Work

Enhancing the Nektar++ spectral/hp element framework for parallel-in-time simulations

Year: 2025

Type: article

Abstract: We describe the efficient implementation of the Parareal algorithm in the Nektar++ software, an open-source spectral/hp element framework for the solution of partial differential equations, which has been designed to achieve high-scalability on high-performance computing (HPC) clusters using distributed parallelism. Recently, time-parallel integration techniques are being recognized as a potential solution to further increase concurrency and computational speed-up beyond the limits of strong scaling obtained from a pure spatial domain decomposition. Amongst the various time-parallel approaches proposed in the literature, the Parareal algorithm is a non-intrusive and iterative approach, exploiting a fine and a coarse solvers to achieve time-parallelism, and can be applied to both linear and non-linear problems. We discuss the details of the implementation and discuss the specific techniques used to adapt the code to a time-parallel framework. We demonstrate the application of these methods to multiple linear and non-linear problems provided by the existing Nektar++ solvers.

Source: Computer Physics Communications

DOI: 10.1016/j.cpc.2025.109584

Authors: Jacques Y. Xing, Chris D. Cantwell, David Moxey

Institutions: King's College London, Imperial College London

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,160

Funder: UK Research and Innovation