An inverse problem in static thermo-elasticity is investigated. The aim is to reconstruct the unspecified boundary data, as well as the temperature and displacement inside a body from over-specified boundary data measured on an accessible portion of its boundary. The problem is linear but ill-posed. The uniqueness of the solution is established but the continuous dependence on the input data is violated. In order to reconstruct a stable and accurate solution, the method of fundamental solutions is combined with Tikhonov regularization where the regularization parameter is selected based on the L-curve criterion. Numerical results are presented in both two and three dimensions showing the feasibility and ease of implementation of the proposed technique.
- method of fundamental solutions
- inverse problem
Marin, L., Karageorghis, A., Lesnic, D., & Johansson, B. T. (2016). The method of fundamental solutions for problems in static thermo-elasticity with incomplete boundary data. Inverse Problems in Science and Engineering, 25(5), 652-673. https://doi.org/10.1080/17415977.2016.1191072