Electromagnetic scattering for dielectrics: iterative methods for solving boundary integral equations
Authors:
B. Bielefeld, Y. Deng, J. Glimm, F. Tangerman and J. S. Asvestas
Journal:
Proc. Amer. Math. Soc. 122 (1994), 719725
MSC:
Primary 65N99; Secondary 49L99, 78A45
MathSciNet review:
1218113
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Abstract: We consider multigrid iterative methods for the solution of electromagnetic scattering for dielectric materials. We show convergence of the iteration using coarse grids which are two to four times coarser in each dimension than the fine grid. These results allow a significant increase in problem size and solution speed, for a given hardware configuration. We report in particular on the solution of scattering problems which require the solution of 31,000 equations on the fine grid, using the direct solution of 3,500 double precision equations on the coarse grid, and project the ability to solve significantly larger systems using larger machines or an outofcore capability.
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Z. Wu and T. Coleman, A parallel row distributed linear algebra system, Technical report CTC92TR93, Cornell University, Ithaca, NY, 1992.
 [1]
 J. A. Asvestas, Integral equations for penetrable electromagnetic scatters, presented as Report RM857, Grumman Corporate Research Center (June 1987).
 [2]
 K. E. Atkinson, Twogrid iteration methods for linear integral equations of the second kind on piecewise smooth surfaces in , Rep. Comp. Math. 14 (1991).
 [3]
 D. Colton and R. Kress, Integral methods in scattering theory, Wiley, New York, 1983. MR 700400 (85d:35001)
 [4]
 T. Cwik, Parallel decomposition methods for the solution of electromagnetic scattering problems, Electromagnetics 12 (1992), 343357.
 [5]
 T. Cwik, J. Patterson, and D. Scott, Electromagnetic scattering calculations on the Intel touchstone, presented at Proceedings IEEE Supercomputing (Nov. 1992).
 [6]
 A. Edelman, Large dense numerical linear algebra in 1993, presented at UCBerkeley, preprint, 1992.
 [7]
 S. M. Rao, D. R. Wilton, and A. W. Glisson, Electromagnetic scattering by surfaces of arbitrary shape, IEEE Trans. Antennas and Propagation AP30 (1982), 409418.
 [8]
 Z. Wu and T. Coleman, A parallel row distributed linear algebra system, Technical report CTC92TR93, Cornell University, Ithaca, NY, 1992.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199412181130
PII:
S 00029939(1994)12181130
Article copyright:
© Copyright 1994 American Mathematical Society
