Spherical Perfectly Matched Absorber for Finite-Volume 3-D Domain Truncation

The theory of 2-D radial perfectly matched Maxwellian absorber is extended to 3-D domain truncation problems using a generalized approximate formulation of a spherical finite-volume absorber. The mathematical modeling of the spherical absorber is presented and update equations are derived. The performance of the absorber is characterized with numerical experiments. As practical application of the technique, a complex problem considering the coupling between two spiral antennas is simulated using the finite-volume time-domain method. The comparison of the results to measured data demonstrates the excellent performance of the spherical absorber.

[1]  Weng Cho Chew,et al.  PML-FDTD in cylindrical and spherical grids , 1997 .

[2]  Andreas C. Cangellaris,et al.  GT-PML: generalized theory of perfectly matched layers and its application to the reflectionless truncation of finite-difference time-domain grids , 1996, 1996 IEEE MTT-S International Microwave Symposium Digest.

[3]  Jian-Ming Jin,et al.  Conformal PML-FDTD schemes for electromagnetic field simulations: a dynamic stability study , 2001 .

[4]  R. Vahldieck,et al.  Uniaxial and Radial Anisotropy Models for Finite-Volume Maxwellian Absorber , 2006, IEEE Transactions on Microwave Theory and Techniques.

[5]  D. Davidson,et al.  Evaluation of a Spherical PML for Vector FEM Applications , 2007, IEEE Transactions on Antennas and Propagation.

[6]  Peter G. Petropoulos,et al.  Reflectionless Sponge Layers as Absorbing Boundary Conditions for the Numerical Solution of Maxwell Equations in Rectangular, Cylindrical, and Spherical Coordinates , 2000, SIAM J. Appl. Math..

[7]  Frederic D. R. Bonnet,et al.  Berenger absorbing boundary condition with time finite-volume scheme for triangular meshes , 1997 .

[8]  Jean-Pierre Berenger,et al.  A perfectly matched layer for the absorption of electromagnetic waves , 1994 .

[9]  R. Vahldieck,et al.  Cell-centered finite-volume-based perfectly matched layer for time-domain Maxwell system , 2006, IEEE Transactions on Microwave Theory and Techniques.

[10]  D. Baumann,et al.  Finite-volume time-domain analysis of a cavity-backed Archimedean spiral antenna , 2006, IEEE Transactions on Antennas and Propagation.

[11]  Richard W. Ziolkowski,et al.  Time-derivative Lorentz material model-based absorbing boundary condition , 1997 .

[12]  S. Rao.  Time domain electromagnetics , 1999 .

[13]  T. Rylander,et al.  Perfectly matched layer in three dimensions for the time-domain finite element method applied to radiation problems , 2005, IEEE Transactions on Antennas and Propagation.

[14]  W. Chew,et al.  Systematic derivation of anisotropic PML absorbing media in cylindrical and spherical coordinates , 1997 .

[15]  M. Gunzburger,et al.  Boundary conditions for the numerical solution of elliptic equations in exterior regions , 1982 .

[16]  Radial Absorbers for Conformal Time-Domain Methods: A Solution to Corner Problems in Mesh Truncation , 2007, 2007 IEEE/MTT-S International Microwave Symposium.

[17]  Raj Mittra,et al.  Investigation of nonplanar perfectly matched absorbers for finite-element mesh truncation , 1997 .

[18]  R. Higdon.  Absorbing boundary conditions for difference approximations to the multi-dimensional wave equation , 1986 .

[19]  S. Gedney.  An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices , 1996 .