Displaying similar documents to “A numerical study on Neumann-Neumann methods for hp approximations on geometrically refined boundary layer meshes II. Three-dimensional problems”

Domain decomposition methods and scientific computing applications

Luca F. Pavarino (2005)

Bollettino dell'Unione Matematica Italiana

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This paper reviews the basic mathematical ideas and convergence analysis of domain decomposition methods. These are parallel and scalable iterative methods for the efficient numerical solution of partial differential equations. Two examples are then presented showing the application of domain decomposition methods to large-scale numerical simulations in computational mechanics and electrocardiology.

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...

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...