Large-Scale Topology Optimisation of Time-dependent Thermal Conduction Using Space-Time Finite Elements and a Parallel Space-Time Multigrid Preconditioner

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Hauptverfasser: Alexandersen, Joe, Appel, Magnus
Format: Preprint
Veröffentlicht: 2025
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author Alexandersen, Joe
Appel, Magnus
author_facet Alexandersen, Joe
Appel, Magnus
contents This paper presents a novel space-time topology optimisation framework for time-dependent thermal conduction problems, aiming to significantly reduce the time-to-solution. By treating time as an additional spatial dimension, we discretise the governing equations using a stabilised continuous Galerkin space-time finite element method. The resulting large all-at-once system is solved using an iterative Krylov solver preconditioned with a parallel space-time multigrid method employing a semi-coarsening strategy. Implemented in a fully parallel computing framework, the method yields a parallel-in-time method that demonstrates excellent scalability on a distributed-memory supercomputer, solving problems up to 4.2 billion degrees of freedom. Comparative studies show up to 52x speed-up over traditional time-stepping approaches, with only moderate increases in total computational cost in terms of core-hours. The framework is validated on benchmark problems with both time-constant and time-varying designs, and its flexibility is demonstrated through variations in material properties. These results establish the proposed space-time method as a promising approach for large-scale time-dependent topology optimisation in thermal applications.
format Preprint
id arxiv_https___arxiv_org_abs_2508_09589
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Large-Scale Topology Optimisation of Time-dependent Thermal Conduction Using Space-Time Finite Elements and a Parallel Space-Time Multigrid Preconditioner
Alexandersen, Joe
Appel, Magnus
Computational Engineering, Finance, and Science
Optimization and Control
35Q93, 65M22, 65M32, 65M60, 65M55, 65Y05, 80M50
This paper presents a novel space-time topology optimisation framework for time-dependent thermal conduction problems, aiming to significantly reduce the time-to-solution. By treating time as an additional spatial dimension, we discretise the governing equations using a stabilised continuous Galerkin space-time finite element method. The resulting large all-at-once system is solved using an iterative Krylov solver preconditioned with a parallel space-time multigrid method employing a semi-coarsening strategy. Implemented in a fully parallel computing framework, the method yields a parallel-in-time method that demonstrates excellent scalability on a distributed-memory supercomputer, solving problems up to 4.2 billion degrees of freedom. Comparative studies show up to 52x speed-up over traditional time-stepping approaches, with only moderate increases in total computational cost in terms of core-hours. The framework is validated on benchmark problems with both time-constant and time-varying designs, and its flexibility is demonstrated through variations in material properties. These results establish the proposed space-time method as a promising approach for large-scale time-dependent topology optimisation in thermal applications.
title Large-Scale Topology Optimisation of Time-dependent Thermal Conduction Using Space-Time Finite Elements and a Parallel Space-Time Multigrid Preconditioner
topic Computational Engineering, Finance, and Science
Optimization and Control
35Q93, 65M22, 65M32, 65M60, 65M55, 65Y05, 80M50
url https://arxiv.org/abs/2508.09589