Numerical Analysis and Scientific Computing
Towing to the massive increase in computing power seen over the past decades, complex numerical simulations have become a key tool both in science and industry. This focus area introduces students to the mathematical and algorithmic foundations underlying numerical methods of various kinds. It comprises their rigorous mathematical analysis, often concerned with issues of stability, approximation, accuracy, and convergence. It also studies efficiency in terms of computational cost and gains in accuracy. Methods from areas of mathematics as diverse as differential geometry, functional analysis and stochastics are employed, as well as concepts from computer science.
Numerical analysis and computational mathematics is covered by the Seminar for Applied Mathematics (SAM). Particular research foci are numerical methods for partial differential equations (finite elements and boundary elements), methods for high-dimensional problems, structure preserving discretization, algorithms for uncertainty quantification (UQ), model-based machine learning, and inverse problems.
Basic courses
Recommended basic courses (usually attended during Bachelor's programme in the third year)
- Numerical Methods for Partial Differential Equations I (Elliptic and Parabolic Problems) (Autumn Semester)
- Numerical Methods for Partial Differential Equations II (Hyperbolic Problems) (Spring Semester)
It is also recommended to attend courses on functional analysis, the theory of partial differential equations, and probability theory.
Advanced courses
Some of these courses are not taught regularly, but some of them are offered each semester.
- Advanced Numerical Methods for CSE
- Mathematical and Computation Methods in Photonics
- Computational Electromagnetics
- Numerical Solution of Stochastic Differential Equations
- Inverse Problems
Algorithmic thinking is an essential component of computational mathematics. Therefore projects in this area will usually involve the software implementation and empiric study of numerical methods. Hence, programming skills in an all-purpose (C++, Pyhton) or domain specific (MATLAB, Julia) programming language are expected.