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Lecture WS 19/20 Numerical Algorithms

Advanced Techniques for the Numerical Solution of PDEs

Lecturer
Prof. Carsten Burstedde
Contact for exercises
Christopher Kacwin
Date
Tuesday, 10 to 12 c.t. and Thursday, 8:30 to 10:00 in room 2.035 (INS, Endenicher Allee 19b).
Tutorial
Wednesday, 8:30 to 10:00 in room 1.008 (Mathematikzentrum).

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.

The oral exams will take place on January 27–29th and on March 25/26th, 2020.