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Lecture WS 23/24 Numerical Algorithms

Techniques for the Numerical Solution of PDEs

Prof. Carsten Burstedde
Contact for exercises
Hannes Brandt
Tuesday, 10 c.t. and Thursday, 8:30 to 10:00 in room 2.035 (INS, Friedrich-Hirzebruch-Allee 7).
Tuesday, 16 c.t. in room N0.003 (Endenicher Allee 60) - Please hand in the exercise sheets until Tuesday, 11:45 either in the lecture or in the Brand(t)/Breiden mailbox on the third floor (opposite of room 3.007)
Final lecture
Thursday, Feb 1st, at 14 c.t. under: Big Blue Button

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.

For the first programming exercise, 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