Courses

All credits stated below are ECTS credits.

Mandatory courses for the 120 credit program: 63 credits

In the order in which these courses and the Master thesis are taken.

Introductory course on scientific programming is given during the first two weeks (start in the middle of August), just before the regular courses start, an. This course gives an introduction to Matlab and to the computer system at NADA.

DN2251 Applied Numerical Methods, 9 credits
Numerical linear and nonlinear algebra. Ordinary and partial differential equations. Estimation of parameters in linear and nonlinear models. The basic concepts of numerical analysis required for further studies in scientific computing are covered, as well as aspects of implementation and available software. Computer labs and application oriented projects. The course will be given for the first time in 2004/2005 and replaces special versions of 2D1250. September-December.

DN2266 Mathematical Models, Analysis and Simulation I, 7.5 credits
This course is oriented to applied mathematics. Basic linear algebra. Equations for equilibrium, discrete and continuous. Minimization and duality, discrete and continuous. Calculus of variations. Some qualitative theory for ordinary differential equations, phase plane and stability. Perturbation techniques and numerical methods for nonlinear equations and ordinary differential equations. Computer labs. September-December.

DN2260 The Finite Element Method, 6 credits
Grid generators, FEM-formulation for linear and non-linear problems, adaptation and error estimation, efficient solution by multigrid method. Applications: heat conduction and convection-diffusion, strength of materials, electromagnetism (the equations of Maxwell), flow problems (the Navier-Stoke equation), mathematics of finance (the Black-Schole equation), reaction-diffusion, quantum mechanics (the Schrödinger equation). November-December

DD2325 Applied Programming and Computer Science, 9 credits
Program structuring in Python and/or C. Debugging, testing and abstraction. International standards, selection of algorithms and complexity. Basic data structures and algorithms in computer science: stacks, queues, binary trees, hash tables, hash functions, etc. November-December

DN2255 Numerical Treatment of Partial Differential Equations, 7.5 credits
Numerical treatment of initial value problems, boundary value problems and eigenvalue problems for ordinary and partial differential equations. Relevant linear algebra, discretizations, convergence, stability, error propagation, finite differences, finite elements, finite volumes, method of lines, conjugate gradient methods, multigrid. Computer labs and application oriented projects. January-May

DN2264 Parallel Computations for large-scale problems, part 1, 6 credits
The aim of the course is to provide the knowledge needed for solving numerically large-scale industrially relevant, computational problems with methods using many processors efficiently. How to develop, select and adopt algorithms/data structures and how to implement and evaluate the performance of such software. January-May

DN2265 Parallel computations for large-scale problems, part 2, 3 credits
Selecting a project as a continuation of 2D1264. April-May

DN2258 Introduction to High Performance Computing, 7.5 credits
Overwiev of computer architecture, structured programming for scientific computing,parallel algorithms, message passing and graphics. Introduction to C++, FORTRAN90, and the hardware at Nada and PDC (Center for Parallel Computers). Summer course in August.

DA2205 Science philosophy and Research methodology, 7.5 credits

Elective courses

Sorted by course number

DN2253 Numerical algebra, methods for large matrices, 6 credits
Direct and iterative methods for large sparse matrices. Eigenvalue problems. Singular value decomposition and its application in data analysis and information retrieval. Model reduction for linear and nonlinear dynamical systems.

DN2257 Visualization, 6 credits
A second course in computer science and numerical analysis focusing on visualization of scientific measurements and computations. Fundamental elements of visualization. Techniques and algorithms for volume visualization. Animation techniques. Software tools. January-March

DN2274 Computational Electromagnetics, 7.5 credits
Numerical methods for electromegnetics wave-problems. Software for electromagnetic simulations. Maxwell's equations. Time-domain methods based on finite differences, finite elements and finite volumes. Frequency-domain methods based on the methods of moments and the finite element method. High-frequency problems based on multipole methods. Given every second year in September-December.

DN2275 Advanced Computation in Fluid Dynamics, 7.5 credits
An inter-disciplinary course which approaches fundamental problems of practical importance in fluid mechanics, with the aid of advanced tools from mathematical analysis and numerical analysis. Given January-March.

DN2281 Numerical Methods for Stochastic Differential Equations, 7.5 credits
Treatment of Stochastic differential equations and their numerical treatment. Applications to financial mathematics, porous media flow, turbulent diffusion, control theory and Monte Carlo methods. Problems like pricing of an option and solving the Black and Scholes partial differential equation are treated. Given every second year in January-May.

DN2290 Advanced Numerical Analysis, 6 credits
Different numerical methods for large problems with different time scales. Spectral methods, wavelets, multipole methods, preconditioned conjugate gradient methods, multigrid methods. March-May

DN2297 Advanced Individual Course in Scientific Computing, 6 credits
This course opens for a possibility for a student with a special interest in some aspects of scientific computing which are not covered by a regular course. Provided there is a teacher with competence in the area, an individual course may be defined.

3A1640 Computational Chemistry, 7.5 credits
Different numerical techniques for the simulation of chemical reactions: ab initio, molecular dynamics, kinetic and continuum models. General numerical algorithms which are important in computational chemistry: Monte Carlo methods, techniques for very large eigenvalue and least squares problems and stiff problems in ordinary differential equations.

5C1212 Computational Fluid Dynamics, 7.5 credits
The course is an elementary introduction to computational fluid dynamics. The emphasis is on the basics of conservation laws, and on high-Reynolds number laminar flows. Both compressible and incompressible flows will be treated. Potential flow and the Kutta condition, quasi-1D flow of a perfect gas through a nozzle, and boundary layer flow over a flat plate are the examples treated in the computer labs. They illustrate such flow phenomena as shocks and boundary layers.

5C1213 Applied Computational Fluid Dynamics, 3 credits
The applied computational fluid dynamics course is a follow-up to the course 5C1212 and contains an introduction to state of art software for flow simulations and visualizations. These computer codes are used to solve selected industrial and research problems within student projects.

4H1725 Simulation and Modelling on the Atomic Scale, 6 credits
Computer simulation techniques for nanotachnology and nano-materials research.

2B1248 Simulation of Semiconductor Devices, 7.5 credits
Simulation of device physics for advanced semiconductor devices. Implementation of semiconductor equations and the solution using the finite volume method. Design of geometries for physical problems.

4E1212 Aerodynamics, 9 credits
Theoretical and experimental aerodynamic design for aircrafts and other vehicles. Turbulent airflow and aerodynamic forces around an airplane.