The method of fundamental solutions for an inverse boundary value problem in static thermo-elasticity

• Application of the MFS to the inverse boundary value problem of static coupled thermo-elasticity.
• Accurate results obtained for exact data.
• Regularization yields stable and accurate results when noise is introduced to the input data.
• The regularization parameter is chosen using the L-curve criterion.

The inverse problem of coupled static thermo-elasticity in which one has to determine the thermo-elastic stress state in a body from displacements and temperature given on a subset of the boundary is considered. A regularized method of fundamental solutions is employed in order to find a stable numerical solution to this ill-posed, but linear coupled inverse problem. The choice of the regularization parameter is based on the L-curve criterion. Numerical results are presented and discussed.