A Preconditioned Conjugate Gradient Multigrid Method for Multi-material Topology Optimization

In recent years, there has been significant progress in the field of topology optimization, with many researchers focusing on improving the computational efficiency of this method through numerical algorithms. Concurrently, the realm of high-performance computing (HPC) has experienced dynamic changes, with manufacturers, systems, and architectures continually evolving. Among the various methods employed in HPC, the preconditioned conjugate gradient multigrid method (pCGMG) has gained popularity, particularly for addressing very large-scale problems. This article introduces a novel concept of leveraging HPC to reduce the computational time associated with multi-material topology optimization (MTO) challenges. In the context of MTO procedures, pCGMG is employed to solve the linear equations resulting from the discretization of differential equations. Notably, pCGMG’s effectiveness is particularly evident in larger-scale problems due to its mesh size-based approach. The study specifically evaluates minimal compliance-based designs for large-scale linear static systems. Its primary contribution lies in the integration of pCGMG into the MTO problem domain. The article includes numerical examples that utilize pCGMG to compare optimal results of iteration count and execution time for various mesh sizes in the context.