Computer Science NASC Seminar

Spectrally Accurate Direct Solution of Variable-media Scattering Problems Via Impedance Maps

Alex Barnett, Dartmouth College

March 07, 2014 10:00AM
Warren Weaver Hall, Room 1302
251 Mercer Street
New York, NY, 10012-1110
(Directions)

Spring 2014 NASC Seminars Calendar

Synopsis

Time-harmonic scattering from a bounded region of smoothly varying
wave speed has applications in ultrasound imaging, underwater
acoustics, and quantum mechanics. Yet, at high frequency, iterative
methods become intolerably slow. We present an efficient direct
numerical algorithm which builds the interior Dirichlet-to-Neumann
(DtN) map for the region via bottom-up recursive merges of
impedance-to-impedance (ItI) maps on a quadtree of boxes. The method
is robust since the ItI map is unitary. On the smallest (leaf) boxes
spectral collocation is used. Coupling to the radiation condition
gives a provably 2nd-kind integral equation. Problems 100
wavelengths in size can be solved to 9 digit accuracy in a few
minutes on a workstation; each new incident wave then requires
around one second.

Joint work with Adrianna Gillman (Dartmouth) and Gunnar Martinsson (CU
Boulder)


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