Substructuring Preconditioners for Parabolic Problems by the Mortar Method
نویسندگان
چکیده
We study substructuring preconditioners for the linear system arising from the discretization of parabolic problems when the mortar method is applied. By using a suitable non standard norm equivalence we build an efficient edge block preconditioner and we prove a polylogarithmic bound for the condition number of the preconditioned matrix.
منابع مشابه
Substructuring Preconditioners for Mortar Discretization of a Degenerate Evolution Problem
In this paper we present new efficient variants of structured preconditioners for algebraic linear systems arising from the mortar discretization of a degenerate parabolic system of equations. The new approaches extend and adapt the idea of substructuring preconditioners to the discretization of a degenerate problem in electrocardiology. A polylogarithmic bound for the condition number of the p...
متن کاملPreconditioners for High Order Mortar Methods based on Substructuring
A class of preconditioners for the Mortar Method based on substructuring is studied. We generalize the results of Achdou, Maday and Widlund (AMW99), obtained for the case of order one finite elements, to a wide class of discretization spaces including finite elements of any orders. More precisely, we show that the condition number of the preconditioned matrix grows at most polylogarithmically w...
متن کاملA Numerical Study of FETI Algorithms for Mortar Finite Element Methods
The Finite Element Tearing and Interconnecting (FETI) method is an iterative substructuring method using Lagrange multipliers to enforce the continuity of the nite element solution across the subdomain interface. Mortar nite elements are nonconforming nite elements that allow for a geometrically nonconforming decomposition of the computational domain into subregions and, at the same time, for t...
متن کاملPreconditioners for the dual-primal FETI methods on nonmatching grids: Numerical study
FETI-DP method is a substructuring method that uses Lagrange multipliers to match the continuity condition on the subdomain boundaries. For the FETI-DP method on nonmatching grids, two different formulations are known with respect to how to employ the mortar matching condition. Keeping step with the developments of the FETI-DP methods, a variety of preconditioners for the FETI-DP operator have ...
متن کاملSubstructuring preconditioners for saddle-point problems arising from Maxwell's equations in three dimensions
This paper is concerned with the saddle-point problems arising from edge element discretizations of Maxwell’s equations in a general three dimensional nonconvex polyhedral domain. A new augmented technique is first introduced to transform the problems into equivalent augmented saddlepoint systems so that they can be solved by some existing preconditioned iterative methods. Then some substructur...
متن کامل