TY - JOUR
T1 - Boundary integral formulations for transient linear thermoelasticity with combined-type boundary conditions
AU - HSIAO, GEORGE C.
AU - SANCHEZ-VIZUET, TONATIUH
N1 - Funding Information:
\ast Received by the editors October 12, 2020; accepted for publication (in revised form) May 6, 2021; published electronically July 12, 2021. https://doi.org/10.1137/20M1372834 \bfF \bfu \bfn \bfd \bfi \bfn \bfg : The work of the second author was partially supported by US Department of Energy grant DE-FG02-86ER53233. \dagger Department of Mathematical Sciences, University of Delaware, Newark, DE 19716-2553 USA ([email protected]). \ddagger Department of Mathematics, University of Arizona, Tucson, AZ 85721-0089 USA (tonatiuh@ math.arizona.edu).
Publisher Copyright:
© 2021 Society for Industrial and Applied Mathematics Publications. All rights reserved.
PY - 2021
Y1 - 2021
N2 - We study boundary integral formulations for an interior/exterior initial boundary value problem arising from the thermo-elasto-dynamic equations in a homogeneous and isotropic domain. The time dependence is handled, based on Lubich's approach, through a passage to the Laplace domain. We focus on the cases where one of the unknown fields satisfies a Dirichlet boundary condition, while the other one is subject to conditions of Neumann type. In the Laplace domain, combined simple- and double-layer potential boundary integral operators are introduced and proven to be coercive. Based on the Laplace domain estimates, it is possible to prove the existence and uniqueness of solutions in the time domain. This analysis complements previous results that may serve as the mathematical foundation for discretization schemes based on the combined use of the boundary element method and convolution quadrature.
AB - We study boundary integral formulations for an interior/exterior initial boundary value problem arising from the thermo-elasto-dynamic equations in a homogeneous and isotropic domain. The time dependence is handled, based on Lubich's approach, through a passage to the Laplace domain. We focus on the cases where one of the unknown fields satisfies a Dirichlet boundary condition, while the other one is subject to conditions of Neumann type. In the Laplace domain, combined simple- and double-layer potential boundary integral operators are introduced and proven to be coercive. Based on the Laplace domain estimates, it is possible to prove the existence and uniqueness of solutions in the time domain. This analysis complements previous results that may serve as the mathematical foundation for discretization schemes based on the combined use of the boundary element method and convolution quadrature.
KW - Boundary integral operators
KW - Fundamental solution
KW - Linear thermoelasticity
KW - Time-domain boundary integral equations
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U2 - 10.1137/20M1372834
DO - 10.1137/20M1372834
M3 - Article
AN - SCOPUS:85110525208
SN - 0036-1410
VL - 53
SP - 3888
EP - 3911
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
IS - 4
ER -