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The Navier equation is the governing equation of elastic waves, and computingits solution accurately and rapidly has a wide range of applications ingeophysical exploration, materials science, etc. In this paper, we focus on theefficient and high-precision numerical algorithm for the time harmonic elasticwave scattering problems from cornered domains via the boundary integralequations in two dimensions. The approach is based on the combination ofNystr\"om discretization, analytical singular integrals and kernel-splittingmethod, which results in a high-order solver for smooth boundaries. It is thencombined with the recursively compressed inverse preconditioning (RCIP) methodto solve elastic scattering problems from cornered domains. Numericalexperiments demonstrate that the proposed approach achieves high accuracy, withstabilized errors close to machine precision in various geometricconfigurations. The algorithm is further applied to investigate the asymptoticbehavior of density functions associated with boundary integral operators nearcorners, and the numerical results are highly consistent with the theoreticalformulas.

A robust and high precision algorithm for elastic scattering problems from cornered domains