Title An efficient multigrid calculation of the far field map for Helmholtz and Schrödinger equations Author Cools, Siegfried Reps, Bram Vanroose, Wim Faculty/Department Faculty of Sciences. Mathematics and Computer Science Publication type article Publication 2014 Philadelphia, Pa , 2014 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 E-info http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000338783300025&DestLinkType=RelatedRecords&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000338783300025&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000338783300025&DestLinkType=CitingArticles&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848 Handle