MATRIX DECOMPOSITION MFS ALGORITHMS FOR ELASTICITY AND THERMO–ELASTICITY PROBLEMS IN AXISYMMETRIC DOMAINS∗

Abstract. In this work, we propose an efficient matrix decomposition algorithm for the Method of Fundamental So-lutions 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 al-gorithm 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. Key words. Method of fundamental solutions, elliptic systems, Cauchy–Navier equations, thermo–elastostatics, circu-lant matrices, fast Fourier transform, fast algorithms. AMS subject classifications. Primary 35E05, 35J55, 65N35; Secondary 35J40, 41A30, 65N38