M. Holtz and A. Kunoth.
B-spline based monotone multigrid methods, with an application to
the pricing of American options.
In P. Wesseling, C. Oosterlee, and P. Hemker, editors,
Multigrid, Multilevel and Multiscale Methods, Proc. EMG, 2005.
Also as SFB 611 preprint No. 0289, 2006.
[ bib | .pdf 1 ]
We propose a monotone multigrid method based on a B-spline basis of arbitrary smoothness for the efficient numerical solution of elliptic variational inequalities on closed convex sets. In order to maintain monotonicity (upper bound) and quasi-optimality (lower bound) of the coarse grid corrections, we propose coarse grid approximations of the obstacle function which are based on B-spline expansion coefficients. To illustrate the potential of the scheme, the method is applied to the pricing of American options in the Black-Scholes framework.