# Seminar WS 23/24 Graduate Seminar on Efficient Simulation

## Parallel Algorithms for Adaptive Mesh Refinement

The numerical simulation of physical systems leads to several challenges when the simulation is supposed to be realistic: (a) The shape of the domain is usually three-dimensional and not just a simple cube, (b) the discretization with high resolution lead to systems of equations with a lot of unknowns (say 1e10), and (c) the resolution may need to be finer in some areas of the domain than in others and (d) the areas of highest resolution may move with time. Examples are the stress analysis of a bridge or skyscraper and the tracking of flames or shocks in fluids, as well as geophysical simulations (of mantle convection, earthquakes, or atmospheric waves).

In this graduate seminar we will assume that the finite element or finite volume method to solve a basic partial differential equation (such as Poisson’s) is understood on a cubic domain. We will revisit the basics and then move on to the topics of mesh generation (addressing a), parallelization and scalable solvers (b) and adaptivity (c, d).

This seminar will expand the students’ knowledge on computational geometry, high performance parallel computing and state-of-the art techniques for adaptive mesh refinement and numerical solution of PDEs.

The lecture Wissenschaftliches Rechnen I (V3E1/F4E1) as well as one class out of Wissenschaftliches Rechnen II (V3E2/F4E2), Numerical Simulation (V4E1) or Numerical Algorithms (V4E2) are prerequisites. We may discuss the requirements further in the Vorbesprechung.

The seminar takes place on Mondays at 14 Uhr c.t. in FHA7 2.035. An initial meeting (Vorbesprechung) takes place in that room on Monday, October 9th 2023 at 14 c.t.