A sweeping preconditioner for time-harmonic Maxwell鈥檚 equations with finite elements

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• 作者：Paul Tsuji^a ; ^{ptsuji@gmail.com} ; Bjorn Engquist^b ; Lexing Ying^b
• 关键词：Maxwell&rsquo ; s equations ; Frequency domain ; Finite element methods ; Preconditioners ; Fast solvers ; Perfectly matched layers ; Block LDLt factorization ; High-frequency waves
• 刊名：Journal of Computational Physics
• 出版年：2012
• 期刊代码：136_00219991
• 类别：cp
• 出版时间：1 May, 2012
• 卷：231
• 期：9
• 页码：3770-3783
• 文件大小：1692 K

摘要

This paper is concerned with preconditioning the stiffness matrix resulting from finite element discretizations of Maxwell鈥檚 equations in the high frequency regime. The moving PML sweeping preconditioner, first introduced for the Helmholtz equation on a Cartesian finite difference grid, is generalized to an unstructured mesh with finite elements. The method dramatically reduces the number of GMRES iterations necessary for convergence, resulting in an almost linear complexity solver. Numerical examples including electromagnetic cloaking simulations are presented to demonstrate the efficiency of the proposed method.