Graphics Processing Unit-Based Element-by-Element Strategies for Accelerating Topology Optimization of Three-Dimensional Continuum Structures Using Unstructured All-Hexahedral Mesh

Abstract

Topology optimization has been successful in generating optimal topologies of various structures arising in real-world applications. Since these applications can have complex and large domains, topology optimization suffers from a high computational cost because of the use of unstructured meshes for discretization of these domains and their finite element analysis (FEA). This paper addresses this challenge by developing three GPU-based element-by-element strategies targeting unstructured all-hexahedral mesh for the matrix-free precondition conjugate gradient (PCG) finite element solver. These strategies mainly perform sparse matrix multiplication (SpMV) arising with the FEA solver by allocating more compute threads of GPU per element. Moreover, the strategies are developed to use shared memory of GPU for efficient memory transactions. The proposed strategies are tested with solid isotropic material with penalization (SIMP) method on four examples of 3D structural topology optimization. Results demonstrate that the proposed strategies achieve speedup up to 8.2× over the standard GPU-based SpMV strategies from the literature.

Development of GPU‐based matrix‐free strategies for large‐scale elastoplasticity analysis using conjugate gradient solver

“…In literature, three kinds of thread assignment have been used: single thread per element, threads equal to total DOFs per element, and threads equal to total nodes per element. The work presented in Reference 51 shows single thread per element strategy performing poorly than the other two. Therefore, the current work explores the remaining two types of thread assignment.…”

“…In another work, 50 $$$ EbE $$$ strategy for unstructured mesh problems is proposed which uses only symmetric part of elemental matrices for computation, reducing the storage requirement as well as global memory access. A detailed analysis of thread allocation strategy in $$$ EbE $$$ matrix‐free solver is presented in Reference 51, where allocation of eight threads per element is recommended for linear hexahedral element. In a recent work, 52 matrix‐free FEM is used to solve up to 500 million DOFs numerical homogenization problem with preconditioned CG solver based on $$$ EbE $$$ and $$$ NbN $$$ strategies.…”

Acceleration of structural topology optimization using symmetric element-by-element strategy for unstructured meshes on GPU

“…A maximum speedup of 7.83 was reported for a finite element model with 15,630,336 hexahedral elements using the same computational setup. Recently, Ratnakar et al (2022) presented three GPUbased EbE strategies targeting unstructured all-hexaheal mesh for the matrix-free precondition conjugate gradient finite element solver. The proposed strategies perform SpMV operation by allocating more compute threads of GPU per element.…”