A domain-decomposed solver for nonlinear elasticity

A domain decomposed solver is introduced for the solution of large three-dimensional problems in finite elasticity. The original problem is first approximated by a standard finite element method and linearized by a Newton technique. The linearized problem is solved by a mixed solver which is based on the Schur complement method. In this solver, a preconditioned conjugate gradient is used for solving the interface problem, while local problems within each subdomain are solved by direct solvers. Compared to the linear case, the present study shows that domain decomposition is better in the nonlinear case, at least as far as coarse grain parallelism and computational efficiency are concerned. Numerical tests are presented consisting of parametric studies and the study of the post-buckling behavior of a three-dimensional beam.