Learning outcomes
Students will remember the basic principles of solving numerical problems in materials science. They memorize the numerical solution strategies for different problems and are able to analyse, select and apply appropriate numerical strategies for a wide variety of numerical modelling tasks in materials science, from the electronic structure to continua. The students appraise the unified, holistic approach to materials simulation which is not centered on or limited to a particular length scale. Furthermore, the students assess and evaluate given numerical problems in materials science and devise and implement optimal solutions.
Subject aims
Numerical methods are the foundation of materials simulation and necessary for the implementation of materials theory and its application to practical problems. The principles of numerical methods are independent of length scale, i.e. the solutions of electronic, atomistic, microstructural and continuum problems often follow closely related strategies. In this course the focus is on numerical problems and challenges in materials science. Applications to different length scales are introduced
by way of example.
- Basics: Differentiation and integration, vectors and tensors, products and norms, series expansions
- Partial differential equations: Numerical integration for electrons, atoms and continuum models
- Variational calculus: Functional derivatives and derivation of partial differential equations
- Optimization: Optimization/root finding algorithms, methods for eigenvalue problems
- Regression and statistical analysis: Data analysis, error estimates, machine learning
- Kursleiter/in: Ralf Drautz
- Kursleiter/in: Christa Hermichen