Iterative Substructuring Preconditioners for Mortar Element Methods in Two Dimensions

The mortar methods are based on domain decomposition and they allow for the coupling of different variational approximations in different subdomains. The resulting methods are nonconforming but still yield optimal approximations. In this paper, we will discuss iterative substructuring algorithms for...

Full description

Saved in:
Bibliographic Details
Published in:SIAM journal on numerical analysis 1999, Vol.36 (2), p.551-580
Main Authors: Achdou, Yves, Maday, Yvon, Widlund, Olof B.
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Computational techniques
Decomposition
Exact sciences and technology
Finite element method
Finite-element and galerkin methods
Lagrange multipliers
Mathematical methods in physics
Mathematical vectors
Mathematics
Methods
Mortars
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Physics
Polynomials
Sciences and techniques of general use
Slaves
Spectral methods
Vertices
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The mortar methods are based on domain decomposition and they allow for the coupling of different variational approximations in different subdomains. The resulting methods are nonconforming but still yield optimal approximations. In this paper, we will discuss iterative substructuring algorithms for the algebraic systems arising from the discretization of symmetric, second-order, elliptic equations in two dimensions. Both spectral and finite element methods, for geometrically conforming as well as nonconforming domain decompositions, are studied. In each case, we obtain a polylogarithmic bound on the condition number of the preconditioned matrix.
ISSN:0036-1429
1095-7170
DOI:10.1137/s0036142997321005