Titlebook: Domain Decomposition Methods in Science and Engineering XVI; Olof B. Widlund,David E. Keyes Conference proceedings 2007 Springer-Verlag Be

puzzle

A Domain Decomposition Solver for a Parallel Adaptive Meshing Paradigm makes extensive use of existing sequential solvers, and exploits in several important ways data generated as part of the adaptive meshing paradigm. Numerical examples illustrate the effectiveness of the procedure.

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垄断

Preconditioning of Saddle Point Systems by Substructuring and a Penalty Approachzation approach of Axelsson in which a related linear system, differing only in the (2,2) block of the coefficient matrix, is introduced. By choosing this block to be negative definite, the dual unknowns of the related system can be eliminated resulting in a positive definite primal Schur complement

监禁

Nonconforming Methods for Nonlinear Elasticity Problemss. In order to retain as much flexibility as possible, we do not require the subdomain grids to match along their common interfaces. Dual Lagrange multipliers are employed to generate efficient and robust transmission operators between the subdomains. Various numerical examples are presented to illu

Inoperable

Finite Element Methods with Patches and Applicationsuse a relaxation method that consists of calculating successive corrections to the solution in patches of finite elements. We analyse the spectral properties of the iteration operator [6]. We show how to evaluate the best relaxation parameter and what is the influence of patches size on the converge

追踪

On Preconditioned Uzawa-type Iterations for a Saddle Point Problem with Inequality Constraintsthe Cahn-Hilliard equation with an obstacle potential. We present a new class of preconditioners based on linear Schur complements associated with successive approximations of the coincidence set. In numerical experiments, we found superlinear convergence and finite termination.

护身符

Multilevel Methods for Eigenspace Computations in Structural Dynamicsdreds or thousands of eigenpairs.We review in this paper methods based on domain decomposition for such eigenspace computations in structural dynamics. We distinguish approaches that solve the eigenproblem algebraically (with minimal connections to the underlying partial differential equation) from

泄露

Recent Developments on Optimized Schwarz Methodswhen overlap is small, typically one mesh size, convergence of the algorithm is slow. A first possible remedy is the introduction of Neumann boundary conditions in the coupling between the local solutions. This idea has led to the development of the Dirichlet-Neuman algorithm [10], Neumann-Neumann m

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Schur Complement Preconditioners for Distributed General Sparse Linear Systemsds are pervasive in numerical linear algebra where they represent a canonical way of implementing divide-and-conquer principles. The goal of this note is to give a brief overview of recent progress made in using these techniques for solving general, irregularly structured, sparse linear systems. The