A flexible sparse matrix data format and parallel algorithms for the assembly of sparse matrices in general finite element applications using atomic synchronisation primitives

TL;DR

This paper introduces a new flexible sparse matrix format and parallel algorithms utilizing atomic primitives to efficiently assemble global stiffness matrices in finite element methods on shared memory systems.

Contribution

It presents a novel sparse matrix storage format and parallel assembly algorithms that leverage atomic synchronization for improved performance in finite element applications.

Findings

The new storage format outperforms compressed row storage in benchmarks.

Atomic-based algorithms achieve data-race free parallel assembly.

Performance varies with matrix size and sparsity patterns.

Abstract

Finite element methods require the composition of the global stiffness matrix from local finite element contributions. The composition process combines the computation of element stiffness matrices and their assembly into the global stiffness matrix, which is commonly sparse. In this paper we focus on the assembly process of the global stiffness matrix and explore different algorithms and their efficiency on shared memory systems using C++. A key aspect of our investigation is the use of atomic synchronization primitives for the derivation of data-race free algorithms and data structures. Furthermore, we propose a new flexible storage format for sparse matrices and compare its performance with the compressed row storage format using abstract benchmarks based on common characteristics of finite element problems.