| Abstract: |
| This talk will present our recent works on the wellposedness analysis and numerical schemes for solving the thermo/poro-elastic scattering problems. Based on the Helmholtz decomposition, the vector coupled governing equations of thermoelastic wave are decomposed into three Helmholtz equations of scalar potentials with different wavenumbers. Then the Dirichlet-to-Neumann (DtN) map and the corresponding transparent boundary condition are constructed by using Fourier series expansions of the scalar potentials. The well-posedness results are established for the variational problem and its modification due to the truncation of the DtN map. A priori and a posteriori error estimates, including both the effects of the finite element approximation and truncation of the DtN operator, are derived. Numerical experiments are presented to validate the theoretical results. |
|