INTERMATHS EMJM FULL PARTNER

ECTS Credits: 8   |   Semester: 2   |   Year: 1   |   Campus: Vienna University of Technology   |   Language: English   |   Code: DT0641

Unit Coordinator: Markus Faustmann, Claudia Blaas-Schenner

Aims:

Scientific Programming
  - formulate (certain) mathematical problems in algorithmic form,
  - explain the difference between imperative and object-oriented programming,
  - implement mathematical algorithms in Matlab, C, and C++,
  - present and explain own solutions, and
  - constructively discuss and analyze own solutions as well as those of other students.

Parallel Programming
  - understand and apply the main concepts of parallel programming
  - master the basic skills to write parallel programs using MPI and OpenMP
  - parallelize serial programs using basic features of MPI and OpenMP
  - be familiar with the components of an high-performance computing cluster
  - know the principles to take advantage of shared and distributed memory systems as well as accelerators and how to exploit the capabilities of modern high-performance computing systems

Content:

Scientific Programming:
  - Introduction to Matlab, C, and C++.
  - Representation of integer and floating point numbers.
  - Conditioning of given problems.
  - Computational cost of algorithms.
  - Variables and standard data types.
  - Pointers.
  - Loops and if-else.
  - Functions and recursion.
  - Call by value vs. call by reference.
  - Objects and classes (resp. structures),
  - Operator overloading, Inheritance.
  - Templates.
  - Visualization in MATLAB.
  - Programming exercises. 

Parallel Programming:
  - Basic features of parallel programming with MPI (Message Passing Interface) and OpenMP (Open Multi-Processing) using C
  - A look at CUDA to offload parts of the computation to GPUs
  - Students will do the hands-on labs directly on the Vienna Scientific Cluster, the high-performance computing facility of Austrian universities, and hence will learn about and get some experience in high-performance computing.  

Pre-requisites:

Basic skills in programming in C (e.g., as learnt during the lecture "Scientific Programming for Interdisciplinary Mathematics") as well as Linux command line and usage of an editor (vi or nano).

Reading list:

• Scientific programming in mathematics:

lecture notes

• Programming with MATLAB:

Otto and Denier, An Introduction to Programming and Numerical Methods in MATLAB

Brian Hahn, Essential MATLAB for Engineers and Scientists

Stormy Attaway, Matlab: A Practical Introduction to Programming and Problem Solving

•  Basics of Parallel Computing:

    Rauber, Rünger: Parallel programming. Second Edition, Springer 2013.

    Schmidt, Gonzalez-Dominguez, Hundt, Schlarb: Parallel Programming. Concepts and Practice. Morgan Kaufmann 2018.

ECTS Credits: 6   |   Semester: 2   |   Year: 1   |   Campus: Vienna University of Technology   |   Language: English   |   Code: DT0371

Unit Coordinator: Kevin Sturm, Phillip Baumann

Aims:

To understand, analyze, formulate and graphically or mathematically solve basic static and dynamic optimization problems. Students will know about the theory, the mathematically principles and various methods for an exact or iterative solution of optimization problems.

They can moreover differentiate between unconstrained and constrained optimization problems and they can select and apply the specifically appropriate solution methods. 

Content:

• Fundamentals of optimization: existence of minima and maxima, gradient, Hessian, convexity, convergence
• Unconstrained static optimization: optimality conditions, computer-aided optimization, line search methods, choice of the step length, principle of nested intervals, Armijo condition, Wolfe condition, gradient method, Newton method, conjugate gradient method, Quasi-Newton method, Gauss-Newton-method, trust region method, Nelder-Mead method
• Static optimization with constraints: equality and inequality constraints, sensitivity considerations, active set method, gradient projection method, reduced gradient method, penalty and barrier functions, sequential quadratic programming (SQP), local SQP, globalization of SQP

Pre-requisites:

• Analysis,
• Linear algebra,
• Numerical mathematics,
• Differential equations.

Reading list:

• lecture notes,
• J. Macki und A. Strauss: Introduction to Optimal Control Theory. New York, Springer, 1982.
• Jorge Nocedal, Stephen J. Wright: Numerical Optimization, Springer 2006

ECTS Credits: 6   |   Semester: 2   |   Year: 1   |   Campus: Vienna University of Technology   |   Language: English   |   Code: DT0639

Unit Coordinator: Lothar Nannen

Aims:

Being able to check if the numerical solution of an ordinary differential equation makes sense. Furthermore, depending on the inherent structure of the differential equation, selecting the appropriate numerical integrator.

Content:

Initial and boundary value problems for ordinary and partial differential equations, one-step and multi-step methods, adaptivity, structure perserving integrators, introduction to numerical methods for partial differential equations.

Pre-requisites:

Basic lectures of analysis, linear algebra and numerical analysis.

Reading list:

Lecture notes will be provided

ECTS Credits: 7   |   Semester: 2   |   Year: 1   |   Campus: Vienna University of Technology   |   Language: English   |   Code: DT0640

Unit Coordinator: Markus Faustmann

Aims:

Being able to solve stationary partial differential equations numerically, analyse the quality of numerical solutions, select proper methods and implement them in a computer program.

Content:

- Variational formulations
- Sobolev spaces, H(div), H(curl)
- Finite element spaces (h, p, hp)
- Mixed formulations,
- Discontinuous Galerkin Methods,
- Time-dependent problems

Pre-requisites:

Applied Mathematics Foundations

Reading list:

• Lecture notes,
• Dietrich Braess: Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics, Cambridge University Press, 2007
• Cleas Johnson: Numerical Solution of Partial Differential Equations by the Finite Element Method, Cambridge Univ. Press, 1987, Dover 2009
• Susanne Brenner & Ridgway Scott: The Mathematical Theory of Finite Elements, Springer 2008
• Alexandre Ern & Jean-Luc Guermond: Theory and Practice of Finite Elements, Springer, 2010 

ECTS Credits: 3   |   Semester: 2   |   Year: 1   |   Campus: Vienna University of Technology   |      |   Code: DT0663

Unit Coordinator: Innes Institue

Aims:

Learn German at level A1 (speak, read, write)

Content:

• Learn German at level A1 (speak, read, write)
• Social & cultural program, waltz workshop

Reading list:

Lecture notes by Innes

ECTS Credits: 6   |   Semester: 1   |   Year: 2   |   Campus: Vienna University of Technology   |   Language: English

Unit Coordinator: Herbert Steinrück

Pre-requisites:

• Partial differential equations,
• Fluid mechanics,
• Numerical methods for fluid mechanics

Reading list:

• Lecture notes,   
• P. G. Drazin, Introduction to Hydrodynamic Stability, Cambridge University Press, Cambridge (2002)  
• S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Oxford University Press (1961) P. G. Drazin, Introduction to Hydrodynamic Stability, Cambridge University Press (2002) 

ECTS Credits: 5   |   Semester: 1   |   Year: 2   |   Campus: Vienna University of Technology   |   Language: English

Unit Coordinator: Manuel Garcia-Villalba

Aims:

To numerically simulate real fluid mechanical problems as well as to give an overview of the methods used in private and educational facilities.

Content:

• Methods for a treatment of convection-diffusion equations,
• Projection methods for incompressible and compressible Navier-Stokes equations,
• Treatment of complex geomtries,
• Turbulence modelling.

Pre-requisites:

Partial differential equations, fluid mechanics

Reading list:

• Lecture notes,   
• C. A. J. Fletcher: Computational techniques for fluid dynamics, vol. 1, Springer (1991)
• J. J. Ferziger, M. Peric: Computational methods for fluid dynamics, Springer (2002)

ECTS Credits: 6   |   Semester: 1   |   Year: 2   |   Campus: Vienna University of Technology   |   Language: English

Unit Coordinator: Anton Arnold

Aims:

Students will be able to specify and apply a selection of PDE-applications in natural sciences and technology, and to discuss them from a mathematics perspective.

They are able to describe the modelling assumptions or restrictions, as well as their essential analytical and numerical properties.

Content:

• Fluid dynamical models (Euler, Navier-Stokes, vortex models),
• Traffic flow models,
• Theory of elasticity,
• Hyperbolic conservation laws,
• Image processing models (nonlinear diffusion filter, shock filter),
• Models for pattern formation (reaktion-diffusion equations, Turing instability),
• Evolution of thin films,
• Collective behavior (kinetic equations)

Pre-requisites:

• Partial differential equations;
• Basic knowledge in physics / mechanics is helpful

Reading list:

• Lecture notes,
• R. J. LeVeque : Numerical Methods for Conservation Laws, Birkhäuser (1990).
• A.J. Chorin, J.E. Marsden: A mathematical introduction to fluid mechanics, Springer (1990).
• C. Marchioro, M. Pulvirenti: Mathematical theory of incompressible nonviscous fluids, Springer (1994).
• G. Aubert, P. Kornprobst: Mathematical Problems in Image Processing, Springer, New York (2006).

ECTS Credits: 7   |   Semester: 1   |   Year: 2   |   Campus: Vienna University of Technology   |   Language: English

Unit Coordinator: Ulrich Schmid

Aims:

•  Introduction to semiconductor physics and devices 360.241

Students will be able to have a basic understanding of the underlying physics involved in the operation of semiconductor devices and will have a consistent base level of comfort and familiarity with the topic before they move to more advanced courses. The primary focus of the course will be on the development of physics and concepts, however a basic introduction to the application of simulation and numerical calculation within the field of semiconductor devices will also be partially covered.

• Theory, modelling and simulation of MEMS & NEMS:

• Model the mechanical behavior of MEMS/NEMS by continuum mechanics.
• State and test the underlying assumptions of the theory of linear elasticity.
• Describe the interaction between MEMS/NEMS and fluids.
• Model the piezoelectric effect.
• Calculate the eigenmodes and eigenfrequencies of selected structures.
• Derive the differences between macroscopic and microscopic systems
• Predict the dynamics of resonators.
• Derive the basic theory of the method of finite elements.
• Explain the working principle of reference oscillators, mass und fluid sensors.
• Discuss novel concepts like phononic crystals and quantum MEMS/NEMS.
• Understand technical subject-specific technical terminology and critically evaluate relevant scientific publications.
• Use open source software for eigenmode analysis.

Content:

• Introduction to semiconductor physics and devices:

In this course we will learn how the quantum mechanics of solids and transport has been harnessed to build the Digital Age. We will explore the physics of semiconductors and semiconductor devices and the role they play in modern technology. We will also lay the ground-work for more advanced discussions of how computational techniques and simulation can be used to push knowledge in this field forward to new horizons.

* Basic Structure of Crystals and Solids, Quantum Mechanics of Solids, Physics of Semiconductors, Transport in Semiconductors, PN junction, PN diode, PN Junctions and Modern Technology (LEDs, Photovoltaics, etc.), MOS transistor, MOS capacitor, MOSFETs and Modern Technology (VLSI, IGFET Sensors, etc.), Metal/semiconductor interfaces, Heterostructures and Modern Technology (Schottky Diodes, 2D-FETs, etc.)

• Theory, modelling and simulation of MEMS & NEMS:

The design of micro- and nanoelectromechanical systems (MEMS/NEMS) is a highly interdisciplinary field which reflects in the variety of topics of this course. Starting from an introduction to continuum mechanics and piezoelectricity we investigate different aspects of the mechanics of basic MEMS/NEMS structures like membranes and beams. By understanding the interaction of MEMS/NEMS with their environment, we are able to understand the outstanding performance of MEMS/NEMS sensors for mass and fluid sensing. Another important aspect for the modelling of MEMS/NEMS is the representation of MEMS/NEMS with discrete lumped element models and we discuss the most important discrete models. For quantitative predictions often numerical methods need to be employed for which the FEM is the most known. We discuss the fundamental theory of the FEM and its limitations. Using the above theory, we study example applications like reference oscillators or fluid sensors. Additionally, we take a look at novel concepts like phononic crystals or quantum MEMS/NEMS. 

Pre-requisites:

• Some basic exposure to the concepts and equations in the physics of electromagnetism;
• (Vector) calculus,
• Differential equations especially. 

Reading list:

Lecture notes 

ECTS Credits: 6   |   Semester: 1   |   Year: 2   |   Campus: Vienna University of Technology   |   Language: English

Unit Coordinator: Josef Weinbub

Aims:

Students will be able to select and apply fundamental methods of scientific computing and to judge the challenges regarding computing time and implementation effort.

Furthermore, the students have solution skills for inter-disciplinary problems, are able to evaluate and analyze computational approaches, and are able to scientifically formulate and extensively analyze compute-intensive problems as well as develop appropriate approaches. 

Content:

• Computer Architectures
• Serial Optimization
• Numerical Derivatives and Integrals
• Finite Difference Discretization
• Numerical Linear Algebra
• Random Number Generation and Monte Carlo Methods
• Shared Memory Parallel Computing
• Algorithmic Complexity and Data Structures
• Mesh Generation and Visualization
• Software Engineering Principles for Scientific Computing

Pre-requisites:

Numerical mathematics, scientific programing.

Reading list:

Lecture notes