Abstract
The 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.
Highlights
The need of engineering simulations of large and complex structures is rapidly growing, requiring numerical methods which are more and more efficient
In Finite Element Tearing and Interconnecting (FETI)-DPEM2, each internal interface apart from the corners is equipped with two Lagrange multipliers, which is equivalent to imposing a Robin type boundary condition, avoiding the appearing of spurious solutions
We show how the method can be strongly accelerated by partly adopting the Evanescent Modes Damping Algorithm (EMDA) [24] when PerfectlyMathed Layers (PML) are present
Summary
The need of engineering simulations of large and complex structures is rapidly growing, requiring numerical methods which are more and more efficient. In FETI-DPEM2, each internal interface apart from the corners is equipped with two Lagrange multipliers, which is equivalent to imposing a Robin type boundary condition, avoiding the appearing of spurious solutions. This boundary condition can be seen as a crude approximation of a transparency operator and many efforts have been performed in order to optimize the coefficients arising in this boundary condition for plane interfaces between subdomains [10], [16], [17], [20].
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