SIAM Journal on Scientific Computing
Optimized Schwarz Methods without Overlap for the Helmholtz Equation
SIAM Journal on Scientific Computing
Journal of Computational Physics
New Nonoverlapping Domain Decomposition Methods for the Harmonic Maxwell System
SIAM Journal on Scientific Computing
Optimized Schwarz Methods for Maxwell's Equations
SIAM Journal on Scientific Computing
Journal of Computational Physics
Finite element domain decomposition with second order transmission conditions for time-harmonic electromagnetic problems
| Hi-index | 31.45 |
Non-overlapping domain decomposition (DD) methods provide efficient algorithms for solving time-harmonic Maxwell equations. It has been shown that the convergence of DD algorithms can be improved significantly by using high order transmission conditions. In this paper, we extend a newly developed second-order transmission condition (SOTC), which involves two second-order transverse derivatives, to facilitate fast convergence in the non-conformal DD algorithms. However, the non-conformal nature of the DD methods introduces an additional technical difficulty, which results in poor convergence in many real-life applications. To mitigate the difficulty, a corner-edge penalty method is proposed and implemented in conjunction with the SOTC to obtain truly robust solver performance. Numerical results verify the analysis and demonstrate the effectiveness of the proposed methods on a few model problems. Finally, drastically improved convergence, compared to the conventional Robin transmission condition, was observed for an electrically large problem of practical interest.