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.
Springer Berlin Heidelberg
; July 2007
802 pages; ISBN 9783540344698Read online
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Title: Domain Decomposition Methods in Science and Engineering XVI
Author: Olof Widlund; David E. Keyes
Plenary Presentations.- A Domain Decomposition Solver for a Parallel Adaptive Meshing Paradigm.- Algebraic Multigrid Methods Based on Compatible Relaxation and Energy Minimization.- Lower Bounds in Domain Decomposition.- Heterogeneous Domain Decomposition Methods for Fluid-Structure Interaction Problems.- Preconditioning of Saddle Point Systems by Substructuring and a Penalty Approach.- Nonconforming Methods for Nonlinear Elasticity Problems.- Finite Element Methods with Patches and Applications.- On Preconditioned Uzawa-type Iterations for a Saddle Point Problem with Inequality Constraints.- Multilevel Methods for Eigenspace Computations in Structural Dynamics.- Recent Developments on Optimized Schwarz Methods.- Schur Complement Preconditioners for Distributed General Sparse Linear Systems.- Schwarz Preconditioning for High Order Simplicial Finite Elements.- Minisymposia.- MINISYMPOSIUM 1: Domain Decomposition Methods for Simulation-constrained Optimization.- Robust Multilevel Restricted Schwarz Preconditioners and Applications.- MINISYMPOSIUM 2: Optimized Schwarz Methods.- Optimized Schwarz Methods in Spherical Geometry with an Overset Grid System.- An Optimized Schwarz Algorithm for the Compressible Euler Equations.- Optimized Schwarz Methods with Robin Conditions for the Advection-Diffusion Equation.- Optimized Algebraic Interface Conditions in Domain Decomposition Methods for Strongly Heterogeneous Unsymmetric Problems.- Optimal and Optimized Domain Decomposition Methods onthe Sphere.- Additive Schwarz Method for Scattering Problems Using the PML Method at Interfaces.- Optimized Restricted Additive Schwarz Methods.- MINISYMPOSIUM 3: Domain Decomposition Methods Applied to Challenging Engineering Problems.- An Overview of Scalable FETI—DP Algorithms for Variational Inequalities.- Performance Evaluation of a Multilevel Sub-structuring Method for Sparse Eigenvalue Problems.- Advection Diffusion Problems with Pure Advection Approximation in Subregions.- Construction of a New Domain Decomposition Method for the Stokes Equations.- MINISYMPOSIUM 4: Domain Decomposition Methods for Electromagnetic Field Problems.- A Domain Decomposition Approach for Non-conformal Couplings between Finite and Boundary Elements for Electromagnetic Scattering Problems in R3.- MINISYMPOSIUM 5: Space-time Parallel Methods for Partial Differential Equations.- Optimized Schwarz Waveform Relaxation Algorithms with Nonconforming Time Discretization for Coupling Convection-diffusion Problems with Discontinuous Coefficients.- Stability of the Parareal Time Discretization for Parabolic Inverse Problems.- A Schwarz Waveform Relaxation Method for Advection—Diffusion—Reaction Problems with Discontinuous Coefficients and Non-matching Grids.- On the Superlinear and Linear Convergence of the Parareal Algorithm.- Optimized Sponge Layers, Optimized Schwarz Waveform Relaxation Algorithms for Convection-diffusion Problems and Best Approximation.- MINISYMPOSIUM 6: Schwarz Preconditioners and Accelerators.- Numerical Implementation of Overlapping Balancing Domain Decomposition Methods on Unstructured Meshes.- OBDD: Overlapping Balancing Domain Decomposition Methods and Generalizations to the Helmholtz Equation.- Developments in Overlapping Schwarz Preconditioning of High-Order Nodal Discontinuous Galerkin Discretizations.- Domain-decomposed Fully Coupled Implicit Methods for a Magnetohydrodynamics Problem.- A Proposal for a Dynamically Adapted Inexact Additive Schwarz Preconditioner.- MINISYMPOSIUM 7: FETI and Neumann-Neumann Methods with Primal Constraints.- Parallel Scalability of a FETI—DP Mortar Method for Problems with Discontinuous Coefficients.- Neumann-Neumann Algorithms (Two and Three Levels) for Finite Element Elliptic Problems with Discontinuous Coefficients on Fine Triangulation ki.- The Primal Alternatives of the FETI Methods Equipped with the Lumped Preconditioner.- Balancing Domain Decomposition Methods for Mortar Coupling Stokes-Darcy Systems.- A FETI-DP Formulation for Compressible Elasticity with Mortar Constraints.- Some Computational Results for Robust FETI-DP Methods Applied to Heterogeneous Elasticity Problems in 3D.- Dual-primal Iterative Substructuring for Almost Incompressible Elasticity.- Inexact Fast Multipole Boundary Element Tearing and Interconnecting Methods.- A BDDC Preconditioner for Saddle Point Problems.- Adaptive Coarse Space Selection in the BDDC and the FETI-DP Iterative Substructuring Methods: Optimal Face Degrees of Freedom.- Applications of the FETI-DP-RBS-LNA Algorithm on Large Scale Problems with Localized Nonlinearities.- Three-level BDDC.- MINISYMPOSIUM 8: Analysis, Development and Implementation of Mortar Elements for 3D Problems in Mechanics.- Two-scale Dirichlet-Neumann Preconditioners for Boundary Refinements.- A Numerical Quadrature for the Schwarz-Chimera Method.- A New Variant of the Mortar Technique for the Crouzeix-Raviart Finite Element.- Contributed Presentations.- A New Probabilistic Approach to the Domain Decomposition Method.- An Adapted Coarse Space for Balancing Domain Decomposition Methods in Nonlinear Elastodynamics.- On Nonlinear Dirichlet—Neumann Algorithms for Jumping Nonlinearities.- Preconditioners for High Order Mortar Methods based on Substructuring.- Adaptive Smoothed Aggregation in Lattice QCD.- Spectral Element Agglomerate AMGe.- Scalable Three-Dimensional Acoustics Using hp-finite/infinite Elements and FETI-DP.- A Multilevel Energy-based Quantization 1Scheme.- A Cousin Formulation for Overlapped Domain Decomposition Applied to the Poisson Equation.- Solving Frictional Contact Problems with Multigrid Efficiency.- The Approximate Integration in the Mortar Method Constraint.- Fault Tolerant Domain Decomposition for Parabolic Problems.- Domain Decomposition for Heterogeneous Media.- Parallel Implicit Solution of Diffusion-limited Radiation Transport.- Adaptive Parareal for Systems of ODEs.- A Fast Helmholtz Solver for Scattering by a Sound-soft Target in Sediment.- Numerical Simulation of Free Seepage Flow on Non-matching Grids.- Stationary Incompressible Viscous Flow Analysis by a Domain Decomposition Method.- New Streamfunction Approach for Magnetohydrodynamics.- Control Volume Finite Difference On Adaptive Meshes.- Preconditioned Eigensolver LOBPCG in hypre and PETSc.- A New FETI-based Algorithm for Solving 3D Contact Problems with Coulomb Friction.- A Discontinuous Galerkin Formulation for Solution of Parabolic Equations on Nonconforming Meshes.- On a Parallel Time-domain Method for the Nonlinear Black-Scholes Equation.- Domain-decomposition Based ?-LU Preconditioners.- Condition Number Estimates for C0 Interior Penalty Methods.- An Iterative Substructuring Method for Mortar Nonconforming Discretization of a Fourth-Order Elliptic Problem in Two Dimensions.- Local Defect Correction for Time-Dependent Partial Differential Equations.- Extending the p-Version of Finite Elements by an Octree-Based Hierarchy.- The Multigrid/ ? -extrapolation Technique Applied to the Immersed Boundary Method.- Overlapping Schwarz Preconditioners for Fekete Spectral Elements.- Solution of Reduced Resistive Magnetohydrodynamics using Implicit Adaptive Mesh Refinement.- Embedded Pairs of Fractional Runge-Kutta Methods and Improved Domain Decomposition Techniques for Parabolic Problems.- Algebraic Multilevel Preconditioners for Nonsymmetric PDEs on Stretched Grids.- A Balancing Algorithm for Mortar Methods.- A Hybrid Parallel Preconditioner Using Incomplete Cholesky Factorization and Sparse Approximate Inversion.- A Three-Scale Finite Element Method for Elliptic Equations with Rapidly Oscillating Periodic Coefficients.- A FETI Domain Decomposition Method Applied to Contact Problems with Large Displacements.