Injectivity of boundary integral operator in direct-indirect mixed Burton–Miller equation for wave scattering problems with transmissive circular inclusion

Abstract

This study proves that the injectivity condition for the integral operator of the direct-indirect mixed Burton–Miller (BM) boundary integral equation (BIE) for Helmholtz transmission problems is identical to that for the ordinary BM BIE for Helmholtz transmission problems with a transmissive circular inclusion. Although some numerical methods based on the direct-indirect mixed BM BIE can be computed faster than the ordinary BM BIE, its well-posedness has been unclear. This study resolves a part of the well-posedness, namely the injectivity of the integral operator with a transmissive circular inclusion.