Lecture WS 23/24 Numerical Algorithms
Techniques for the Numerical Solution of PDEs
Requirements: Numerische Mathematik (V2E1, V2E2), Wissenschaftliches Rechnen/Scientific Computing I or II (V3E1/2/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 fluids, including gases, or elastic solids. The well known Poisson equation can be derived this way as well.
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 adaptive, discontinuous and high-order discretizations. We will also cover the algorithmic techniques required for parallel computing.
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.