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

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 Nyström discretization. Moreover, unlike other formulations such as the PMCHWT or Müller 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.