A CUDA/C++ implementation of the Discontinuous Galerkin method as presented in the book:

Nodal Discontinuous Galerkin Methods - Algorithms, Analysis, and Applications, Jan S. Hesthaven and Tim Warburton, Springer, 2008

The code, built by g++ 7.5.0 and CUDA 10.2, was tested on NVIDIA Volta GPU (CUDA Capability 7.2). It can be configured to run on GPU or CPU-only by the flag USE_CPU_ONLY defined in /src/config.h.

The code adopts the "one-thread-per-element" strategy for parallelization - each thread performs computations for a single element. Layouts of degree-of-freedoms (DOFs) in the solution vectors promote coalesced memory access. CUDA constant memory is used to store small-sized, but frequently accessed, data to improve performance.

The code contains only header files in the /src folder and there is no third-party dependencies except CUDA. A few example problems are provided in the /examples folder. To build and run these examples, go to the individual subfolder and run make. If your CUDA installation directory is different from /usr/local/cuda-10.2, change the path of CUDA_PATH accordingly in the makefile.

In the subfolder of each example, there is a PDF file describing the problem, the boundary and initial conditions, the analytical solutions (if any), the meshes, and the performance results.

Example problems:

• Stokes equation in 2D
• Incompressible Navier-Stokes equation in 2D

3D problems will be covered by a future repository (flux-reconstruction-schemes).