Summer Argonne Students Symposium (SASSy) Part I
Discretization Effects on Accuracy and Efficiency of the Spectral Element Method
The Spectral Element Method regarded as a high-order refinement of the Finite Element Method is based on a representation of the solution as a linear combination of polynomial basis functions over Gaussian-type grids. In this context we define such a non-uniform grid as being a grid over which integration can be performed with spectral accuracy.
The specific case under consideration is a grid given by the Gauss-Legendre-Lobatto(GLL) points, which has a point distribution clustered at the end of the boundaries and sparse in the center. Such grids lead to high CFL contraints when used in the discretization of advection equations. GLL grids also lead to large or singular Jacobians when mapped to and from irregular geometries. To deepen the understanding of the impact such grids have on canonical partial differential equation we assessed convection and diffusion problems in one and two dimensions.
The Cost of Adjoint Checkpointing