Accelerated solution of stiffness matrix for isoparametric elements based on CUDA

Abstract

High precision results in structural with the shortest time consumption are expected when methods are introduced to solve FEM(Finite element method). Solving of stiffness matrix assembled by isoparametric elements and solving the assembled stiffness matrix are the most time-consuming. In the previous serial algorithms, there is always a time limitation for some applications and it is hard to achieve. However, break-through in programming and feasibility of general-purpose applications executed on GPU (Graph Processing Unit), such as the parallel computing platform and programming model CUDA (Compute Unified Device Architecture) released by NVIDIA corporation, make it possible for some large scale FEM explicit dynamic simulation in real time. Authors present an approach to accelerate calculation in element stiffness matrices, taking the three-dimensional hexahedral isoparametric element in different scale as an example. A speedup of about 15 times is achieved with respect to parallel algorithms using boost on CPU. The results show that the parallel algorithm based on CUDA can satisfy the fast simulation of finite element model of structural problems with certain computational scale.