A study of efficient concurrent integration methods of B-Spline basis functions in IGA-FEM

TL;DR

This paper investigates efficient concurrent integration techniques for B-spline basis functions in IGA-FEM, focusing on parallelization strategies on hybrid memory systems like GPUs and clusters.

Contribution

It introduces novel methods for concurrent integration of B-spline basis functions, optimizing performance on hybrid memory architectures using trace theory and sum factorization.

Findings

Parallelization improves integration efficiency on GPUs.

Sum factorization enhances computational performance.

Strategies for practical implementation on modern clusters.

Abstract

Based on trace theory, we study efficient methods for concurrent integration of B-spline basis functions in IGA-FEM. We consider several scenarios of parallelization for two standard integration methods; the classical one and sum factorization. We aim to efficiently utilize hybrid memory machines, such as modern clusters, by focusing on the non-obvious layer of the shared memory part of concurrency. We estimate the performance of computations on a GPU and provide a strategy for performing such computations in practical implementations.