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A new method of internal auxiliary source-sinks (MIASS) for two-dimensional interior Dirichlet acoustic problems

2020; Elsevier BV; Volume: 386; Linguagem: Inglês

10.1016/j.cam.2020.113231

1879-1778

Yuri Eremin, George Fikioris, Nikolaos L. Tsitsas, Thomas Wriedt,

Numerical methods in engineering

A new Method of Internal Auxiliary Source–Sinks (MIASS) is developed for the numerical solution of the two-dimensional interior Dirichlet acoustic problem for the Helmholtz equation. We give two versions of MIASS, one for a closed auxiliary curve (MIASS-C) and another for an open auxiliary curve (MIASS-O). The mathematical and numerical foundations of both versions are provided. In particular, we show that the integral operator that pertains to the associated integral equation has a dense range. We then demonstrate completeness and linear independence of the discrete system of source-sinks. Indicative numerical results are given and numerical implementation aspects are discussed.