Parallelization of Finite Element Method on Graphics Processing Unit

Abstract

Abstract newlineFinite Element Analysis (FEA) is an integral part of engineering simulations such as newlinestructures, biomedical implants, vehicles, to mention but a few. Finite Element Method newline(FEM) is a widely used numerical solution technique to find the solution for the Partial newlineDifferential Equations (PDEs) arising from different fields of science and engineering. newlineFor complex problems the solution using FEM is sluggish on single core computers. newlineOver a decade parallelization of the FEM has been carried out by the High Performance newlineComputing (HPC) community to achieve many-fold improvement in the performance. newlineMost of the computations involved in FEM pipeline are of Single Instruction Multiple newlineData (SIMD) type. These kind of computations favor parallelization on shared memory newlineparallel architectures. Graphics Processing Unit (GPU)1 is a shared memory parallel architecture newlinewhich basically supports the SIMD computing pattern. Over a decade GPU newlinecomputing has been extensively adopted to accelerate the science and engineering applications newlinesuccessfully. newlineAll the FEM pipeline stages are efficiently deployed on the GPU over a decade. We newlinehave performed a comprehensive literature survey for parallelization of FEM on the newlineGPU and presented a constructive review on each stage FEM pipeline. The assembly newlineand the solver are the most computationally intensive stages of the FEM pipeline, hence newlinemost of the literature concentrated on these topics to accelerate the FEA procedure. The newlinesolver stage is often performed using Conjugate Gradient (CG) type iterative solver. A newlinecompute intensive Sparse Matrix Vector Multiplication (SpMV) is encapsulated in the newlineCG solver. We have highlighted some of the prominent sparse matrix storage formats newlineand their corresponding SpMV strategy on the GPU. Furthermore, different preconditioning newlinetechniques to improve the convergence rate of the CG solver and their construction, newlineapplication and parallel implementation are also discussed. In addition to this newline1When we say GPU, it referred as NVIDIA GPU throughout the thesis un