Matrix decomposition MFS algorithms for elasticity and thermo-elasticity problems in axisymmetric domains

In this work, we propose an efficient matrix decomposition algorithm for the Method of Fundamental Solutions when applied to three-dimensional boundary value problems governed by elliptic systems of partial differential equations. In particular, we consider problems arising in linear elasticity in axisymmetric domains. The proposed algorithm exploits the block circulant structure of the coefficient matrices and makes use of fast Fourier transforms. The algorithm is also applied to problems in thermo-elasticity. Several numerical experiments are carried out.