Master of Science in Scientific Computing
During the first two weeks (start in the middle of August), just before
the regular courses start, an
Introductory Course on Scientific Programming is given. This course will give an introduction
of C-programming, Matlab 5 and an
the Computer System at Nada.
The following courses can be chosen in the Master's program.
Introduction to High Performance Computing, 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
(Center for Parallel Computers).
Applied Numerical Methods, 6 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.
Mathematical Models, Analysis and Simulation I, 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.
Numerical Methods for
Stochastic Differential Equations, 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.
Numerical Treatment of Partial Differential Equations, 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.
Object Oriented Program Construction for Scientific Computing, 4 credits
The aim of the course is to provide the knowledge needed for solving
numerically a large scale, industrially relevant, computational problem.
Difference methods on curvilinear grids. Time stepping schemes.
Overview of grid generation. Overview of numerically important properties
of various partial differential equations.
Object oriented software construction for numerical methods using
the language C++. Overview of parallel computers. How to write
efficient code for RISC processors, optimal use of cache memory.
Data structures for dealing with boundary conditions and geometry.
Visualization. Applications to problems in fluid mechanics.
Visualization, 4 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.
Algorithms for Parallel Computations, 4 credits
In this course methods for efficient construction of vectorized code and use
of distributed memory are studied. Applications on different numerical
algorithms such as fast fourier transforms,
iterative methods, solutions of full, tridiagonal and sparse
systems of linear equations, particle methods. Computer labs.
Advanced Numerical Analysis, 4 credits
Different numerical methods for large problems with different time scales.
Spectral methods, wavelets, multipole methods, preconditioned conjugate
gradient methods, multigrid methods.
Computational Fluid Dynamics, 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.
Applied Computational Fluid Dynamics, 2 credits
This course is a follow-up to the CFD-course and contains an introduction to the
state of the art software for flow simulations and visualizations.
The Finite Element Method, 4 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).
Computational Physics, 5 credits
Consequences of physical theories verified by numerical
computation. How to understand some nonlinear PDEs by an
interplay of normal form theory and numerical simulations of amplitude
equations; tools for the microscopic simulations of
liquids, solids, gases, and other more exotic states of matter.
Computational Chemistry, 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.
Computational Electromagnetics, 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.
Upp till Nadas ingångssida.
Senast ändrad 23 augusti 2005
Tekniskt stöd: <email@example.com>