Fast Multipole / Wavelet-IML Hybrids for Electromagnetic Analysis
Final progress rept. 1 Aug 2000-30 Apr 2004
ILLINOIS UNIV AT URBANA DEPT OF ELECTRICAL AND COMPUTER ENGINEERING
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In recent years, a variety of computational schemes have been developed that accelerate the iterative solution of the dense matrix equations that arise upon discretizing boundary integral equations pertinent to the description of electromagnetic scattering problems. These schemes largely fall into two categories i fast multipole methods and ii waveletmultiresolution schemes. The overall goal of this project is to develop and catalogue all practical hybrids between fast multipole solvers and multiresolution schemes useful to the analysis of electromagnetic boundary value problems. To this end, we developed i hybrid plane wave time domain PWTD multiresolution schemes pertinent to the construction of PWTD schemes for lossy media, ii PWTD schemes for 2D environments, iii PWTD solvers for microstrip structures, iv PWTD schemes for low-frequency solvers, v PWTD schemes for quasi-planar environments, vi PWTD schemes for periodic kernels, vii Time-Domain Adaptive Integral TD-AIM kernels for solving timedomain integral equations, viii TD-AIM accelerated hybrid time domain integral equation SPICE based circuit solvers, and ix a novel multigrid accelerator for the full wave finite element analysis of electromagnetic phenomena. Each and every of these solvers uses a multiresolution framework, either in space, time, or space-time to accelerate a boundary integral or finite element solver pertinent to the analysis of electromagnetic radiation, scattering, or guidance problems beyond what is possible using vanilla fastmultipole methods.
- Electricity and Magnetism