A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
Journal of Computational Physics
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
SIAM Journal on Numerical Analysis
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
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Nonoverlapping domain decomposition methods have been shown to provide efficient iterative algorithms for the solution of the time-harmonic Maxwell's equations. Convergence of the algorithms depends strongly upon the nature of the transmission conditions that communicate information between adjacent subdomains. In this work, we introduce a new second order transmission condition that improves convergence. In contrast to previous high order interface conditions, the new condition uses two second order transverse derivatives to improve the convergence of evanescent modes without deteriorating the convergence of propagating modes. An analysis using a splitting of the field into traverse electric and magnetic components demonstrates the improved convergence provided by the transmission condition. Numerical experiments demonstrate the effectiveness of the algorithm.