Mesh Partitioning and Efficient Equation Solving Techniques by Distributed Finite Element Methods: A Survey

The mesh partitioning in parallel Finite Element Method (FEM) is an NP-hard problem. During the past few decades, several heuristic approaches have been proposed to address this problem. In addition to mesh distribution, solving a large set of algebraic equations also significantly contributes to the performance of a parallel solution. A number of efficient equation solving techniques are developed which exploit inherent properties of large coefficient matrices (for instance, symmetry and positive definiteness). In the present study, the performance of a distributed FEM system on the basis of the mesh partitioning approaches and equation solvers is discussed. The work contributes towards: (i) categorizing mesh partitioning methods, (ii) examining implementation variations in linear and nonlinear solution of equations, and (iii) exploring the impact of mesh partitioning and an equation solver on the performance of a distributed FEM system.