A GPU Parallel Finite Volume Method for a 3D Poisson Equation on Arbitrary Geometries

Abstract

In this paper, we present a parallelization technique developed to solve an unstructured-grid based Poisson equation on arbitrary three-dimensional geometries using CUDA over a GPU. The Poisson problem discretization is based on a second-order finite-volume technique on prisms elements, consisting of triangular grids in the horizontal direction and bounded by an irregular free surface and bottom in the vertical direction. The resulting linear system is solved using the Jacobi method, and the parallelization is designed by using different GPU memory management as shared, texture and managed memory. Numerical experiments are conducted to test and compare the performance of the proposed parallel technique.