An analysis of domain decomposition methods using deal.II

Abstract

Iterative solvers have attracted significant attention since the mid-20th century as the computational problems of interest have grown to a size beyond which direct methods are viable. Projection methods, and the two classical iterative schemes, Jacobi and Gauss-Seidel, provide a framework in which many other methods may be understood. Parallel methods or Jacobi-like methods are particularly attractive as Moore's Law and computer architectures transition towards multiple cores on a chip. We implement and explore two such methods, the multiplicative and restricted additive Schwarz algorithms for overlapping domain decomposition. We implement these in deal.II software, which is written in C++ and uses the finite element method. Finally, we point out areas for potential improvement in the implementation and present a possible extension of this work to an agent-based modeling prototype currently being developed by the Air Force Research Laboratory's Autonomy Capability Team (ACT3).