Domain Decomposition Methods in Science and Engineering (eBook)

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