Regularized Boundary Integral Equation Methods for Open-Arc Scattering Problems in Thermoelasticity

Abstract. This paper is devoted to developing novel boundary integral equation (BIE) solvers for the problems of thermoelastic scattering by open arcs with four different boundary conditions in two dimensions. The proposed methodology is inspired by the analysis of the Calderón identities on closed boundaries and leads to formulations with eigenvalues that accumulate at particular points depending only on Lamé parameters. Incorporating with certain edge singularities, regularized BIEs in terms of compositions of weighted boundary integral operators are constructed to effectively reduce the required iteration number for solving the corresponding discretized linear systems. We implement the new formulations utilizing regularization of singular integrals, which reduces the strongly singular and hypersingular integrals into weakly singular integrals. Combined with spectrally accurate quadrature rules, numerical examples are presented to illustrate the accuracy and efficiency of the proposed solvers.