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A fast directional algorithm for high frequency acoustic scattering in two dimensions
Department of Mathematics, The University of Texas at Austin, Austin, USA.
Department of Mathematics, The University of Texas at Austin, Austin, USA.
2009 (English)In: Communications in Mathematical Sciences, ISSN 1539-6746, E-ISSN 1945-0796, Vol. 7, no 2, 327-345 p.Article in journal (Refereed) Published
Abstract [en]

This paper is concerned with fast solution of high frequency acoustic scattering problems in two dimensions. We introduce a directional multiscale algorithm for the $N$-body problem of the two dimensional Helmholtz kernel. The algorithm follows the approach developed in Engquist and Ying, SIAM J. Sci. Comput., 29 (4), 2007, where the three dimensional case was studied. The main observation is that, for two regions that follow a directional parabolic geometric conguration, the interaction between these two regions through the 2D Helmholtz kernel is approximately low rank. We propose an improved randomized procedure for generating the low rank separated representation for the interaction between these regions. Based on this representation, the computation of the far field interaction is organized in a multidirectional and multiscale way to achieve maximum efficiency. The proposed algorithm is accurate and has the optimal $O(NlogN)$ complexity for problems from two dimensional scattering applications. Finally, we combine this fast directional algorithm with standard boundary integral formulations to solve acoustic scattering problems that are of thousands of wavelengths in size.

Place, publisher, year, edition, pages
2009. Vol. 7, no 2, 327-345 p.
Keyword [en]
N-body problem, Helmholtz equation, oscillatory kernels, fast multipole methods, multidirectional computation, multiscale methods
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-72324ISI: 000267289000003OAI: oai:DiVA.org:kth-72324DiVA: diva2:487483
Note
QC 20120217Available from: 2012-01-31 Created: 2012-01-31 Last updated: 2017-12-08Bibliographically approved

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