Wave scattering with the UV multilevel partitioning method: 1. Two‐dimensional problem of perfect electric conductor surface scattering

[1] A UV method with multilevel partitioning (UVMLP) is developed to solve electromagnetic problem. In this paper we demonstrate the technique to treat electromagnetic problem for large surface in a two-dimensional (2-D) problem. Using the multilevel partitioning (MLP), the decomposition preprocessing, and the matrix vector multiplication require CPU of O(N logN) per iteration with a smaller constant factor for matrix column multiplication than decomposition. The memory requirement is of O(N logN). We demonstrate the technique for a rough surface scattering problem with surface length up to 13,000 wavelengths and RMS height up to ten wavelengths. Computations are based on using PC with a single Pentium 4–2.4 GHz processor and 1 G RAM. For the case of 65,536 unknowns, it requires about CPU from 3.3 to 5.33 s per iteration and a total CPU of 3.9–14.3 min with 49–146 conjugate gradient iterations.

[1]  Peng Xu,et al.  Wave scattering with UV multilevel partitioning method: 2. Three‐dimensional problem of nonpenetrable surface scattering , 2004 .

[2]  Leung Tsang,et al.  Multiple scattering among vias in planar waveguides using preconditioned SMCG method , 2004 .

[3]  Qin Li,et al.  Parallel implementation of the sparse-matrix/canonical grid method for the analysis of two-dimensional random rough surfaces (three-dimensional scattering problem) on a Beowulf system , 2000, IEEE Trans. Geosci. Remote. Sens..

[4]  V. Rokhlin Rapid Solution of Integral Equations of Scattering Theory , 1990 .

[5]  Leung Tsang,et al.  A sparse‐matrix canonical‐grid method for scattering by many scatterers , 1995 .

[6]  Joel T. Johnson,et al.  A novel acceleration algorithm for the computation of scattering from rough surfaces with the forward‐backward method , 1998 .

[7]  Weng Cho Chew,et al.  Fast steepest descent path algorithm for analyzing scattering from two‐dimensional objects , 1996 .

[8]  Weng Cho Chew,et al.  Fast algorithm for the analysis of scattering by dielectric rough surfaces , 1998 .

[9]  Evgenii Mikhailovich Lifshitz,et al.  SCATTERING OF ELECTROMAGNETIC WAVES , 1984 .

[10]  Kapur,et al.  IES/sup 3/: a fast integral equation solver for efficient 3-dimensional extraction , 1997, 1997 Proceedings of IEEE International Conference on Computer Aided Design (ICCAD).

[11]  Leung Tsang,et al.  Wave scattering with UV multilevel partitioning method for volume scattering by discrete scatterers , 2004 .

[12]  R. Mittra,et al.  Characteristic basis function method for solving large problems arising in dense medium scattering , 2003, IEEE Antennas and Propagation Society International Symposium. Digest. Held in conjunction with: USNC/CNC/URSI North American Radio Sci. Meeting (Cat. No.03CH37450).

[13]  Leung Tsang,et al.  Monte-Carlo simulations of large-scale problems of random rough surface scattering and applications to grazing incidence with the BMIA/canonical grid method , 1995 .