Institute for
Numerical Simulation

Research Group
M. Griebel

Teaching Activity

• SS 2008:
  Lecture Finanznumerik II, module V5E2
  
• SS 2007:
  Praktische Mathematik II, module 6517
  Lecture with Prof. Dr. Rolf Krause.
• SS 2006:
  Numerische Verfahren der Finanzmathematik (Computational Finance)
  Laboratory with Prof. Dr. Michael Griebel, Dr. Markus Holtz and Dr. Daniel Oeltz.
• WS 2005/2006:
  Numerische Simulation in der Moleküldynamik (Numerical Simulation in Molecular Dynamics)
  Laboratory with Prof. Dr. Michael Griebel, Dr. Jan Hamaekers and Dipl.-Math. Ralf Wildenhues.
• WS 2004/2005:
  Lecture Finanznumerik (Computational Finance)
  
• WS 2004/2005:
  Numerische Verfahren der Finanzmathematik (Computational Finance)
  Laboratory with Dr. Markus Holtz.
• SS 2003:
  Numerische Verfahren der Finanzmathematik (Computational Finance)
  Laboratory with Prof. Dr. Michael Griebel.

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Exercises:

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

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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.

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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.
  • Hierarchical adaptive finite elements.

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Master Theses (co-supervised):

• F. Schumacher: Adaptive hierarchical data compression with error control based on space-filling curves (in German, 2000).
• S. Wahl: Numerical valuation of financial derivatives by sparse grid integration methods (in German, 2001).

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