Master's Programme Computational Science and Engineering

Course ID

UE 066 646 - Master's Programme Computational Science and Engineering

Duration of course

4 Semester

Credits

120 ECTS

Language

English

Certificate received upon completion

Master of Science

Course programme

Download Curriculum (in German)

Masterstudium_CSE.pdf pdf 194 KB

The steady progress in science and technology is increasingly dependent on computationally intensive computer simulations. Out of the need to perform these computer simulations precisely and quickly, Computational Science and Engineering has emerged internationally as an independent and interdisciplinary research area. It combines numerical and computer science with natural sciences and engineering to provide efficient computer simulations in a variety of civil engineering, chemical, electrical, mechanical, materials, mechatronics and physics applications, from single workstations to large scale computer systems Computational clusters and supercomputers.

The English master's programme Computational Science and Engineering teaches the necessary interdisciplinary as well as scientific and excellent specialist skills.

The master's programme Computational Science and Engineering is aimed at graduates of a scientific or technical bachelor's programme. Applicants should have a strong interest in the development and implementation of computer simulations. The basis for this is an enthusiasm for the development of efficient program codes for applied mathematics as well as for the physical modeling of complex systems.

The details of the admission requirements can be found in the curriculum.

The master's programme Computational Science and Engineering is suitable for graduates of a scientific or technical bachelor's programme.

Such bachelor's programmes at TU Wien are Civil Engineering, Electrical Engineering and Information Technology, Media Informatics and Visual Computing, Medical informatics, Software & Information Engineering, Computer Engineering, Mechanical Engineering, Technical Chemistry, Statistics and Mathematical Methods in Economics, Financial and Actuarial Mathematics, Technical Physics, Process Engineering, Geodesy and Geoinformation, Business Informatics and Mechanical Engineering - Management.

Other programmes are suitable as well, as long as they compare to one of the listed bachelor's programmes. In particular a programme is suitable if the following knowledge, skills and competencies amount to at least 30 ECTS:

  • Computer Science:
    • Programming languages (at least one): C; C++; Fortran; Java; Python.
    • Topics: Data Structures; Algorithms; Functions; Classes; Objectoriented Programming; Computer Architectures..
  • Mathematics:
    • Linear algebra with eigenvalue problems: matrix and vector calculus; Inverting matrices; Solving linear systems of equations; Determination of determinants, eigenvalues and eigenvectors.
    • Differential and integral calculus in one and several variables: real and complex numbers; Concept of function; sequences and series; Derivation in a variable; Integration in a variable; Power series; Gradients and total derivative; simple multidimensional domain integrals (rectangles, triangles).

Ordinary differential equations: linear differential equations; Solution by means of separation of the variables.

 

Further Information

Detailed information on the formal process and deadlines regarding the Application and Admission Procedure.

Persons whose native language is not English have to prove their knowledge of the English language. For a successful course of study, English is recommended according to reference level B2 (equivalent to the Austrian Matura level) of the Common European Framework of Reference for Languages. Some supplementary courses to obtain full equivalence of the completed studies are offered in German. Therefore, German language skills are recommended according to reference level B1 of the Common European Framework of Reference for Languages.

The aim of the Master’s degree program Computational Science and Engineering is to introduce students to  basic knowledge in the field of applied mathematics and informatics and to allow them to further specialize in at least two key areas which can be chosen from a transfaculty course portfolio (in alphabetical order):  Computational Building Science, Computational Chemistry and Material Science, Computational Electronics, Computational Fluid Dynamics and Acoustics, Computational Informatics, Computational Mathematics, Computational Mechatronics, Computational Solid Mechanics. These specializations enable students to complement their previous studies and furthermore allow them to focus on their personal interests and strengths.

Basic Modules

APPLIED MATHEMATICS

Applied Mathematics Foundations (4 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 (7 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.

SCIENTIFIC COMPUTING

Scientific Computing (15 ECTS)

This module teaches core competencies in the field of computational science and engineering. Important application fields are presented and the place of this master’s course is resorted in the spirit of the TU-Wien slogan “Technik für Menschen” with respect to its role in the context of digitization an ethical aspects. The main part of this module teaches a wide spectrum of techniques and methods constituting the groundwork for the other more specific modules of this master’s course “Computational Science and Engineering”.

COMPUTER SCIENCE

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.

Key Areas

Computational Mathematics  (15 ECTS)

This module broadens the knowledge in numerics and is build 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.

Computational Chemistry and Materials Science (15 ECTS)

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.

Computational Building Science (15 ECTS):

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.

Computational Electronics (15 ECTS)

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 sencors, 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.

Computational Fluid Dynamics and Acoustics (15 ECTS)

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.

Computational Mechatronics (15 ECTS)

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.

Computational Solid Mechanics (15 ECTS)

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

Computational Informatics (15,0ECTS)

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.

 

In case students complete more than 30 ECTS worth of key areas,  their restricts their ECTS points which can be accomplished within the module Free Electives and Transferable Skills to the same extent. However, students have to complete a minimum of 4.5 ECTS in the field of Transferable Skills.

Electives and Transferable Skills (10 ECTS)

These courses allow students to specialize in their chosen field and furthermore to obtain extracurricular knowledge, skills and competences.

Diploma Thesis (30 ECTS)

The aim of the diploma thesis is to demonstrate a student's ability to deal with a scientific topic independently meeting adequate standards of content and methodology. The theme of the thesis can freely be selected and has to be consistent with the qualification profile. The thesis has to be written in English language.

RECOMMENDED COURSE SEQUENCE

1st semester (WS)

VO Introduction to Computational Science and Engineering (3 ECTS)
VU Numerical Simulation and Scientific Computing (6 ECTS)
VU Scientific Programming with Python (2 ECTS)
VU Foundations of Applied Mathematics (4 ECTS)
VO Numerical Computation (4 ECTS)
UE Numerical Computation (3 ECTS)

2nd semester (SS)

VU Advanced Multiprocessor Programming (4,5 ECTS)
VU Numerical Simulation and Scientific Computing II (6 ECTS)
VO Numerical Methods for PDEs (4 ECTS)
UE Numerical Methods for PDEs (3 ECTS)

3rd semester (WS)

VU Computational Science on Many-Core Architectures (3 ECTS)
VU High Performance Computing (4,5 ECTS)
VU Advanced Programming with C++ (3 ECTS)

Please note that it it’s mandatory to attend lectures from your two chosen key areas from the first semester on.

STARTING IN SUMMER SEMESTER

It’s possible to start in both, winter and summer semester in general. However, please note that most of the courses are solely offered in one of the two semesters. Therefore and due to the consecutive character of the degree programme starting in winter semester will benefit the sequence of your chosen course, even though there’s no formal restriction to the order in which you participate in the courses in general.

 

Regarding the key areas following course combinations and course sequences are recommend (KX stands for the respective combination recommendations, which are most convenient content and ECTS-point wise):

 

COMPUTATIONAL BUILDING SCIENCE

1st semester (winter semester)

  • 3.0 ECTS VU „Foundations of Building Science“ (mandatory)
  • 2.0 ECTS VU „Introduction to Digital Twins for Buildings and Cities“ (mandatory)

semester overall: mandatory: 5.0 ECTS

2nd semester (summer semester)

  • 3.0 ECTS VU „Advanced Numerical Methods in Building Science 1“ (mandatory)
  • 3.0 ECTS VO „Multiscale Material Modelling“ (K2)
  • 2.0 ECTS UE „Multiscale Material Modelling“ (K2)
  • 1.5 ECTS VO „Modelling and Simulation in Water Resource Systems“ (K3)
  • 2.0 ECTS UE „Modelling and Simulation in Water Resource Systems“ (K3)

semester overall: mandatory: 3.0 ECTS + optional: K2: 5.0 ECTS or K3: 3.5 ECTS

3rd  semester (winter semester)

  • 3.5 ECTS SE „Advanced Visualization and Numerical Methods in City Science“ (mandatory)
  • 3.5 ECTS VU „Advanced Numerical Methods in Building Science 2“ (K1)
  • 3.0 ECTS VO „Engineering Biochemoporomechanics“ (K4)
  • 1.0 ECTS „Data Management“ (K1, K4)

semester overall: mandatory 3.5 ECTS + optional: K1: 4.5 ECTS or K4: 4.0 ECTS

 

COMPUTATIONAL CHEMISTRY AND MATERIALS SCIENCE:

1st semester (winter semester)

  • 3.0 ECTS VU „Introduction to Atomistic Calculations“ (mandatory)
  • 3.0 ECTS VU „Concepts in Condensed Matter Physics“ (mandatory)

semester overall: mandatory: 6.0 ECTS

2nd semester (summer semester)

  • 3.0 ECTS VO „Theoretical Molecular Chemistry“ (K1)
  • 3.0 ECTS VO „Physical and Theoretical Solid State Chemistry“ (K1)
  • 3.0/2.0 VU „Computational Materials Science“ (K2)

semester overall: optional: K1: 6.0 ECTS or K2: 3.0 ECTS

3rd  semester (winter semester)

  • 3.0 ECTS PR „Selected Topics in Theoretical Chemistry“ (K1)
  • 3.0 ECTS „Simulations of Solids“ (K2)
  • 3.0 ECTSPR „Selected Topics in Materials Science“ (K2)

semester overall: optional: K1: 3.0 ECTS or K2: 6.0 ECTS

 

COMPUTATIONAL ELECTRONICS:

1st semester (winter semester)

  • 4.0 ECTS VU „Introduction to Semiconductor Physics and Devices“ (mandatory)

semester overall: mandatory: 4.0 ECTS

2nd semester (summer semester)

  • 3.0 ECTS „Introduction to Finite Element Methods in Solid Mechanics“ (mandatory)
  • 4.0 ECTS „Simulation of Semiconductor Device Fabrication“ (K1, K2)

semester overall: mandatory: 3.0 ECTS + optional: K1 & K2: 4.0 ECTS

3rd  semester (winter semester)

  • 4.0 ECTS PR „Selected Topics - Computational Electronics“ (K1)
  • 4.0 ECTS „Semiconductor Sensors“ (K2)
  • 3.0 ECTS VO „Theory, Modelling and Simulation of MEMS and NEMS Devices“ (K3, K4)
  • 5.0 ECTS PR „Selected Topics - MEMS and NEMS“ (K3)
  • 1.0 ECTS SE „Recent Advances in Computational Electronics“ (K4)
  • 4.0 ECTS VU „Finite Element for Multi-Physics I“ (K4)

semester overall: mandatory: K1: 4.0 ECTS or K2: 4.0 ECTS or K3: 8.0 ECTS or K4: 8.0 ECTS

 

COMPUTATIONAL FLUID DYNAMICS AND ACOUSTICS:

1st semester (winter semester)

  • 3.0 ECTS VO „Numerical Methods for Fluid Mechanics“ (mandatory)

semester overall: mandatory: 3.0 ECTS

2nd semester (summer semester)

  • 5.0 ECTSVU „Fundamentals in Fluid Mechanics“ (mandatory)
  • 2.0 ECTS SE „Seminar on Stability and Pern Formation” (K1)

semester overall: mandatory: 5.0 ECTS + optional: K1: 2.0 ECTS

3rd  semester (winter semester)

  • 3.0 ECTS UE „Calculating Turbulent Flows with CFD-Codes“ (K2)
  • 2.0 ECTS UE „Numerical Methods in Fluid Dynamics“ (K3)
  • 3.0 ECTS VO „Hydrodynamic Stability and Transition to Turbulence“ (K4)
  • 3.0 ECTS VU „Aeroacustics“ (K5)
  • 5.0 ECTS VU „Computational Aerodynamics“ (K1, K3)
  • 4.0 ECTS PA „Project Study in Fluid Mechanics“ (K2, K4, K5)

semester overall: optional: K1: 5.0 ECTS or K2 & K4 &K5: 7.0 ECTS or K3: 7.0 ECTS

 

COMPUTATIONAL MATHEMATICS:

1st semester (winter semester)

  • 4.5 ECTS VO „Modelling with Partial Differential Equations“ (K1, K3)
  • 1.5 ECTS UE „Modelling with Partial Differential Equations“ (K3)

semester overall: optional: K1: 4.5 ECTS or K3: 6.0 ECTS

2nd semester (summer semester)

  • 4.5 ECTS VO „Numerics of Partial Differential Equations: Instationary Problems“ (K1, K2)
  • 1.5 ECTS UE „Numerics of Partial Differential Equations: Instationary Problems“ (K2)
  • 3.0 ECTS SE „Computational Mathematics“ (K1, K2, K3, K4)
  • 4.5 ECTS VO „AKNUM Iterative Solution of Large Systems of Equations“ (K3, K4)
  • 1.5 ECTS UE „AKNUM Iterative Solution of Large Systems of Equations“ (K4)

semester overall: optional: K1: 7.5 ECTS or K2: 9.0 ECTS or K3: 7.5 ECTS or K4: 9.0 ECTS

3rd  semester (winter semester)

  • 3.5 ECTS VU „Optimization with PDE Constraints“ (K1, K3, K4)
  • 4.5 ECTS VO „AKFVM-AKNUM Computational Finance“ (K2)
  • 3.0 ECTS UE „AKFVM-AKNUM Computational Finance“ (K2)
  • 4.5 ECTS VU „AKNUM Finite Eement Methods in Technical Applications“ (K4)

semester overall: optional: K1 & K3: 3.5 ECTS or K2: 7.5 ECTS or K4: 8.0 ECTS

 

COMPUTATIONAL MECHATRONICS:

1st semester (winter semester)

  • 4.0 ECTS VU „Finite Elements for Multi-Physics I“ (mandatory)

semester overall: mandatory: 4.0 ECTS

2nd semester (summer semester)

  • 3.0 ECTS VO „Finite Element Methods for Multi-Physics II“ (mandatory)
  • 2.0/2.0 UE „Finite Element Methods for Multi-Physics II“ (K2, K3)
  • 3.0/2.0 VU „Nanoelectromechanical Systems“ (K2)

semester overall: mandatory: 3.0 ECTS + optional: K2: 5.0 ECTS or K3: 2.0 ECTS

3rd  semester (winter semester)

  • 3.0 ECTS VO „Theory, Modelling and Simulation of MEMS and NEMS Devices“ (K2, K3)
  • 4.0 ECTS VU „Implementation of a Finite Element Program“ (K1)
  • 4.0 ECTS VU „Computational Methods in Structural Mechanics“ (K1)
  • 3.0 ECTS SE „Seminar Mechatronic Systems“ (K3)

semester overall: optional: K1: 8.0 ECTS or K2: 3.0 ECTS or K3: 6.0 ECTS

 

COMPUTATIONAL SOLID MECHANICS:

1st semester (winter semester)

  • 4.0 ECTS VU „Finite Element for Multi-Physics I“ (K1)
  • 4.0 ECTS VU „Composites Engineering“ (K2)

semester overall: optional: K1 & K2: 4.0 ECTS

2nd semester (summer semester)

  • 3.0 ECTS VU „Introduction to Finite Element Methods in Solid Mechanics“ (mandatory)
  • 3.0 ECTS VO „Finite Element Methods for Multi-Physics II“ (K1)
  • 2.0 ECTS UE „Finite Element Methods for Multi-Physics II“ (K1)
  • 2.0 ECTS UE „Design of Composite Structures“ (K2)
  • 3.0 ECTS VO „Advanced Material Models for Structural Analysis“ (K2, K3)

semester overall mandatory: 3.0 ECTS + optional: K1 & K2: 5.0 ECTS or K3: 3.0 ECTS

3rd  semester (winter semester)

  • 4.0 ECTS VU „Implementation of a Finite Element Program“ (mandatory)
  • 3.0 ECTS VO „Nonlinear Finite Element Methods“ (K3)
  • 2.0 ECTS UE „Nonlinear Finite Element Methods“ (K3)

semester overall: mandatory: 4.0 ECTS + optional: K3: 5.0 ECTS

 

COMPUTATIONAL INFORMATICS:

Please note that there’s no temporal priorization recommended here.

 

Vocal Folds

Two Dop Quantum Density

Radiated Sound

Acoustic Source Terms

Contact

Katharina Zeh

Program Administration and Student Services
Institute for Microelectronics
Gußhausstraße 27-29/E360, 1040 Wien
Office: CD 05 46
Phone: +43 1 58801 36005
Email: cse-master@tuwien.ac.at

 

Program Management

Prof. Dr. Joachim Schöberl

Dean of Studies
Institute of Analysis and Scientific Computing

Ass.Prof. Dr. Josef Weinbub

Chairman of the Study Commission
Institute for Microelectronics

 

Students' Union

Fachschaft Technische Mathematik

Wiedner Hauptstraße 8-10, 1040 Wien
Freihaus, 1. floor, red area
Phone: +43 1 58801 49544
Email: stv@fsmat.at
Web: http://www.fsmat.at/