# Lecture SS 24 Numerical Simulation

## Scalable and high performance computing

Requirements: Wissenschaftliches Rechnen/Scientific Computing I (V3E1/F4E1), basic programming skills.

In this lecture we consider partial differential equations (PDEs) that formalize the conservation of physical quantities, namely mass, momentum, and energy. Such equations arise for example from the physics of continuum mechanics. The well known Poisson equation can be derived this way. Vector-valued more gerenal forms describe for example the elasticity of solids or the velocity and pressure fields of viscous flow.

The goal of the lecture is to lead the students to a deeper understanding of essential modern and high-performance computational methods for the numerical solution of PDEs. In particular, we will discuss generalizations and extensions such as geometric mappings and mixed and high-order discretizations. We will also cover the algorithmic techniques required for large-scale computing, in particular multilevel preconditioning and adaptive mesh refinement.

This class will be accompanied by theoretical and programming exercises. The focus will not be on language details but on the succinct implementation of numerical principles.

For our programming exercises, you can use the following 3D example files p8est_box_tetgen.node p8est_box_tetgen.ele For 2D the Florida State University provides several examples under https://people.sc.fsu.edu/~jburkardt/data/triangle_files/triangle_files.html