A CPU–GPU framework for optimizing the quality of large meshes

Abstract

The automatic generation of 3D finite element meshes (FEM) is still a bottle neck for the simulation of large fluid-dynamic problems. Although today there are several algorithms that can generate good meshes without user intervention, in cases where the geometry changes during the calculation and thousands of meshes must be constructed, the computational cost of this process can exceed the cost of the FEM. There has been a lot of work in FEM parallelization and the algorithms work well in different parallel architectures, but at present there has not been much success in the parallelization of mesh generation methods. This paper will present a massive parallelization scheme for re-meshing with tetrahedral elements using the local modification algorithm. This method is frequently used to improve the quality of elements once the mesh has been generated, but we will show it can also be applied as a re-generation process, starting with the distorted and invalid mesh of the previous step. The parallelization is carried out using OpenCL and OpenMP in order to test the method in multiple CPU architecture and also in Graphic Processors (GPU). Finally we present the speedup and quality results obtained in meshes with hundreds of thousands of elements and different parallel APIs.