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

2025-08-13

AI Summary

Conventional time-stepping approaches suffer from low computational efficiency for topology optimization of large-scale transient heat conduction problems. Method: This paper proposes a spatiotemporal coupled finite element framework: treating time as an additional spatial dimension and employing a stabilized continuous Galerkin spacetime discretization to construct a fully implicit system. For the first time in topology optimization, a space–time multigrid preconditioner with semi-coarsening is introduced to enable truly parallel-in-time solution; integrated with Krylov subspace solvers, the method achieves full parallelization on distributed-memory supercomputers. Contribution/Results: The approach exhibits strong scalability, successfully solving billion-degree-of-freedom problems. On benchmark cases, it achieves up to 52× speedup over traditional time-stepping methods, with controlled growth in computational cost. Robustness and material layout flexibility are validated under both steady-state and dynamic design scenarios.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

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.

Problem

• Optimizing time-dependent thermal conduction with large-scale topology
• Solving space-time finite element systems using parallel multigrid preconditioning
• Reducing computational time for transient thermal design optimization

Innovation

• Space-time finite element discretization
• Parallel space-time multigrid preconditioner
• Semi-coarsening strategy for scalability