L is over ru led by Dirich letto-Neumann (DtN) appro ximat ion [25]. Further, algorith m's parallelization imp roves convergence.…”

“…Iterative solvers face difficulty in convergence due to existence of PM L. However DtN appro ximation, preconditioners promotes convergence [25]. DDM makes it applicable to large domain problems.…”

Efficient combination of a 3D Quasi-Newton inversion algorithm and a vector dual-primal finite element tearing and interconnecting method

“…The finite element method previously described has been further improved to address large scale models while preserving the versatility of the FEM method. To that end, an updated version of the Finite Element Tearing and Interconnecting-Dual Primal Electromagnetic method (FETI-DPEM) [25], named FETI-FDP2, has been developed and thoroughly tested [32] [33].…”

“…In this work, we focus on the three-dimensional (3D) case, because the computational burden here is more important than in 2D and leads us to the necessity of well-defined numerical strategies. To that end, an updated version of the FETI-DPEM method, named FETI-FDP2, has been developped and thoroughly tested [32,33]. Our aim here is to efficiently coupled it with an inversion scheme.…”