21st GAMM-Seminar Leipzig on
Robust Fast Solvers

Max-Planck-Institute for Mathematics in the Sciences
Inselstr. 22-26, D-04103 [O->]Leipzig
Phone: +49.341.9959.752, Fax: +49.341.9959.999

  21st GAMM-Seminar
January, 26th-28th, 2005
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  Abstract Angela Kunoth, Fri, 09.00-10.00 Previous Contents Next  
  A Monotone Multigrid Method Based on Higher Order B-Splines
Angela Kunoth (Univ. Bonn)

For the efficient numerical solution of elliptic variational inequalities on closed convex sets, monotone multigrid methods based on piecewise linear finite elements have been investigated over the past decades. In these methods, the appropriate approximation of the obstacle on coarser grids is essential, which is achieved by considering point values in the piecewise linear case but which does not give rise to admissible obstacles in the case of higher order basis functions. On the other hand, there are a number of problems which profit from higher order approximations, among these the problem of prizing American options, formulated as a parabolic free boundary value problem.

Here a monotone multigrid method will be presented for discretizations in terms of B-splines of arbitrary order to solve elliptic variational inequalities. In order to maintain monotonicity (upper bound) and quasi-optimality (lower bound) of the coarse grid corrections for the equivalent linear complementary problem, an optimized coarse grid correction algorithm based on B-spline evaluation coefficients will be introduced. This algorithm is of optimal complexity of the degrees of freedom of the coarse grid, yielding optimal multigrid complexity for the resulting monotone multigrid method.


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Last updated:
28.01.2005 Impressum
Concept, Design and Realisation
[O->]Jens Burmeister (Uni Kiel), Kai Helms (MPI Leipzig)
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