An Adaptive, 3-Dimensional, Hexahedral Finite Element Implementation for Distributed Memory

Abstract

Abstract. Finite elements are an effective method to solve partial differential equations. However, the high computation time and memory needs, especially for 3-dimensional finite elements, restrict the usage of sequential realizations and require efficient parallel algorithms and implementations to compute real-life problems in reasonable time. Adaptivity together with parallelism can reduce execution time significantly, however may introduce additional difficulties like hanging nodes and refinement level hierarchies. This paper presents a parallel adaptive, 3-dimensional, hexahedral finite element method on distributed memory machines. It reduces communication and encapsulates communication details like actual data exchange and communication optimizations by a modular structure.