Communication-Avoiding Krylov Techniques on GPUs

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