AN UNCONVENTIONAL DOMAIN DECOMPOSITION METHOD FOR AN EFFICIENT PARALLEL SOLUTION OF LARGE-SCALE FINITE-ELEMENT SYSTEMS

A domain decomposition algorithm based on a hybrid variational principle is developed for the parallel finite element solution of selfadjoint elliptic partial differential equations. The spatial domain is partitioned into a set of totally disconnected subdomains, each assigned to an individual processor. Lagrange multipliers are introduced to enforce compatibility at the interface points. Within each subdomain, the singularity due to the disconnection is resolved in a two-step procedure. First, the null space component of each local operator is eliminated from the local problem. Next, its contribution to the local solution is related to the Lagrange multipliers through an orthogonality condition. Finally, a conjugate projected gradient algorithm is developed for the solution of the coupled system of local null space components and Lagrange multipliers. When implemented on local memory multiprocessors, the proposed hybrid method requires fewer interprocessor communications than conventional Schur methods. It is also suitable for parallel/vector computers with shared memory. Moreover, unlike parallel direct solvers, it exhibits a degree of parallelism that is not limited by the bandwidth of the finite element system of equations. In this paper, it is applied to the solution of large-scale structural and solid mechanics problems.