An integral equation technique for scattering problems with mixed boundary conditions

TL;DR

This paper introduces a novel integral equation method for Helmholtz scattering problems with mixed boundary conditions, leveraging a global boundary charge density to improve stability and computational efficiency.

Contribution

The proposed technique uniquely employs a global boundary charge density and Calderón identities, avoiding hypersingular operators and spurious resonances in mixed boundary value problems.

Findings

Effective in avoiding spurious resonances

Utilizes Calderón identities for simplified operators

Demonstrates promising numerical results

Abstract

This paper presents an integral formulation for Helmholtz problems with mixed boundary conditions. Unlike most integral equation techniques for mixed boundary value problems, the proposed method uses a global boundary charge density. As a result, Calder\'on identities can be utilized to avoid the use of hypersingular integral operators. More importantly, the formulation avoids spurious resonances. Numerical results illustrate the performance of the proposed solution technique.