A Coupling Strategy Between The BEM And
Kansa’s Method For Acoustic Analysis Of
Heterogeneous Media
Author(s)
L. Godinho & A. Tadeu
Abstract
The BEM is well established as a solid numerical technique for the analysis of
acoustic and wave propagation problems. Its numerical formulation relies on
previous knowledge of the Green’s functions for the specific problem to be
studied, and thus it is usually limited to homogeneous media or to media
incorporating regions with piecewise constant or with well-defined variations
(such as linearly varying) of properties. In fact, the definition of these Green’s
functions becomes difficult whenever more generic cases are considered, such as
when the properties of the propagation media vary from point to point. For this
case, when the properties of the medium inside a sub-region exhibit spatial
variations, alternative approaches have to be used. In this work, a frequency
domain model based on the joint use of the BEM and of the Kansa’s method is
proposed to model such systems. In that model, the BEM is used to model the
homogeneous part of the propagation domain, while Kansa’s method is used to
model an heterogeneity, which may exhibit velocity variations from point to
point. In the interface between the two parts of the domain, continuity of
velocities and pressures are imposed. Kansa’s method is applied here making use
of Multiquadric (MQ) RBFs, which incorporate a shape parameter that strongly
influence the quality of its results. To overcome this problem, a general strategy
based on the assessment of the domain error in the enforcement of the governing
PDE is introduced to allow the definition of adequate values of this shape
parameter.
Keywords: boundary elements, Kansa’s method, acoustics, coupled methods.
Keywords
boundary elements, Kansa’s method, acoustics, coupled methods.
Related Book
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