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arXiv · 2505.09217

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

Yasuhiro Matsumoto·Kei Matsushima
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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.

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Yasuhiro Matsumoto, Kei Matsushima. 2025-05-14. Injectivity of boundary integral operator in direct-indirect mixed Burton-Miller equation for wave scattering problems with transmissive circular inclusion. https://doi.org/10.14495/jsiaml.17.61

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