Displaying similar documents to “On a Parallel Implementation of the Mortar Element Method”

Analysis of two-level domain decomposition preconditioners based on aggregation

Marzio Sala (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper we present two-level overlapping domain decomposition preconditioners for the finite-element discretisation of elliptic problems in two and three dimensions. The computational domain is partitioned into overlapping subdomains, and a coarse space correction is added. We present an algebraic way to define the coarse space, based on the concept of aggregation. This employs a (smoothed) aggregation technique and does not require the introduction of a coarse grid. We...

Composite grid finite element method: Implementation and iterative solution with inexact subproblems

Radim Blaheta, P. Byczanski, Roman Kohut (2002)

Applications of Mathematics

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This paper concerns the composite grid finite element (FE) method for solving boundary value problems in the cases which require local grid refinement for enhancing the approximating properties of the corresponding FE space. A special interest is given to iterative methods based on natural decomposition of the space of unknowns and to the implementation of both the composite grid FEM and the iterative procedures for its solution. The implementation is important for gaining all benefits...

Numerical comparison of different choices of interface weights in the BDDC method

Čertíková, Marta, Burda, Pavel, Šístek, Jakub

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Balancing Domain Decomposition by Constraints (BDDC) belongs to the class of primal substructuring Domain Decomposition (DD) methods. DD methods are iterative methods successfully used in engineering to parallelize solution of large linear systems arising from discretization of second order elliptic problems. Substructuring DD methods represent an important class of DD methods. Their main idea is to divide the underlying domain into nonoverlapping subdomains and solve many relatively...

A multilevel preconditioner for the mortar method for nonconforming finite element

Talal Rahman, Xuejun Xu (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

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A multilevel preconditioner based on the abstract framework of the auxiliary space method, is developed for the mortar method for the nonconforming finite element or the lowest order Crouzeix-Raviart finite element on nonmatching grids. It is shown that the proposed preconditioner is quasi-optimal in the sense that the condition number of the preconditioned system is independent of the mesh size, and depends only quadratically on the number of refinement levels. Some...

A Domain Decomposition Algorithm for Contact Problems: Analysis and Implementation

J. Haslinger, R. Kučera, T. Sassi (2009)

Mathematical Modelling of Natural Phenomena

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The paper deals with an iterative method for numerical solving frictionless contact problems for two elastic bodies. Each iterative step consists of a Dirichlet problem for the one body, a contact problem for the other one and two Neumann problems to coordinate contact stresses. Convergence is proved by the Banach fixed point theorem in both continuous and discrete case. Numerical experiments indicate scalability of the algorithm for some choices of the relaxation parameter. ...