Fast Algorithms for High Frequency Wave Propagation

Chapter
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 83)

Abstract

High frequency wave propagation is computationally challenging due to the very large number of unknowns that are needed in direct numerical approximations. We will present new fast algorithms for the solution of the linear systems, which follow from discretization of the Helmholtz equation and its related integral equation formulation. For the Helmholtz equation we present a new type of preconditioner, which, together with the GMRES iterative method, results in a near optimal computational complexity. The cost of the preconditioner scales essentially linearly with the number of unknowns and the number of iterations is independent of frequency. In the integral equation case, a directional fast multilevel technique also results in a near optimal computational complexity.

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Notes

Acknowledgements

B. E. is partially supported by the NSF grants DMS-0714612 and DMS-1016577. L. Y. is partially supported by the NSF CAREER award DMS-0846501, the NSF grant DMS-1016577, and an Alfred P. Sloan Fellowship. The authors thank the reviewer for detailed comments and suggestions.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of Mathematics and ICESThe University of Texas at AustinAustinUSA

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