Teaching Activity

Exercises:

• Praktische Mathematik II (with M. Griebel, SS 2002).

Seminars:

• Efficient numerical algorithms and information-based complexity (with M. Griebel, SS 1996).
Contents:
• Information-based complexity.
• Monte Carlo methods.
• Quasi-Monte Carlo methods.
• Low discrepancy sequences.
• Lattice methods.
• Hyperbolic crosses.
• Sparse grids.
• Higher order sparse grids.
• Parallelization of numerical methods (with M. Griebel, WS 1996/97).
Contents:
• Introduction to parallelization.
• Parallelization of direct methods for the solution of linear systems.
• Parallelization of solvers for eigenvalue problems.
• Parallelization of the fast Fourier transform.
• Parallelization of numerical integration methods.
• Parallelization of domain decomposition methods.
• Load balancing as an optimization problem.
• Parallelization of the BPX preconditioner.
• Parallelization of adaptive multigrid methods.
• Parallelization of algebraic multigrid methods.
• Parallelization of sparse grid algorithms.
• Parallelization of time-dependent processes.
• Parallelization of particle methods.
• Preconditioners (with M. Griebel, WS 1997/98).
Contents:
• Introduction to standard preconditioners.
• The BPX preconditioner.
• Wavelet preconditioners.
• Preconditioners for Toeplitz matrices.
• Frobenius-norm minimizing preconditioners.
• Tyrtischnikov preconditioners.
• AMG preconditioners.
• Numerical methods for high--dimensional partial differential equations (with A. Schweitzer and M. Griebel, SS 2003).
Contents:
• Fokker-Plank equation.
• Option pricing as integration problem.
• Option pricing using PDEs for European options.
• Option pricing using PDEs for American options.
• Option pricing using the fast Gauss transformation.
• Data mining using sparse grids.

Labs:

• Numerical simulation and visualization (with S. Knapek and M. Griebel, SS 1996).
Contents:
• The Navier-Stokes equations.
• Discretization and numerical solution.
• Data structures.
• Example: driven cavity
• Further boundary conditions.
• General geometries.
• Example: Karman vortex street.
• Visualization with particle tracing and streaklines.
• Free boundary problems.
• Parallelization by domain decomposition under PVM/MPI.
• Heat transport.
• Example: natural convection
• Particle methods and gridless discretizations (with S. Knapek and M. Griebel, WS 1996/97).
Contents:
• The Hamiltonian equations of motion.
• Verlet time discretization.
• Data structures.
• The linked-cell scheme and its parallelization.
• The particle-mesh method and its parallelization.
• The P3M method.
• The Barnes-Hut algorithm and its parallelization.
• Many examples.
• Numerical simulation and visualization (with F. Koster and M. Griebel, SS 1997).
Contents: (see above).
• Numerical simulation and visualization (with F. Koster and M. Griebel, SS 1998).
Contents: (see above).
• Particle methods and molecular dynamics (with D. Oeltz and M. Griebel, WS 2001/02).
Contents: (see above).
• Computational Finance (with M. Griebel, SS 2003).
Contents:
• Black-Scholes model.
• Black-Scholes formula.
• Historical and implied volatility.
• Examples: European and American options.
• Binomial method.
• Simulation by Monte Carlo and Quasi-Monte Carlo methods.
• Stochastic mesh method.
• Example: Asian options.
• Product quadrature methods and sparse grids.
• Examples: barrier and lookback options.
• Black-Scholes PDE.
• Finite difference space discretization.
• Explicit, implicit and Crank-Nicolson time discretization.
• Linear complementary problem.
• Projective SOR.