PhD transfer exam | Andrew Giuliani, Efficient adaptive mesh algorithms for the discontinuous Galerkin (DG) method for solving nonlinear hyperbolic conservation laws on graphics processing units (GPUs)

Efficient adaptive mesh algorithms for the discontinuous Galerkin (DG) method for solving nonlinear hyperbolic conservation laws on graphics processing units (GPUs)

In the natural sciences, many physical phenomena such as fluid behaviour can be described with conserved quantities, e.g. mass, momentum and energy.  Hyperbolic conservation laws are a type of partial differential equation (PDE) that result from this conservation property. The Euler equations of gas dynamics are one notable example; they can be used to describe the flow around an airfoil or aircraft. Because the solutions of these equations may exhibit shocks or discontinuities, a numerical method that can accurately represent such features is needed. The discontinuous Galerkin (DG) method is a high-order method without an extensive stencil that can successfully describe shocks. In the Scientific Computing research group of Applied Mathematics, we have software implementing the DG method on NVIDIA GPUs in CUDA C. This seminar will focus on the current work being done to extend this high-performance software to support h-adaptivity, whereby the mesh is spatially refined. Future avenues of research will also be discussed relative to mesh adaptivity such as p-enrichment and adaptivity indicators.