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

• The development of a framework to optimize tetrahedral meshes in parallel.
• A proposal of a family of local topology operators that improve the mesh quality.
• An implementation of a non-Laplacian smoothing method on the GPU.
• A scheduling algorithm for processing and updating mesh structures in parallel.

The automatic generation of 3D finite element meshes (FEM) is still a bottleneck 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 regeneration 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 a multiple CPU architecture and also in Graphics Processing Units (GPUs). Finally we present the speedup and quality results obtained in meshes with hundreds of thousands of elements and different parallel APIs.