Numerical Analysis and Scientific Computing seminar | Marty Fuhry, Discontinuous Galerin Methods on Graphics Processing Units

The Discontinuous Galerkin (DG) method has become popular in a wide range of problems due to its high-order accuracy and flexibility. In addition, DG methods handle finite elements independently, allowing for parallelization. While most high-performance computers cost thousands of dollars, recent developments in low-cost graphics processing units (GPUs) have reintroduced high performance computing to the masses. The current availability of software architectures such as CUDA has made programming GPUs much easier. We implement a DG method in CUDA using NVIDIA GPUs. We show example problems, specifically of the Euler equations, over unstructured meshes in two dimensions. We describe the algorithm, including memory management, data coalescion, and program structure.