Boundary integral approximation of a heat-diffusion problem in time-harmonic regime |
| |
Authors: | María-Luisa Rapún Francisco-Javier Sayas |
| |
Institution: | (1) Departmento Matemática e Informática, Universidad Pública de Navarra, Campus de Arrosadía, 31006 Pamplona, Spain;(2) Departmento Matemática Aplicada, Universidad de Zaragoza, C.P.S., 50018 Zaragoza, Spain |
| |
Abstract: | In this paper we propose and analyse numerical methods for the approximation of the solution of Helmholtz transmission problems
in the half plane. The problems we deal with arise from the study of some models in photothermal science. The solutions to
the problem are represented as single layer potentials and an equivalent system of boundary integral equations is derived.
We then give abstract necessary and sufficient conditions for convergence of Petrov–Galerkin discretizations of the boundary
integral system and show for three different cases that these conditions are satisfied. We extend the results to other situations
not related to thermal science and to non-smooth interfaces. Finally, we propose a simple full discretization of a Petrov–Galerkin
scheme with periodic spline spaces and show some numerical experiments. |
| |
Keywords: | thermal waves Petrov– Galerkin methods boundary integral equations Helmholtz transmission problems |
本文献已被 SpringerLink 等数据库收录! |