An object oriented parallel finite element scheme for computations of PDEs: Design and implementation

TL;DR

This paper presents an object-oriented parallel finite element scheme with a novel data structure, enabling efficient large-scale PDE computations on supercomputers, and demonstrates its performance and scalability.

Contribution

The paper introduces a new object-oriented data structure for parallel finite element methods, including a parallel geometric multigrid solver, implemented in the ParMooN package.

Findings

Good speedup up to 960 processors

Effective handling of large-scale problems on supercomputers

Performance analysis up to 1080 processors

Abstract

Parallel finite element algorithms based on object-oriented concepts are presented. Moreover, the design and implementation of a data structure proposed are utilized in realizing a parallel geometric multigrid method. The ParFEMapper and the ParFECommunicator are the key components of the data structure in the proposed parallel scheme. These classes are constructed based on the type of finite elements (continuous or nonconforming or discontinuous) used. The proposed solver is compared with the open source direct solvers, MUMPS and PasTiX. Further, the performance of the parallel multigrid solver is analyzed up to 1080 processors. The solver shows a very good speedup up to 960 processors and the problem size has to be increased in order to maintain the good speedup when the number of processors are increased further. As a result, the parallel solver is able to handle large scale problems on massively parallel supercomputers. The proposed parallel finite element algorithms and multigrid solver are implemented in our in-house package ParMooN.