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

Antunes, Pedro R. S.; Valtchev, Svilen S.

http://hdl.handle.net/10400.8/14578

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A meshfree numerical method for acoustic wave propagation problems in planar domains with corners and cracks.pdf	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.	4.22 MB	Adobe PDF	Download

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Authors

Antunes, Pedro R. S.

Valtchev, Svilen S.

Abstract(s)

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.

Description

Fonte: https://www.researchgate.net/publication/222298491_A_meshfree_numerical_method_for_acoustic_wave_propagation_problems_in_planar_domains_with_corners_and_cracks

Keywords

Meshfree methods Method of Fundamental Solutions Singular problems Acoustic wave propagation Room acoustics Acoustic resonance

URI

http://hdl.handle.net/10400.8/14578

Citation

Antunes, Pedro & Valtchev, Svilen. (2010). A meshfree numerical method for acoustic wave propagation problems in planar domains with corners and cracks. Journal of Computational and Applied Mathematics. 2646-2662. DOI: https://doi.org/10.1016/j.cam.2010.01.031.