Multigrid ADI method for two-dimensional electromagnetic simulations

We propose a multigrid alternating-direction implicit (ADI) method for solving two-dimensional Maxwell's equations. This method is based on interpreting the ADI method as an iterative solver for the Crank-Nicolson (CN) scheme. By introducing a special procedure to solve the residual equation within the ADI framework, multigrid methods are incorporated into the iterative ADI method. The accuracy and efficiency of the proposed method are further demonstrated by numerical examples.

[1]  M. F. Iskander,et al.  A new 3D FDTD multigrid technique with dielectric traverse capabilities , 2001 .

[2]  Pre-iterative ADI-FDTD method for conductive medium , 2005 .

[3]  J. W. Thomas.  Numerical Partial Differential Equations: Finite Difference Methods , 1995 .

[4]  N. Uzunoglu,et al.  A multilevel formulation of the finite-element method for electromagnetic scattering , 1999 .

[5]  William L. Briggs,et al.  A multigrid tutorial, Second Edition , 2000 .

[6]  S. McCormick,et al.  A multigrid tutorial (2nd ed.) , 2000 .

[7]  T. Namiki,et al.  Investigation of numerical errors of the two-dimensional ADI-FDTD method [for Maxwell's equations solution] , 2000 .

[8]  K. Demarest,et al.  A multilevel formulation of the method of moments (EM scattering) , 1993 .

[9]  F. Teixeira,et al.  An efficient PML implementation for the ADI-FDTD method , 2003, IEEE Microwave and Wireless Components Letters.

[10]  Gang Liu,et al.  Perfectly matched layer media with CFS for an unconditionally stable ADI-FDTD method , 2001 .

[11]  C. Christopoulos,et al.  Solving electromagnetic field problems using a multiple grid transmission-line modeling method , 1994 .

[12]  Allen Taflove,et al.  Computational Electrodynamics the Finite-Difference Time-Domain Method , 1995 .

[13]  R. J. Joseph,et al.  Advances in Computational Electrodynamics: The Finite - Di erence Time - Domain Method , 1998 .

[14]  Tae-Woo Lee,et al.  On the accuracy of the ADI-FDTD method , 2002, IEEE Antennas and Wireless Propagation Letters.

[15]  Zhizhang Chen,et al.  A finite-difference time-domain method without the Courant stability conditions , 1999 .

[16]  Gene H. Golub,et al.  Matrix computations (3rd ed.) , 1996 .

[17]  T. Namiki,et al.  A new FDTD algorithm based on alternating-direction implicit method , 1999 .

[18]  Zhizhang Chen,et al.  Numerical dispersion analysis of the unconditionally stable 3-D ADI-FDTD method , 2001 .

[19]  Y. Zhu,et al.  Nested multigrid vector and scalar potential finite element method for fast computation of two-dimensional electromagnetic scattering , 2002 .

[20]  Ji Chen,et al.  An iterative ADI-FDTD with reduced splitting error , 2005, IEEE Microwave and Wireless Components Letters.

[21]  Shumin Wang,et al.  On the current source implementation for the ADI-FDTD method , 2004 .

[22]  H. Keller,et al.  Analysis of Numerical Methods , 1969 .