A robust solver for large-scale heat transfer topology optimization

TL;DR

This paper introduces a scalable parallel solver for heat transfer topology optimization that significantly improves convergence and speed in high-resolution, high-contrast problems using advanced preconditioning and interpolation techniques.

Contribution

The paper presents a novel large-scale parallel solver with a multiscale multigrid preconditioner and interpolation method, optimized for high-contrast heat transfer topology problems.

Findings

Achieves over 2x speedup compared to default PETSc multigrid.

Effectively handles high-contrast coefficient fields.

Demonstrates robustness and efficiency up to 1024^3 resolution.

Abstract

This paper presents a large-scale parallel solver, specifically designed to tackle the challenges of solving high-dimensional and high-contrast linear systems in heat transfer topology optimization. The solver incorporates an interpolation technique to accelerate convergence in high-resolution domains, along with a multiscale multigrid preconditioner to handle complex coefficient fields with significant contrast. All modules of the optimization solver are implemented on a high performance computing cluster by the PETSc numerical library. Through a series of numerical investigations, we demonstrate the effectiveness of our approach in enhancing convergence and robustness during the optimization process, particularly in high-contrast scenarios with resolutions up to $1024^3$. Our performance results indicate that the proposed preconditioner achieves over $2\times$ speedup against the default algebraic multigrid in PETSc for high-contrast cases.