Scientific Computing Master of Science an der Universität Bayreuth

Numerical Methods for General Types of PDEs

Continuation of A1 focused on non-conforming, mixed finite element methods, finite element methods for Navier-Stokes equations, and finite volume methods for realistic applications.

Discontinuous and Multiscale Methods for PDEs

Covers discontinuous Galerkin finite element methods for hyperbolic and parabolic PDEs and efficient numerical treatment of multiscale problems including homogenization and heterogeneous multiscale methods.

Constructive Approximation Methods

Teaches multivariate approximation methods including radial basis functions, moving least-squares methods, and partition of unity methods with error analysis and implementation.

Mathematical Control Theory

Covers methods and concepts of mathematical control theory including controller design techniques from linear algebra, optimal control, and Lyapunov functions.

Nonlinear Optimization

Teaches optimality conditions and algorithms for unconstrained and constrained nonlinear optimization problems with practical applications.

Optimization of Partial Differential Equations

Covers derivation and analysis of optimality conditions for PDE optimization problems including linear-quadratic problems and basic numerical methods.

Partial Differential Equations and Integral Equations

Teaches existence, uniqueness and properties of solutions for integral equations and various types of PDEs including parabolic, wave, and Schrödinger equations.

Modeling with Differential Equations

Covers general modeling principles and applications of differential equations in mathematical biology, mechanics, physics, and finance.

Mathematical Modeling for Climate and Environment

Teaches physical principles and mathematical models for climate and environmental sciences including earth system components and hierarchy of climate models.

Ergodic Theory and Data Science

Covers measure-theoretic analysis of dynamical systems including transfer operators, Koopman operators, and data-based approximation methods.

Pattern Recognition

Teaches advanced methods for pattern recognition and classification in data including Bayesian classification, neural networks, and supervised/unsupervised learning.

Mechanics of Continua

Covers fundamental concepts of continuum mechanics including stress tensors, Euler and Navier-Stokes equations with applications to turbulence and microfluids.

Molecular Dynamics Simulations of Biophysical Systems

Teaches theoretical background and practical application of molecular dynamics simulations including Verlet integration, force fields, thermostating, and coarse-graining methods.

Bioinformatics: Molecular Modeling

Covers theoretical foundations and numerical methods for molecular modeling including molecular dynamics, energy minimization, quantum chemistry, and biochemical reactions.

Foundations of Bioinformatics

Teaches basic bioinformatic applications including database searching, sequence alignments, phylogenetic trees, structure prediction, and drug design.

Quantum Chemistry: Methods and Algorithms

Covers theoretical foundations of quantum chemistry including LCAO approach, density functional theory, basis sets, and self-consistent field algorithms.

Advanced Strength of Materials

Teaches theory of elasticity, material models, plastic design, stress analysis, strength hypotheses, and operational strength under static and cyclic loading.

Computer Aided Engineering

Numerical Methods for Partial Differential Equations

Lays ground to the programme by teaching finite difference and finite element methods for partial differential equations including convergence analysis and multigrid methods.

Applied Functional Analysis

Teaches basic solution spaces for partial differential equations including Sobolev spaces, weak solutions, and spectral theory for compact operators.