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We consider the Helmholtz transmission problem with piecewise-constantmaterial coefficients, and the standard associated direct boundary integralequations. For certain coefficients and geometries, the norms of the inversesof the boundary integral operators grow rapidly through an increasing sequenceof frequencies, even though this is not the case for the solution operator ofthe transmission problem; we call this phenomenon that of spuriousquasi-resonances. We give a rigorous explanation of why and when spuriousquasi-resonances occur, and propose modified boundary integral equations thatare not affected by them.

Spurious Quasi-Resonances in Boundary Integral Equations for the Helmholtz Transmission Problem