Time-domain boundary integral methods in linear thermoelasticity

George C. Hsiao, Tonatiuh Sánchez-Vizuet

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

This paper is concerned with the application of time-domain boundary integral methods to a nonstationary 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 Hörmander method. Simpleand 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 semidiscretization and full-discretization schemes based on the boundary element method and the convolution quadrature method for time domain boundary integral equations arising in thermoelasticity.

Original languageEnglish (US)
Pages (from-to)2463-2490
Number of pages28
JournalSIAM Journal on Mathematical Analysis
Volume52
Issue number3
DOIs
StatePublished - 2020
Externally publishedYes

Keywords

  • Boundary integral operators
  • Fundamental solution
  • Linear thermoelasticity
  • Time-domain boundary integral equations

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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