Core Courses
The scope of numerical mathematics ranges from the design of numerical methods, their analysis, the incorporation of optimization techniques, to the use of complex methods for simulating problems from applications (scientific computing). The BMS Core Course sequences in RTA 6 introduce major concepts for the design of numerical methods and their analysis concerning stability, convergence, and efficiency. Advanced methods, which are derived from the basic ones, have been and will be utilized in many projects. This area provides a strong link to partners from engineering, the natural sciences, and industry.
Nonlinear Optimization
This course presents the mathematical foundations and numerical methods for several classes of nonlinear optimization problems. Both, unconstrained and constrained problems are covered.
This course covers numerical methods for initial value problems with ordinary differential equations. It discusses, e.g., explicit and implicit Runge-Kutta schemes, stability analysis, and multi-step methods. In addition, advanced topics from numerical linear algebra will be presented, e.g., iterative solvers for linear systems of equations or numerical methods for differential-algebraic equations.
Numerical Methods for PDEs
This course discusses numerical methods for boundary value problems with partial differential equations. Important aspects are approaches like finite difference, finite element, and finite volume methods and their numerical analysis.
Spectrum of Advanced Courses
Advanced Finite Element Methods, Uncertainty Quantification, Numerical Analysis of PDAEs, Optimal Control of PDEs, Control Theory, Theory and Numerics of Non-Smooth Optimization, Variational Inequalities, Inverse Problems
