Time-Domain Boundary Integral Methods in Linear Thermoelasticity

TL;DR

This paper develops and analyzes time-domain boundary integral methods for solving non-stationary thermo-elasto-dynamic problems, providing mathematical foundations for numerical schemes in thermoelasticity.

Contribution

It constructs explicit fundamental solutions, introduces boundary integral operators, and proves existence and uniqueness results for the thermoelastic boundary value problem.

Findings

Explicit fundamental solutions for thermo-elasto-dynamic equations.

Coercivity of boundary integral operators established.

Existence and uniqueness of solutions in the time domain proved.

Abstract

This paper is concerned with the application of time domain boundary integral methods(TDBIMs) to a non-stationary boundary value problem for the thermo-elasto-dynamic equations, based on the Lubich approach via the Laplace transform. Fundamental solutions of the transformed thermo-elasto-dynamic equations are constructed explicitly by the H\"{o}rmander method. Simple- and double-layer potential boundary integral operators are introduced in the transformed domain and their coercivity is established. Based on the estimates of various boundary integral operators in the transformed domain, existence and uniqueness results of solutions are established in the time domain. These results may serve as a mathematical foundation for the semi-discretization and full-discretization schemes based on the boundary element method and convolution quadrature method for time domain boundary integral equations arising in thermoelasticity.