Special Numerical Methods - Boundary Element Methods
Lecturer: Dr. Clemens Pechstein
| Date | Time | Room | Note |
|---|---|---|---|
| Wednesday, March 4 | 14.30 – 16.00 | T 111 | 1st lecture |
| Thursday, March 12 | 12.00 – 13.30 | P 215 | 2nd lecture |
| Wednesday, March 18 | 14.30 – 16.00 | T 111 | 3rd lecture |
except in the easter holidays and on May 21 and June 11 (Christi Himmelfahrt / Fronleichnam, holidays)
Lecture notes
General information
Aims
- Getting basic knowledge on the boundary integral approach to elliptic boundary value problems
- Discussion of numerical methods to discretize and solve such equations by the boundary element method (BEM)
Contents
- Formulation of boundary value problems as boundary integral equations
- Properties of these equations and the underlying boundary integral equations
- Numerical methods: Collocation and projection (Galerkin) methods
- Further topics (only sketchy, and only if time permits): Error estimates, fast BEM, BEM-FEM coupling
Required Knowledge
- Numerical Analysis
- Partial Differential Equations
- Integral Equations
- Numerical Methods for Partial Differential Equations
- Ideally (but not required): Numerical Methods for Elliptic Partial Differential Equations
Required for
- Special topics/seminar in Computational Mathematics
Examination
- Oral
Literature
- Steinbach O.: Numerische Näherungsverfahren für elliptische Randwertprobleme - Finite Elemente und Randelemente. B.G. Teubner, Stuttgart, Leipzig, Wiesbaden, 2003.
- Steinbach O.: Numerical Approximation Methods for Elliptic Boundary Value Problems - Finite and Boundary Elements. Springer, New York, 2008.
- Rjasanow S., Steinbach O.: The Fast Solution of Boundary Integral Equations - Mathematical and Analytical Techniques with Applications to Engineering. Springer, New York, 2007.
- Sauter S., Schwab C.: Randelementmethoden - Analyse, Numerik und Implementierung schneller Algorithmen. B.G. Teubner, Stuttgart, Leipzig, Wiesbaden, 2004.
- McLean W.: Strongly Elliptic Systems and Boundary Integral Equations. Cambridge University Press, Cambridge, 2000
- Bebendorf, M.: Hierarchical Matrices - A Means to Efficiently Solve Elliptic Boundary Value Problems. Vol. 63 of Lecture Notes in Computational Science and Engineering, Springer, Berlin, Heidelberg, 2008.
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last change:
2013-12-05
