Parallel Direct Domain Decomposition Methods (D3M) for Finite Elements

Abstract: A parallel direct solution approach based on domain decomposition method (DDM) and directed acyclic graph (DAG) scheduling is outlined. Computations are represented as a sequence of small tasks that operate on domains of DDM or dense matrix blocks of a reduced matrix. These tasks can be statically scheduled for parallel execution using their DAG dependencies and weights that depend on estimates of computation and communication costs. Performance comparison with MUMPS 5.1.2 on electrically large problems suggest up to 20% better parallel efficiency, 30% less memory and slightly faster in run-time, while maintaining the same accuracy.