A novel finite element method assembler for co-processors and accelerators

Abstract

Finite element method (FEM) is a popular approach to solving Differential equations [5]. Among its many attractive features is its ability to handle complex geometries. The domain is discretised using simple elements whose local contributions are assembled into a global system of equations. This is in contrast to the finite difference method (FDM) which can typically only handle regular geometries. However before solution is possible the system of equations of the FEM has to be assembled, a procedure which can be significant to the computational performance of the FEM solver, particularly when coupled with highly parallel execution [3]. In this work we outline a new algorithm for achieving a highly parallel assembler routine compatible with Intel® Xeon Phi and GPU architectures. We also present performance comparison and analysis of our algorithm and the globalNZ algorithm outlined by Cecka et al. in [2], as implemented on Intel Xeon Phi architecture and compare these to the serial implementation of Hughes [5]. © 2013 ACM.