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.

翻译：本文提出了一种大规模并行求解器，专门用于解决传热拓扑优化中高维高对比度线性系统的求解难题。该求解器采用插值技术以加速高分辨率域中的收敛，并结合多尺度多重网格预处理器来处理具有显著对比度的复杂系数场。优化求解器的所有模块均通过PETSc数值库在高性能计算集群上实现。通过一系列数值实验，我们证明了该方法在优化过程中（特别是在分辨率高达$1024^3$的高对比度场景下）对提升收敛性与鲁棒性的有效性。性能测试结果表明，对于高对比度案例，所提出的预处理器相较于PETSc默认的代数多重网格方法实现了超过$2\times$的加速比。