Efficient Representation of Computational Meshes

TL;DR

This paper introduces a versatile and efficient method for representing computational meshes using sets of mesh entities and their incidence relations, optimizing storage and computation for finite element analysis.

Contribution

The paper proposes a general, efficient mesh representation scheme and algorithms for incidence relation computation, adaptable to various mesh types including simplicial meshes.

Findings

Demonstrates improved CPU time and memory efficiency in benchmarks.

Provides a unified framework for mesh representation and incidence computation.

Facilitates parallel assembly of variational forms in finite element methods.

Abstract

We present a simple yet general and efficient approach to representation of computational meshes. Meshes are represented as sets of mesh entities of different topological dimensions and their incidence relations. We discuss a straightforward and efficient storage scheme for such mesh representations and efficient algorithms for computation of arbitrary incidence relations from a given initial and minimal set of incidence relations. The general representation may harbor a wide range of computational meshes, and may also be specialized to provide simple user interfaces for particular meshes, including simplicial meshes in one, two and three space dimensions where the mesh entities correspond to vertices, edges, faces and cells. It is elaborated on how the proposed concepts and data structures may be used for assembly of variational forms in parallel over distributed finite element meshes. Benchmarks are presented to demonstrate efficiency in terms of CPU time and memory usage.