A fast high-order solver for problems of scattering by heterogeneous bodies

Creators: Bruno, Oscar P.; Sei, Alain

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Abstract

A new high-order integral algorithm for the solution of scattering problems by heterogeneous bodies is presented. Here, a scatterer is described by a (continuously or discontinuously) varying refractive index n(x) within a two-dimensional (2D) bounded region; solutions of the associated Helmholtz equation under given incident fields are then obtained by high-order inversion of the Lippmann-Schwinger integral equation. The algorithm runs in O(Nlog(N)) operations where N is the number of discretization points. A wide variety of numerical examples provided include applications to highly singular geometries, high-contrast configurations, as well as acoustically/electrically large problems for which supercomputing resources have been used recently. Our method provides highly accurate solutions for such problems on small desktop computers in CPU times of the order of seconds.

Additional Information

"Printed 2003 IEEE. U.S. Government work not protected by U.S. copyright." Manuscript received May 25, 1999; revised November 25, 2002. This work was supported in part by the Air Force Office of Scientific Research, Air Force Materials Command, USAF, by Grants F49620-96-1-0008, F49620-98-1-0368, F49620-99-1-0010, and F49620-02-1-0049, and by the NSF under Contract numbers DMS-9596152, DMS-9523292, DMS-9816802, and DMS-0104531, and by the Powell Research Foundation. The authors wish to thank E. M. Hyde for providing the numerical implementation which was used to produce the tables concerning angular integration.

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