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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Electromagnetic scattering for dielectrics: iterative methods for solving boundary integral equations
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by B. Bielefeld, Y. Deng, J. Glimm, F. Tangerman and J. S. Asvestas PDF
Proc. Amer. Math. Soc. 122 (1994), 719-725 Request permission

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 out-of-core capability.
References
    J. A. Asvestas, Integral equations for penetrable electromagnetic scatters, presented as Report RM-857, Grumman Corporate Research Center (June 1987). K. E. Atkinson, Two-grid iteration methods for linear integral equations of the second kind on piecewise smooth surfaces in ${\mathcal {R}^3}$, Rep. Comp. Math. 14 (1991).
  • David L. Colton and Rainer Kress, Integral equation methods in scattering theory, Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1983. A Wiley-Interscience Publication. MR 700400
    • T. Cwik, Parallel decomposition methods for the solution of electromagnetic scattering problems, Electromagnetics 12 (1992), 343-357. T. Cwik, J. Patterson, and D. Scott, Electromagnetic scattering calculations on the Intel touchstone, presented at Proceedings IEEE Supercomputing (Nov. 1992). A. Edelman, Large dense numerical linear algebra in 1993, presented at UC-Berkeley, preprint, 1992. S. M. Rao, D. R. Wilton, and A. W. Glisson, Electromagnetic scattering by surfaces of arbitrary shape, IEEE Trans. Antennas and Propagation AP-30 (1982), 409-418. 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
  • © Copyright 1994 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 122 (1994), 719-725
  • MSC: Primary 65N99; Secondary 49L99, 78A45
  • DOI: https://doi.org/10.1090/S0002-9939-1994-1218113-0
  • MathSciNet review: 1218113