A meshfree numerical method for acoustic wave propagation problems in planar domains with corners and cracks

Authors:
Pedro R. S. Antunes;Svilen S. Valtchev
Affiliations:
Group of Mathematical Physics of the University of Lisbon, Complexo Interdisciplinar, Av. Prof. Gama Pinto 2, P-1649-003 Lisbon, Portugal;CEMAT, Instituto Superior Técnico, TU Lisbon, Av. Rovisco Pais, 1049-001 Lisbon, Portugal and Department of Mathematics, ESTG, Instituto Politécnico de Leiria, Leiria, Portugal
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

The numerical solution of acoustic wave propagation problems in planar domains with corners and cracks is considered. Since the exact solution of such problems is singular in the neighborhood of the geometric singularities the standard meshfree methods, based on global interpolation by analytic functions, show low accuracy. In order to circumvent this issue, a meshfree modification of the method of fundamental solutions is developed, where the approximation basis is enriched by an extra span of corner adapted non-smooth shape functions. The high accuracy of the new method is illustrated by solving several boundary value problems for the Helmholtz equation, modelling physical phenomena from the fields of room acoustics and acoustic resonance.