Iterative Operator Splitting Methods with embedded Multi-grid methods

Juergen Geiser

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 25 pp.

MSC 2000

35K15 Initial value problems for second-order, parabolic equations

35K57 Reaction-diffusion equations

Abstract
In this article a new approach is considered for implementing iterative operator splitting methods for differential equations. The underlying idea is to embed fast Multi-grid methods to accelerate the iterative splitting schemes. The main problem are fast iterative solvers for multi-scale physics, while different scales, we have to apply multi-grid methods to obtain the optimal scale, which can be solved by an iterative splitting schemes. Here we discuss the embedding of such spatial- and time-scale methods, e.g. Multi-grid (spatial) and BDF (time) methods, to taken into account the different scales.