Domain Decomposition Methods in Science and Engineering XVIII / Edition 1

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These are the proceedings of the 18th international conference on Domain Decomposition Methods in Science and Engineering held in Jerusalem, January 12-17, 2008. Domain decomposition methods are iterative methods for solving the often very large linear or nonlinear systems of algebraic equations that arise when various problems in continuum mechanics are discretized using finite elements. They are designed for massively parallel computers and take the memory hierarchy of such systems into account. This is essential for approaching peak floating point performance. There is an increasingly well developed theory which is having a direct impact on the development and improvements of these algorithms.

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Table of Contents

Part I Plenary Presentations

A Domain Decomposition Approach for Calculating the Graph Corresponding to a Fibrous Geometry Achi Brandt Oleg Iliev Joerg Willems 3

Adaptive Multilevel Interior-Point Methods in PDE Constrained Optimization Harbir Antil Ronald H.W. Hoppe Christopher Linsenmann 15

Numerical Homogeneisation Technique with Domain Decomposition Based a-posteriori Error Estimates Patrick Le Tallec 27

Multiscale Methods for Multiphase Flow in Porous Media Jan M. Nordbotten 39

Mixed Plane Wave Discontinuous Galerkin Methods Ralf Hiptmair Ilaria Perugia 51

Numerical Zoom and the Schwarz Algorithm Frédéric Hecht Alexei Loziriski Olivier Pironneau 63

BDDC for Nonsymmetric Positive Definite and Symmetric Indefinite Problems Xuemin Tu Jing Li 75

Accomodating Irregular Subdomains in Domain Decomposition Theory Olof B. Widlund 87

Auxiliary Space Preconditioners for Mixed Finite Element Methods Ray S. Tuminaro Jinchao Xu Yunrong Zhu 99

Part II Minisymposia

A Multilevel Domain Decomposition Solver Suited to Nonsmooth Mechanical Problems Damien Iceta Pierre Alart David Dureisseix 113

A FETI-2LM Method for Non-Matching Grids François-Xavier Roux 121

Truncated Nonsmooth Newton Multigrid Methods for Convex Minimization Problems Carsten Gräser Uli Sack Oliver Sander 129

A Recursive Trust-Region Method for Non-Convex Constrained Minimization Christian Gros Rolf Krause 137

A Robin Domain Decomposition Algorithm for Contact Problems: Convergence Results Mohamed Ipopa Taoufik Sassi 145

Patch Smoothers for Saddle Point Problems with Applications to PDE-Constrained Optimization Problems René Simon Walter Zulehner 153

A DomainDecomposition Preconditioner of Neumann-Neumann Type for the Stokes Equations Vitorita Dolean Frédéric Nataf Gerd Rapin 161

Non-overlapping Domain Decomposition for the Richards Equation via Superposition Operators Heiko Berninger 169

Convergence Behavior of a Two-Level Optimized Schwarz Preconditioner Olivier Dubois Martin J. Gander 177

An Algorithm for Non-Matching Grid Projections with Linear Complexity Martin J. Gander Caroline Japhet 185

A Maximum Principle for L²-Trace Norms with an Application to Optimized Schwarz Methods Sébastien Loisel Daniel B. Szyld 193

An Extended Mathematical Framework for Barrier Methods in Function Space Anton Schiela 201

Optimized Schwarz Preconditioning for SEM Based Magnetohydrodynamics Amik St-Cyr Duane Rosenberg Sang Dong Kim 209

Nonlinear Overlapping Domain Decomposition Methods Xiao-Chuan Cai 217

Optimized Schwarz Waveform Relaxation: Roots, Blossoms and Fruits Laurence Halpern 225

Optimized Schwarz Methods F. Nataf 233

The Development of Coarse Spaces for Domain Decomposition Algorithms Olof B. Widlund 241

Part III Contributed Presentations

Distributed Decomposition Over Hyperspherical Domains Aron Ahmadia David Keyes David Melville Alan Rosenbluth Kehan Tian 251

Domain Decomposition Preconditioning for Discontinuous Galerkin Approximations of Convection-Diffusion Problems Paola F. Antonietti Endre Siili 259

Linearly Implicit Domain Decomposition Methods for Nonlinear Time-Dependent Reaction-Diffusion Problems A. Arrarás L. Portero J.C. Jorge 267

NKS for Fully Coupled Fluid-Structure Interaction with Application Andrew T. Barker Xiao-Chuan Cai 275

Weak Information Transfer between Non-Matching Warped Interfaces Thomas Dickopf Rolf Krause 283

Computational Tool for a Mini-Windmill Study with SOFT M. Garbey M. Smaoui N. De Brye C. Picard 291

On Preconditioners for Generalized Saddle Point Problems with an Indefinite Block Piotr Krzyzanowski 299

Lower Bounds for Eigenvalues of Elliptic Operators by Overlapping Domain Decomposition Yuri A. Kuznetsov 307

From the Boundary Element Domain Decomposition Methods to Local Trefftz Finite Element Methods on Polyhedral Meshes Dylan Copeland Ulrich Langer David Pusch 315

An Additive Neumann-Neumann Method for Mortar Finite Element for 4th Order Problems Leszek Marcinkowski 323

A Numerically Efficient Scheme for Elastic Immersed Boundaries F. Pacull M. Garbey 331

A Domain Decomposition Method Based on Augmented Lagrangian with a Penalty Term Chang-Ock Lee Eun-Hee Park 339

Parallelization of a Constrained Three-Dimensional Maxwell Solver F. Assous J. Segré E. Sonnendrücker 347

A Discovery Algorithm for the Algebraic Construction of Optimized Schwarz Preconditioners Amik St-Cyr Martin J. Gander 355

On the Convergence of Optimized Schwarz Methods by way of Matrix Analysis Sébastien Loisel Daniel B. Szyld 363

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