A parallel finite-element tearing and interconnecting algorithm for solution of the vector wave equation with PML absorbing medium

Abstract

A domain decomposition method based on the finite-element tearing and interconnecting (FETI) algorithm is presented for the solution of the large sparse matrices associated with the finite-element method (FEM) solution of the vector wave equation. The FETI algorithm is based on the method of Lagrange multipliers and leads to a reduced-order system, which is solved using the biconjugate gradient method (BiCGM). It is shown that this method is highly scalable and is more efficient on parallel platforms when solving large matrices than traditional iterative methods such as a preconditioned conjugate gradient algorithm. This is especially true when a perfectly matched layer (PML) absorbing medium is used to terminate the problem domain.

Stabilized interior penalty methods for the time-harmonic Maxwell equations

“…However the success of this method applied to low frequency eddy current problems (in which case the resulting bilinear forms are coercive) suggests that mortar methods or similar domain decomposition methods could be useful for scattering problems [33]. Another domain decomposition approach is the FETI method applied to the Maxwell equations [34]. A Lagrange multiplier based version of this method was analyzed in [35] for the coercive Maxwell problem arising in time stepping.…”

The Iterative Multi-Region Algorithm Using a Hybrid Finite Difference Frequency Domain and Method of Moment Techniques

“…Therefore the complexity of the problem can be reduced, and a time and memory efficiency algorithm can be achieved. Another advantage of the DDM methods is that they are suitable to develop parallel processing techniques [14][15][16], and thus enable highly scalable algorithms.…”

“…A class of time and memory efficient algorithms is developed through which, the computational domain is divided into smaller sub-regions and then the sub-regions solutions, after introducing the effect of interactions between these sub-regions, are used to provide the entire domain solution. A group of methods that decomposes the computational domain into sub-domains is known as the domain decomposition methods (DDM) [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. These methods in general require common boundaries between sub-domains and boundary conditions are enforced on sub-domain interfaces.…”

A least-squares approximation method for the time-harmonic Maxwell equations

“…The implementation of this procedure may be quite involved since one needs to deal explicitly with the singular functions. Many other alternatives, such as mortar and FETI methods applied to the Maxwell's equations [3,29], have been proposed. Adaptive hp solvers have also been investigated, see [12].…”