Lecture SS 25 Selected Topics in Scientific Computing
Parallel adaptive mesh refinement
Requirements: Basic theory on the discretization of PDEs such as Laplace's equation; programming skills: variables, arrays, structured types, loops, functions.
In this lecture we focus on the concept of the computational mesh. The mesh subdivides a domain of interest into cells. In the simplest case it looks just like the grid of a checkerboard, but near arbitrary generalizations are possible. Many may have seen a triangulation of a curved surface in space, maybe in trivial contexts like TV commercials. The construction of virtually every large building, engineering structure, or vehicle makes use of meshes at some point.
The mesh is universally useful since it can be used to further define a discrete function space or another set of variables, where degrees of freedom are associated with cells in a well defined way. We may then use the discrete space to approximate the solution of a PDE, or continue to work on computational geometry or graphics problems. In this lecture, we place a special interest on the parallelization of the mesh, that is, its storage as disjoint sets of primitives that live on the various processors of a parallel computer. We will also consider adaptive meshes, that is, local refinement and coarsening by recursive concepts. We hope to illustrate how adaptivity and parallelism combine into efficient and generic tools for high performance computing.
This class is without exercises, but we may repurpose some of the lecture time for community practical programming.