A sweeping preconditioner for Yee’s finite difference approximation of time-harmonic Maxwell’s equations

This paper is concerned with the fast iterative solution of linear systems arising from finite difference discretizations in electromagnetics. The sweeping preconditioner with moving perfectly matched layers previously developed for the Helmholtz equation is adapted for the popular Yee grid scheme for wave propagation in inhomogeneous, anisotropic media. Preliminary numerical results are presented for typical examples.

[1]  김덕영.  [신간안내] Computational Electrodynamics (the finite difference time - domain method) , 2001 .

[2]  John R. Cary,et al.  A stable FDTD algorithm for non-diagonal, anisotropic dielectrics , 2007, J. Comput. Phys..

[3]  Carretera de Valencia,et al.  The finite element method in electromagnetics , 2000 .

[4]  A. Majda,et al.  Absorbing boundary conditions for the numerical simulation of waves , 1977 .

[5]  B. Engquist,et al.  Sweeping preconditioner for the Helmholtz equation: Hierarchical matrix representation , 2010, 1007.4290.

[6]  James G. Berryman,et al.  3D finite-difference frequency-domain code for electromagnetic induction tomography , 1998 .

[7]  Jian-Ming Jin,et al.  Fast and Efficient Algorithms in Computational Electromagnetics , 2001 .

[8]  E. Weinan,et al.  Fast algorithm for extracting the diagonal of the inverse matrix with application to the electronic structure analysis of metallic systems , 2009 .

[9]  Jian-Ming Jin,et al.  The Finite Element Method in Electromagnetics , 1993 .

[10]  Weng Cho Chew,et al.  A 3D perfectly matched medium from modified maxwell's equations with stretched coordinates , 1994 .

[11]  James G. Berryman,et al.  FDFD: a 3D finite-difference frequency-domain code for electromagnetic induction tomography , 2001 .

[12]  Lexing Ying,et al.  Sweeping Preconditioner for the Helmholtz Equation: Moving Perfectly Matched Layers , 2010, Multiscale Model. Simul..

[13]  G. Mur.  Absorbing Boundary Conditions for the Finite-Difference Approximation of the Time-Domain Electromagnetic-Field Equations , 1981, IEEE Transactions on Electromagnetic Compatibility.