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arXiv · 2606.24492

Well-posedness of the weakly singular Burton-Miller equation for Helmholtz transmission problems

Yasuhiro Matsumoto
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Abstract

Although various boundary integral formulations are available for the Helmholtz transmission problem, the weakly singular Burton-Miller (BM) equation is promising because it is well-suited for the Nystr\"om discretization. Moreover, unlike other formulations such as the PMCHWT or M\"uller equations, its fictitious eigenvalues do not coincide with eigenvalues of a different transmission problem. This paper rigorously shows that the weakly singular BM equation is well-posed.

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Yasuhiro Matsumoto. 2026-06-23. Well-posedness of the weakly singular Burton-Miller equation for Helmholtz transmission problems. https://arxiv.org/abs/2606.24492

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