Applied Mathematics Foundations (5,5 ECTS)

The aim of this module is to introduce basic mathematical concepts necessary for further studies. The focus is on a thorough introduction to partial differential equations, differential operators and vector analysis. Besides the module recalls concepts such as integration and function theory as well as calculus of calculus of variations, optimization and tensor calculus.

Numerical Computation (5,5 ECTS)

The module numerical computation introduces basic numerical solution methods and their algorithmic implementation. In particular solution techniques for linear and nonlinear systems, polynomial interpolation as well as error analysis will be discussed. Many applications will illustrate the theoretical foundations and help to understand the concepts.

Numerical Partial Differential Equations (7 ECTS)

Numerical partial differential equations belongs to the mathematical field of numerical analysis and covers the numerical solution of partial differential equations. The module treats the foundations of the numerical solution of partial differential equations. Solution methods such as the finite element method and the finite difference method are discussed. The theoretical methods are illustrated through numerous examples and applications and also practical implementations. After the successful participation students are able to solve partial differential equations with several methods.

This examination subject consists of only one module with the same name.

Scientific Computing (15 ECTS)

Numerical partial differential equations belongs to the mathematical field of numerical analysis and covers the numerical solution of partial differential equations. The module treats the foundations of the numerical solution of partial differential equations. Solution methods such as the finite element method and the finite difference method are discussed. The theoretical methods are illustrated through numerous examples and applications and also practical implementations. After the successful participation students are able to solve partial differential equations with several methods.

Parallel Computing (12 ECTS)

This module teaches basics and advanced topics in efficient programming for modern parallel computer architectures including shared-memory, large distributed-memory systems, as well as heterogeneous systems with accelerators. Common metrics for performance efficiency of parallel algorithms, design patterns for different computer architectures and barriers to enable parallelism are introduced through different didactic approaches. Further contents are the properties of the computer architectures which are important for the efficient use of a system (memory and cache), common interfaces for parallel computing (OpenMP and MPI, C++ threads), as well as scientific computing in python. Further, important libraries and tools are introduced.

Programming (5 ECTS)

This module teaches knowledge in programming with a focus on scientific computing. The module comprises lectures on basic Python programming and advanced programming in C++. The focus lies on basic programming concepts and programming styles. Important standard libraries are introduced and form a basis for the introduction and use of relevant external software packages. Basics of object-oriented programming and design patterns covered, as well as high performance aspects, library design, and interface design.

This module provides in-depth training to further develop numerical computational and simulation methods for the analysis, design, implementation and operation of the built environment. In order to be able to support decisions in the direction of a sustainable, reliable circular economy the following issues have to be evaluated: Aspects of interior quality (thermal, acoustic, visual comfort and air quality) over the long term. Minimizing risks of early failure (durability of structures under environmental exposure, and load bearing behavior even under extreme events or in case of fire). Analyzing the effects of changes in social structure on the building stock or utilization of the infrastructure (mobility, energy supply) in the urban and rural context. Numerical methods are applied to all system components: in the forecasting of macro and microclimate, in the behavior of people in buildings, in the forecast of the modal split, in the effects of a construction’s heat and mass flux on factors such as deformation, physical, chemical and biological corrosion, and in the utilization of transport and energy supply systems.

This module focuses on the techniques required to understand and predict the properties of condensed matter based on atomistic calculations, both for molecular and for solid-state systems. It consists of two mandatory introductory courses to lay the groundwork and of specialization courses dealing with the conceptual background and the implementation of the most relevant topics in quantum chemistry, electronic structure and atomistic simulations as used in academia and industry today.

This selective module provides academic training in the field of simulation-intensive topics of computational electronics. An introduction into semiconductor physics and semiconductor devices as well as the finite element method are mandatory and are covered at the beginning. Electives allow a specialization for simulation of semiconductor devices, semiconductor sensors, micro- and nanoelectromechanical systems, and multi-field problems. A discussion of current research questions is enabled by including seminar classes and internships among the catalog of elective classes.

The module will introduce fundamental concepts of Computational Fluid Dynamics, aerodynamics and acoustics, starting from the governing physical principles up to their mathematical description, approximation and numerical solution. Specific attention will be given to the presentation of the different available numerical approaches for the study of compressible and incompressible fluid dynamics and aeroacoustics. Complex fluid flow behaviors, including transitional flow and turbulence, which are a current challenge for computational science and engineering, will be also considered.

This module teaches continuative concepts in the field of data management and solution strategies for efficient algorithms. After completion of the module students are able to elaborate problem-specific solutions for the analysis of large quantities of data, develop high-performance algorithms and identify current research topics.

This module broadens the knowledge in numerics and is built upon the modules Module Numerical Computation and Numerical Partial Differential Equations. Possible study tracks are the numerical solution of instationary problems, optimization with partial differential equations as well as the finite element method with a focus on applications. Moreover, the module introduces central aspects of modelling, algorithms, technology and methods for the solution of real-life applications. Students have the opportunity to work on state-of the-art research areas.

The module provides in-depth knowledge in the field of physical modelling and numerical simulation applying the finite element method for coupled problems, as they typically occur in the development of mechatronic systems (electromagnetic rail brakes, acoustics of air conditioning systems, piezoelectric MEMS loudspeakers, MEMS and NEMS pressure and viscosity sensors as well as microphones, electromagnetic induction systems for steel strip heating in production systems, etc.). The required physical background knowledge of mechanical, electromagnetic, fluid mechanical, thermal and acoustic fields as well as their couplings will be provided in order to be able to deal with concrete problems from practice. After successful completion of this module, students are able to identify research-relevant topics, create mathematical-physical models of real problems, solve them using suitable simulation programs and interpret the results in a physically correct way.

This module imparts in-depth knowledge on the application of numerical methods in the field of solid mechanics. Besides the fundamentals of the finite element method, students are taught the required theoretical knowledge to independently treat concrete research-related problems with suitable programs. Within the module students can choose between three thematic areas (Multiphysics, Material Modelling, Nonlinear Finite Element Methods).
After successful completion of the module, students are able to transfer actual technical problems into mathematical models, solve the underlying equations with appropriate programs, interpret the results, and write technical reports. Furthermore, they are qualified to implement finite element routines and to extend an existing finite element program with self- implemented modules.