Finite-element-wise domain decomposition iterative solvers with polynomial preconditioning

A highly scalable finite-element-wise domain decomposition (EDD) iterative solver (with particular emphasis on the flexible GMRES method) based on polynomial preconditioning is discussed in this paper. Compared to alternative methods, finite-element-wise domain decomposition solvers with polynomial preconditioning circumvent the assembly of the matrix, reordering of the degree-of-freedom, redundant computations associated with the interface elements, numerical problems associated with the local preconditioner, and costly global preconditioner construction. A dramatic reduction in parallel overhead is achieved, both in terms of computation and communication results, in a highly scalable solver. This work is implemented using MPI C++and applied to solve static and dynamic structural mechanics problems. The corresponding numerical performance, with emphasis on iterative convergence and parallel scalability, of the proposed approach over the SGI Origin machine is critically assessed.