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Effective discretization of the two‐dimensional wave equation
Author(s) -
Görner Torsten,
Kunis Stefan
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410454
Subject(s) - discretization , cartesian coordinate system , computation , wave equation , plane wave , mathematical analysis , grid , mathematics , regular grid , physics , classical mechanics , geometry , optics , algorithm
The wave equation and associated spherical means are a widespread model in modern imaging modalities like photoacoustic tomography. We consider a discretization for the Cauchy problem of the two dimensional wave equation by plane waves. The considered frequencies lie on a Cartesian or on a polar grid which gives rise to efficient algorithms for the computation of the spherical means. The theoretical findings are illustrated by a some numerical experiments. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)