Domain Decomposition Methods in Science and Engineering XVI

Randolph E. Bank (auth.), Olof B. Widlund, David E. Keyes (eds.)9783540344681, 3540344683

Domain decomposition is an active, interdisciplinary research area concerned with the development, analysis, and implementation of coupling and decoupling strategies in mathematical and computational models of natural and engineered systems. Since the advent of hierarchical distributed memory computers, it has been motivated by considerations of concurrency and locality in a wide variety of large-scale problems, continuous and discrete. Historically, it emerged from the analysis of partial differential equations, beginning with the work of Schwarz in 1870. The present volume sets forth new contributions in areas of numerical analysis, computer science, scientific and industrial applications, and software development.

Table of contents :
Front Matter….Pages I-XXI
Front Matter….Pages I-XXI
A Domain Decomposition Solver for a Parallel Adaptive Meshing Paradigm….Pages 3-14
Algebraic Multigrid Methods Based on Compatible Relaxation and Energy Minimization….Pages 15-26
Lower Bounds in Domain Decomposition….Pages 27-39
Heterogeneous Domain Decomposition Methods for Fluid-Structure Interaction Problems….Pages 41-52
Preconditioning of Saddle Point Systems by Substructuring and a Penalty Approach….Pages 53-64
Nonconforming Methods for Nonlinear Elasticity Problems….Pages 65-76
Finite Element Methods with Patches and Applications….Pages 77-89
On Preconditioned Uzawa-type Iterations for a Saddle Point Problem with Inequality Constraints….Pages 91-102
Multilevel Methods for Eigenspace Computations in Structural Dynamics….Pages 103-113
Recent Developments on Optimized Schwarz Methods….Pages 115-125
Schur Complement Preconditioners for Distributed General Sparse Linear Systems….Pages 127-138
Schwarz Preconditioning for High Order Simplicial Finite Elements….Pages 139-150
Front Matter….Pages I-XXI
MINISYMPOSIUM 1: Domain Decomposition Methods for Simulation-constrained Optimization….Pages 153-153
Robust Multilevel Restricted Schwarz Preconditioners and Applications….Pages 155-162
MINISYMPOSIUM 2: Optimized Schwarz Methods….Pages 163-163
Optimized Schwarz Methods in Spherical Geometry with an Overset Grid System….Pages 165-172
An Optimized Schwarz Algorithm for the Compressible Euler Equations….Pages 173-180
Optimized Schwarz Methods with Robin Conditions for the Advection-Diffusion Equation….Pages 181-188
Optimized Algebraic Interface Conditions in Domain Decomposition Methods for Strongly Heterogeneous Unsymmetric Problems….Pages 189-196
Optimal and Optimized Domain Decomposition Methods onthe Sphere….Pages 197-204
Front Matter….Pages I-XXI
Additive Schwarz Method for Scattering Problems Using the PML Method at Interfaces….Pages 205-212
Optimized Restricted Additive Schwarz Methods….Pages 213-220
MINISYMPOSIUM 3: Domain Decomposition Methods Applied to Challenging Engineering Problems….Pages 221-221
An Overview of Scalable FETI—DP Algorithms for Variational Inequalities….Pages 223-230
Performance Evaluation of a Multilevel Sub-structuring Method for Sparse Eigenvalue Problems….Pages 231-238
Advection Diffusion Problems with Pure Advection Approximation in Subregions….Pages 239-246
Construction of a New Domain Decomposition Method for the Stokes Equations….Pages 247-254
MINISYMPOSIUM 4: Domain Decomposition Methods for Electromagnetic Field Problems….Pages 255-255
A Domain Decomposition Approach for Non-conformal Couplings between Finite and Boundary Elements for Electromagnetic Scattering Problems in R 3 ….Pages 257-264
MINISYMPOSIUM 5: Space-time Parallel Methods for Partial Differential Equations….Pages 265-265
Optimized Schwarz Waveform Relaxation Algorithms with Nonconforming Time Discretization for Coupling Convection-diffusion Problems with Discontinuous Coefficients….Pages 267-274
Stability of the Parareal Time Discretization for Parabolic Inverse Problems….Pages 275-282
A Schwarz Waveform Relaxation Method for Advection—Diffusion—Reaction Problems with Discontinuous Coefficients and Non-matching Grids….Pages 283-290
On the Superlinear and Linear Convergence of the Parareal Algorithm….Pages 291-298
Optimized Sponge Layers, Optimized Schwarz Waveform Relaxation Algorithms for Convection-diffusion Problems and Best Approximation….Pages 299-306
MINISYMPOSIUM 6: Schwarz Preconditioners and Accelerators….Pages 307-307
Numerical Implementation of Overlapping Balancing Domain Decomposition Methods on Unstructured Meshes….Pages 309-315
OBDD: Overlapping Balancing Domain Decomposition Methods and Generalizations to the Helmholtz Equation….Pages 317-324
Developments in Overlapping Schwarz Preconditioning of High-Order Nodal Discontinuous Galerkin Discretizations….Pages 325-332
Domain-decomposed Fully Coupled Implicit Methods for a Magnetohydrodynamics Problem….Pages 333-340
Front Matter….Pages I-XXI
A Proposal for a Dynamically Adapted Inexact Additive Schwarz Preconditioner….Pages 341-345
Parallel Scalability of a FETI—DP Mortar Method for Problems with Discontinuous Coefficients….Pages 347-347
Neumann-Neumann Algorithms (Two and Three Levels) for Finite Element Elliptic Problems with Discontinuous Coefficients on Fine Triangulation ki….Pages 349-356
The Primal Alternatives of the FETI Methods Equipped with the Lumped Preconditioner….Pages 357-364
Balancing Domain Decomposition Methods for Mortar Coupling Stokes-Darcy Systems….Pages 365-371
A FETI-DP Formulation for Compressible Elasticity with Mortar Constraints….Pages 373-380
Some Computational Results for Robust FETI-DP Methods Applied to Heterogeneous Elasticity Problems in 3D….Pages 381-388
Dual-primal Iterative Substructuring for Almost Incompressible Elasticity….Pages 389-396
Inexact Fast Multipole Boundary Element Tearing and Interconnecting Methods….Pages 397-404
A BDDC Preconditioner for Saddle Point Problems….Pages 405-412
Adaptive Coarse Space Selection in the BDDC and the FETI-DP Iterative Substructuring Methods: Optimal Face Degrees of Freedom….Pages 413-420
Applications of the FETI-DP-RBS-LNA Algorithm on Large Scale Problems with Localized Nonlinearities….Pages 421-428
Three-level BDDC….Pages 429-436
MINISYMPOSIUM 8: Analysis, Development and Implementation of Mortar Elements for 3D Problems in Mechanics….Pages 437-444
Two-scale Dirichlet-Neumann Preconditioners for Boundary Refinements….Pages 445-445
A Numerical Quadrature for the Schwarz-Chimera Method….Pages 447-454
A New Variant of the Mortar Technique for the Crouzeix-Raviart Finite Element….Pages 455-462
Front Matter….Pages 463-470
A New Probabilistic Approach to the Domain Decomposition Method….Pages I-XXI
An Adapted Coarse Space for Balancing Domain Decomposition Methods in Nonlinear Elastodynamics….Pages 473-480
Front Matter….Pages 481-488
On Nonlinear Dirichlet—Neumann Algorithms for Jumping Nonlinearities….Pages I-XXI
Preconditioners for High Order Mortar Methods based on Substructuring….Pages 489-496
Adaptive Smoothed Aggregation in Lattice QCD….Pages 497-504
Spectral Element Agglomerate AMGe….Pages 505-512
Scalable Three-Dimensional Acoustics Using hp-finite/infinite Elements and FETI-DP….Pages 513-521
A Multilevel Energy-based Quantization 1Scheme….Pages 523-530
A Cousin Formulation for Overlapped Domain Decomposition Applied to the Poisson Equation….Pages 531-538
Solving Frictional Contact Problems with Multigrid Efficiency….Pages 539-546
The Approximate Integration in the Mortar Method Constraint….Pages 547-554
Fault Tolerant Domain Decomposition for Parabolic Problems….Pages 555-563
Domain Decomposition for Heterogeneous Media….Pages 565-572
Parallel Implicit Solution of Diffusion-limited Radiation Transport….Pages 573-578
Adaptive Parareal for Systems of ODEs….Pages 579-586
A Fast Helmholtz Solver for Scattering by a Sound-soft Target in Sediment….Pages 587-594
Numerical Simulation of Free Seepage Flow on Non-matching Grids….Pages 595-602
Stationary Incompressible Viscous Flow Analysis by a Domain Decomposition Method….Pages 603-610
New Streamfunction Approach for Magnetohydrodynamics….Pages 611-618
Control Volume Finite Difference On Adaptive Meshes….Pages 619-626
Preconditioned Eigensolver LOBPCG in hypre and PETSc….Pages 627-633
A New FETI-based Algorithm for Solving 3D Contact Problems with Coulomb Friction….Pages 635-642
Front Matter….Pages 643-650
A Discontinuous Galerkin Formulation for Solution of Parabolic Equations on Nonconforming Meshes….Pages I-XXI
On a Parallel Time-domain Method for the Nonlinear Black-Scholes Equation….Pages 651-658
Domain-decomposition Based ℌ -LU Preconditioners….Pages 659-666
Condition Number Estimates for C 0 Interior Penalty Methods….Pages 667-674
An Iterative Substructuring Method for Mortar Nonconforming Discretization of a Fourth-Order Elliptic Problem in Two Dimensions….Pages 675-682
Local Defect Correction for Time-Dependent Partial Differential Equations….Pages 683-690
Extending the p -Version of Finite Elements by an Octree-Based Hierarchy….Pages 691-698
The Multigrid/ τ -extrapolation Technique Applied to the Immersed Boundary Method….Pages 699-706
Overlapping Schwarz Preconditioners for Fekete Spectral Elements….Pages 707-714
Solution of Reduced Resistive Magnetohydrodynamics using Implicit Adaptive Mesh Refinement….Pages 715-722
Embedded Pairs of Fractional Runge-Kutta Methods and Improved Domain Decomposition Techniques for Parabolic Problems….Pages 723-729
Algebraic Multilevel Preconditioners for Nonsymmetric PDEs on Stretched Grids….Pages 731-738
A Balancing Algorithm for Mortar Methods….Pages 739-746
A Hybrid Parallel Preconditioner Using Incomplete Cholesky Factorization and Sparse Approximate Inversion….Pages 747-754
A Three-Scale Finite Element Method for Elliptic Equations with Rapidly Oscillating Periodic Coefficients….Pages 755-762
A FETI Domain Decomposition Method Applied to Contact Problems with Large Displacements….Pages 763-770
Back Matter….Pages 771-778
….Pages 779-784