This page is organized in 5 sections. You can select the desired section or wait for the first one. Sections are.
Professor: Rolf Krause
Assistant: Dorian Krause
Course type: Lecture
Value in ECTS: 6
Bibliographic references available on the University Library website
Academic year 2012/2013 - Spring semester – not offered
Prerequisites: PDEs – Mathematical Modeling and Numerical Simulations.
Contents
Multilevel methods are a widely used and highly efficient tool in computational science for solving large scale linear and nonlinear system. In this course, we present the state of the arte for linear as well as nonlinear multilevel and multigrid methods.
Objective
The solution of large linear and nonlinear systems of equations is one of the
most important tasks in numerical simulation. Since standard solution methods
as, e.g., Gaußian elimination do not scale optimally with respect to the
number of unknowns, alternative solution strategies have been developed
during the last decades. In particular multilevel or multiscale solution strategies
have been developed, which are often employed due to their high efficiency.
Prominent examples are multilevel methods for linear elliptic problems,
which allow for the solution of symmetric positive definite systems with
computational effort proportional to the number of unknowns, which turns
them into "optimal" solution methods. However, in particular for nonlinear
and constrained problems, the derivation of reliable as well as efficient multilevel
solution strategies is far from trivial, since convergence is much more
difficult to achieve than in the linear case. In this course, we start from well
known subspace correction methods for linear problems and proceed to more
recent developments as are nonlinear multigrid and monotone multigrid. We
will see in what way multilevel hierarchies can be adapted to certain smooth
and non-smooth nonlinearities and in what way robust and efficient multilevel
methods for nonlinear problems can be derived. Finally, we will consider (recursive) trust-region methods and their application to minimization problems
in computational mechanics. For all methods, we will also discuss their parallelisation.
Besides the theoretical presentation and analysis of the algorithm, we will
also comment on their implementation. Bothe, theoretical as well as practical
exercises are part of this course.
Contents
References
William L. Briggs, Van Emden Henson, and Steve F. McCormick, A Multigrid
Tutorial, Second Edition, SIAM, 2000 (book home page), ISBN 0-89871-4621.
Wolfgang Hackbusch, Multigrid Methods and Applications, Springer, 1985.
Pieter Wesseling, An Introduction to Multigrid Methods, Corrected Reprint.
Philadelphia: R.T. Edwards, Inc., 2004. ISBN 1-930217-08-0.
Gene H. Golub and Charles F. Van Loan, Matrix computations
Toselli, Widlund, Domain Decomposition Methods Nocedal Wright, Numerical
Optimisation.
Conn Gould Toint, Trust-Region Methods.
R. Fletcher, Practical Methods of Optimisation.
Numerical Optimization, Series: Springer Series in Operations Research and
Financial Engineering , Nocedal, Jorge, Wright, Stephen 2nd ed., 2006, XXII,
664 p. 85 illus.,
http://www.springer.com/mathematics/book/978-0-387-30303-1
Your are browsing the content Course description of the topic People directory. You arrived from.