Nonlinear elasticity solved by a domain decomposition method on a hypercube
The author has proposed a domain decomposition method for the solution of large three-dimensional problems in nonlinear elasticity on distributed memory supercomputers. The original problem is 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 method 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 can do more in the nonlinear case, at least as far as coarse grain parallelism and computational efficiency are concerned. Various details of implementation are given that show how to match the solution algorithm with the hardware specificity of the hypercube, especially because of the message passing interconnection procedure.
preconditioned conjugate gradient method
scientific article; zbMATH DE number 425895