A method of finite element tearing and interconnecting and its parallel solution algorithm

TLDR

The paper presents a novel domain decomposition approach for parallel finite element solution of equilibrium equations. The method partitions the domain into disconnected subdomains on separate processors, enforces interface compatibility with Lagrange multipliers, eliminates rigid body modes in parallel, and solves the resulting coupled system using a parallel conjugate projected gradient algorithm. In static problems, the approach resolves local singularities in two phases, requires less interprocessor communication than classical substructuring, is suitable for shared‑memory parallel/vector computers, and offers parallelism not limited by the finite element system bandwidth.

Abstract

Abstract A novel domain decomposition approach for the parallel finite element solution of equilibrium equations is presented. 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 nodes. In the static case, each floating subdomain induces a local singularity that is resolved in two phases. First, the rigid body modes are eliminated in parallel from each local problem and a direct scheme is applied concurrently to all subdomains in order to recover each partial local solution. Next, the contributions of these modes are related to the Lagrange multipliers through an orthogonality condition. A parallel conjugate projected gradient algorithm is developed for the solution of the coupled system of local rigid modes components and Lagrange multipliers, which completes the solution of the problem. When implemented on local memory multiprocessors, this proposed method of tearing and interconnecting requires less interprocessor communications than the classical method of substructuring. 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.