Title
An efficient multigrid calculation of the far field map for Helmholtz and Schrödinger equationsAn efficient multigrid calculation of the far field map for Helmholtz and Schrödinger equations
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Research group
Applied mathematics
Publication type
article
Publication
Philadelphia, Pa,
Subject
Mathematics
Source (journal)
SIAM journal on scientific computing. - Philadelphia, Pa
Volume/pages
36(2014):3, p. B367-B395
ISSN
1064-8275
ISI
000338783300025
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
In this paper we present a new highly efficient calculation method for the far field amplitude pattern that arises from scattering problems governed by the $d$-dimensional Helmholtz equation and, by extension, Schrödinger's equation. The new technique is based upon a reformulation of the classical real-valued Green's function integral for the far field amplitude to an equivalent integral over a complex domain. It is shown that the scattered wave, which is essential for the calculation of the far field integral, can be computed very efficiently along this complex contour (or manifold, in multiple dimensions). Using the iterative multigrid method as a solver for the discretized damped scattered wave system, the proposed approach results in a fast and scalable calculation method for the far field map. The complex contour method is successfully validated on Helmholtz and Schrödinger model problems in two and three spatial dimensions, and multigrid convergence results are provided to substantiate the wavenumber scalability and overall performance of the method.
Full text (open access)
https://repository.uantwerpen.be/docman/irua/70aa1f/d4124eea.pdf
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