Alternate Parallel Processing Approach for FEM

In this work we present a new alternate way to formulate the finite element method (FEM) for parallel processing based on the solution of single mesh elements called FEM-SES. The key idea is to decouple the solution of a single element from that of the whole mesh, thus exposing parallelism at the element level. Individual element solutions are then superimposed node-wise using a weighted sum over concurrent nodes. A classic 2-D electrostatic problem is used to validate the proposed method obtaining accurate results. Results show that the number of iterations of the proposed FEM-SES method scale sublinearly with the number of unknowns. Two generations of CUDA enabled NVIDIA GPUs were used to implement the FEM-SES method and the execution times were compared to the classic FEM showing important performance benefits.

I. Introduction

Solving increasingly complex electromagnetic (EM) problems using modern computing resources inevitably requires employing parallel programming paradigms in response to the current trend of advances in microprocessor architecture. The advent of the multicore/manycore processors brings about an important turning point in programming practices; in particular, for EM practitioners and the scientific community this translates to rewriting legacy libraries and applications with new parallel formulations that can efficiently realize the performance benefits offered by these modern computing resources as shown recently in [1], [2]. This work focuses on the finite element method (FEM), a popular numerical simulation technique, and proposes an alternate way for solving the linear systems derived that is well suited for parallel manycore (graphic processing unit-GPU) implementations. The remaining sections describe the new proposed method, sources of parallelism, its advantages and current limitations and the GPU implementations details. Finally the results and conclusions are presented.