Griebel / Roose / Schlick Domain Decomposition Methods in Science and Engineering

1. Auflage 2006
ISBN: 978-3-540-26825-3
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 690 Seiten

Domain decomposition is an active, interdisciplinary research area that is devoted to the development, analysis and implementation of coupling and decoupling strategies in mathematics, computational science, engineering and industry. A series of international conferences starting in 1987 set the stage for the presentation of many meanwhile classical results on substructuring, block iterative methods, parallel and distributed high performance computing etc. This volume contains a selection from the papers presented at the 15th International Domain Decomposition Conference held in Berlin, Germany, July 17-25, 2003 by the world's leading experts in the field. Its special focus has been on numerical analysis, computational issues,complex heterogeneous problems, industrial problems, and software development.

Autoren/Hrsg.

Griebel, Michael

Roose, Dirk

Schlick, Tamar

Ral,

Kornhuber, Ralf

Périaux, Jacques

Pironneau, Olivier

Widlund, Olof

Xu, Jinchao

Inhaltsverzeichnis

1;Preface;5
2;Contents;10
3;Invited Talks;18
3.1;Non-matching Grids and Lagrange Multipliers;19
3.2;A FETI Method for a Class of Indefinite or Complex Second- or Fourth- Order Problems;35
3.3;Hybrid Schwarz-Multigrid Methods for the Spectral Element Method: Extensions to Navier- Stokes;51
3.4;Numerical Approximation of Dirichlet- to- Neumann Mapping and its Application to Voice Generation Problem;66
3.5;Selecting Constraints in Dual-Primal FETI Methods for Elasticity in Three Dimensions;81
3.6;Coupled Boundary and Finite Element Tearing and Interconnecting Methods;96
3.7;Parallel Simulation of Multiphase/ Multicomponent Flow Models;111
3.8;Uncoupling-Coupling Techniques for Metastable Dynamical Systems;126
4;Minisymposium: Domain Decomposition Methods for Wave Propagation in Unbounded Media;141
4.1;On the Construction of Approximate Boundary Conditions for Solving the Interior Problem of the Acoustic Scattering Transmission Problem;142
4.2;Approximation and Fast Calculation of Non- local Boundary Conditions for the Time- dependent Schrödinger Equation;150
4.3;Domain Decomposition and Additive Schwarz Techniques in the Solution of a TE Model of the Scattering by an Electrically Deep Cavity;158
5;Minisymposium: Parallel Finite Element Software;166
5.1;A Model for Parallel Adaptive Finite Element Software;167
5.2;Towards a Unified Framework for Scientific Computing;175
5.3;Distributed Point Objects. A New Concept for Parallel Finite Elements;183
6;Minisymposium: Collaborating Subdomains for Multi- Scale Multi- Physics Modelling;191
6.1;Local Defect Correction Techniques Applied to a Combustion Problem;192
6.2;Electronic Packaging and Reduction in Modelling Time Using Domain Decomposition;200
6.3;Improving Robustness and Parallel Scalability of Newton Method Through Nonlinear Preconditioning;208
6.4;Iterative Substructuring Methods for Indoor Air Flow Simulation;216
6.5;Fluid-Structure Interaction Using Nonconforming Finite Element Methods;224
6.6;Interaction Laws in Viscous-Inviscid Coupling;232
7;Minisymposium: Recent Developments for Schwarz Methods;240
7.1;Comparison of the Dirichlet-Neumann and Optimal Schwarz Method on the Sphere;241
7.2;Finite Volume Methods on Non-Matching Grids with Arbitrary Interface Conditions and Highly Heterogeneous Media;249
7.3;Nonlinear Advection Problems and Overlapping Schwarz Waveform Relaxation;257
7.4;A New Cement to Glue Nonconforming Grids with Robin Interface Conditions: The Finite Element Case;265
7.5;Acceleration of a Domain Decomposition Method for Advection- Diffusion Problems;273
7.6;A Stabilized Three-Field Formulation and its Decoupling for Advection- Diffusion Problems;281
7.7;Approximation of Optimal Interface Boundary Conditions for Two- Lagrange Multiplier FETI Method;289
7.8;Optimized Overlapping Schwarz Methods for Parabolic PDEs with Time- Delay;297
8;Minisymposium: Trefftz-Methods;305
8.1;A More General Version of the Hybrid-Trefftz Finite Element Model by Application of TH- Domain Decomposition;306
9;Minisymposium: Domain Decomposition on Nonmatching Grids;314
9.1;Mixed Finite Element Methods for Diffusion Equations on Nonmatching Grids;315
9.2;Mortar Finite Elements with Dual Lagrange Multipliers: Some Applications;323
9.3;Non-Conforming Finite Element Methods for Nonmatching Grids in Three Dimensions;331
9.4;On an Additive Schwarz Preconditioner for the Crouzeix- Raviart Mortar Finite Element;339
10;Minisymposium: FETI and Neumann- Neumann Domain Decomposition Methods;347
10.1;A FETI-DP Method for the Mortar Discretization of Elliptic Problems with Discontinuous Coefficients;348
10.2;A FETI-DP Formulation for Two-dimensional Stokes Problem on Nonmatching Grids;356
10.3;Some Computational Results for Dual-Primal FETI Methods for Elliptic Problems in 3D;364
10.4;The FETI Based Domain Decomposition Method for Solving 3D- Multibody Contact Problems with Coulomb Friction;372
10.5;Choosing Nonmortars: Does it Influence the Performance of FETI- DP Algorithms?;380
11;Minisymposium: Heterogeneous Domain Decomposition with Applications in Multiphysics;388
11.1;Domain Decomposition Methods in Electrothermomechanical Coupling Problems;389
11.2;A Multiphysics Strategy for Free Surface Flows;397
12;Minisymposium: Robust Decomposition Methods for Parameter Dependent Problems;405
12.1;Weighted Norm-Equivalences for Preconditioning;406
12.2;Preconditioning for Heterogeneous Problems;415
13;Minisymposium: Recent Advances for the Parareal in Time Algorithm;423
13.1;On the Convergence and the Stability of the Parareal Algorithm to Solve Partial Differential Equations;424
13.2;A Parareal in Time Semi-implicit Approximation of the Navier- Stokes Equations;432
13.3;The Parareal in Time Iterative Solver: a Further Direction to Parallel Implementation;440
13.4;Stability of the Parareal Algorithm;448
14;Minisymposium: Space Decomposition and Subspace Correction Methods for Linear and Nonlinear Problems;456
14.1;Multilevel Homotopic Adaptive Finite Element Methods for Convection Dominated Problems;457
14.2;A Convergent Algorithm for Time Parallelization Applied to Reservoir Simulation;467
14.3;Nonlinear Positive Interpolation Operators for Analysis with Multilevel Grids;475
15;Minisymposium: Discretization Techniques and Algorithms for Multibody Contact Problems;483
15.1;On Scalable Algorithms for Numerical Solution of Variational Inequalities Based on FETI and Semi- monotonic Augmented Lagrangians;484
15.2;Fast Solving of Contact Problems on Complicated Geometries;492
16;Contributed Talks;500
16.1;Generalized Aitken-like Acceleration of the Schwarz Method;501
16.2;The Fat Boundary Method: Semi-Discrete Scheme and Some Numerical Experiments;509
16.3;Modelling of an Underground Waste Disposal Site by Upscaling and Simulation with Domain Decomposition Method;517
16.4;Non-Overlapping DDMs to Solve Flow in Heterogeneous Porous Media;525
16.5;Domain Embedding/Controllability Methods for the Conjugate Gradient Solution of Wave Propagation Problems;533
16.6;An Accelerated Block-Parallel Newton Method via Overlapped Partitioning;543
16.7;Generation of Balanced Subdomain Clusters with Minimum Interface for Distributed Domain Decomposition Applications;551
16.8;Iterative Methods for Stokes/Darcy Coupling;559
16.9;Preconditioning Techniques for the Bidomain Equations;567
16.10;Direct Schur Complement Method by Hierarchical Matrix Techniques;577
16.11;Balancing Neumann-Neumann Methods for Elliptic Optimal Control Problems;585
16.12;Domain Decomposition Preconditioners for Spectral N´ed´elec Elements in Two and Three Dimensions;593
16.13;Parallel Distributed Object-Oriented Framework for Domain Decomposition;601
16.14;A Domain Decomposition Based Two-Level Newton Scheme for Nonlinear Problems;611
16.15;Domain Decomposition for Discontinuous Galerkin Method with Application to Stokes Flow;619
16.16;Hierarchical Matrices for Convection- Dominated Problems;627
16.17;Parallel Performance of Some Two-Level ASPIN Algorithms;635
16.18;Algebraic Analysis of Schwarz Methods for Singular Systems;643
16.19;Schwarz Waveform Relaxation Method for the Viscous Shallow Water Equations;649
16.20;A Two-Grid Alternate Strip-Based Domain Decomposition Strategy in Two- Dimensions;657
16.21;Parallel Solution of Cardiac Reaction-Diffusion Models;665
16.22;Predictor-Corrector Methods for Solving Continuous Casting Problem;673
17;Editorial Policy;681
18;General Remarks;682