Abstract
In this paper, we consider a source problem for a time harmonic acoustic wave in two-dimensional space. Based on the boundary integral equation method, a Dirichlet-to-Neumann map in terms of boundary integral operators on the boundary of the source is constructed to transform this problem into two boundary value problems for the Helmholtz equation.
Highlights
The realization of many physical phenomena mathematically leads to the resolution of the Helmholtz equation in a bounded or an unbounded domain with suitable conditions, for example, radiation or scattering of waves [1, 2] and swirling flow in the fluid mechanics [3].Using the boundary integral equation (BIE) approach, the above problems can be transformed into a Fredholm integral equation of the second kind or a system of the same kind
Unlike in the case of a homogeneous equation where only boundary integrals appear [4,5,6], using boundary integral equation methods in dealing with a source problem usually leads to some boundary integrals and a domain integral [7,8,9]
It is appropriate to draw some conclusive remarks for the proposed DtN method from our numerical experiments
Summary
We consider a source problem for a time harmonic acoustic wave in two-dimensional space. Based on the boundary integral equation method, a Dirichlet-to-Neumann map in terms of boundary integral operators on the boundary of the source is constructed to transform this problem into two boundary value problems for the Helmholtz equation
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