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

Abstract

PurposeStructural topology optimization is computationally expensive due to the involvement of high-resolution mesh and repetitive use of finite element analysis (FEA) for computing the structural response. Since FEA consumes most of the computational time in each optimization iteration, a novel GPU-based parallel strategy for FEA is presented and applied to the large-scale structural topology optimization of 3D continuum structures.Design/methodology/approachA matrix-free solver based on preconditioned conjugate gradient (PCG) method is proposed to minimize the computational time associated with solution of linear system of equations in FEA. The proposed solver uses an innovative strategy to utilize only symmetric half of elemental stiffness matrices for implementation of the element-by-element matrix-free solver on GPU.FindingsUsing solid isotropic material with penalization (SIMP) method, the proposed matrix-free solver is tested over three 3D structural optimization problems that are discretized using all hexahedral structured and unstructured meshes. Results show that the proposed strategy demonstrates 3.1× –3.3× speedup for the FEA solver stage and overall speedup of 2.9× –3.3× over the standard element-by-element strategy on the GPU. Moreover, the proposed strategy requires almost 1.8× less GPU memory than the standard element-by-element strategy.Originality/valueThe proposed GPU-based matrix-free element-by-element solver takes a more general approach to the symmetry concept than previous works. It stores only symmetric half of the elemental matrices in memory and performs matrix-free sparse matrix-vector multiplication (SpMV) without any inter-thread communication. A customized data storage format is also proposed to store and access only symmetric half of elemental stiffness matrices for coalesced read and write operations on GPU over the unstructured mesh.

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

“…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. Apart from the aforementioned works, there are numerous other research works that show significant computational performance by matrix‐free solvers with GPUs in wide range of areas like elasticity, 48,49 topology optimization, 53,54 earthquake simulation, 55 fluid mechanics 56 and so forth.…”