Domain Decomposition Methods in Science and Engineering XXIII

Name: Domain Decomposition Methods in Science and Engineering XXIII
Brand: Springer
Price: 149.79 EUR
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Chang-Ock Lee Xiao-Chuan Cai David E. Keyes Hyea Hyun Kim Axel Klawonn Eun-Jae Park Olof B. Widlund(Editor)

Springer (Publisher)

Published on 15. March 2017

XVIII, 415 pages

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978-3-319-52389-7 (ISBN)

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Content

Intro
Preface of DD23 Book of Proceedings
Background of the Conference Series
International Scientific Committee on Domain Decomposition Methods
About the 23rd Conference
Sponsoring Organizations
Local Organizing/Program Committee Members
Research Activity in Domain Decomposition According to DD23 and Its Proceedings
Plenary Presentations
Minisymposia
Contributed Presentations and Posters
Organization
Program Chairs
Program Committee
Contents
Part I Plenary Talks (PT)
Global Convergence Rates of Some Multilevel Methods for Variational and Quasi-Variational Inequalities
1 Introduction
2 One- and Two-Level Methods
3 Multilevel and Multigrid Methods
4 One- and Two-Level Methods for Variational Inequalities of the Second Kind and Quasi-Variational Inequalities
5 Multigrid Methods for Inequalities with a Term Given by a Lipschitz Operator
References
Parallel Sum Primal Spaces for Isogeometric Deluxe BDDC Preconditioners
1 Introduction
2 Model Elliptic Problem and Isogeometric Analysis (IGA)
3 Isogeometric BDDC Deluxe Preconditioners
4 Numerical Results
References
Development of Nonlinear Structural Analysis Using Co-rotational Finite Elements with Improved Domain Decomposition Method
1 Introduction
2 Domain Decomposition Method: FETI-Local
3 Co-rotational (CR) Finite Elements
4 Unified Computational Algorithm
5 Numerical Investigation Regarding Nonlinear Problems
5.1 Computational Efficiency for Nonlinear Problem
5.2 Application for Nonlinear Flexible Multi-body Dynamics
6 Conclusion
References
An Adaptive Coarse Space for P.L. Lions Algorithm and Optimized Schwarz Methods
1 Introduction
2 Symmetrized ORAS Method
3 Two-Level SORAS Algorithm
4 Nearly Incompressible Elasticity
References
On the Time-Domain Decomposition of Parabolic Optimal Control Problems
1 Introduction
2 Optimized Schwarz Methods in Time for Control
2.1 Energy Estimates
2.2 Choice of Parameters and Convergence Rates
3 More Convergence Results
4 Numerical Experiments
References
Parallel Solver for H(div) Problems Using Hybridization and AMG
1 Introduction
2 Hybridization
3 Discussion
4 Numerical Examples
4.1 Weak Scaling
4.2 Strong Scaling
References
Preconditioning for Nonsymmetry and Time-Dependence
1 Introduction
2 Real Nonsymmetric Toeplitz Matrices
3 Preconditioning for Time-Dependence
3.1 Theta Method
3.2 Multi-Step Method
4 Conclusions
References
Algebraic Adaptive Multipreconditioning Applied to Restricted Additive Schwarz
1 Preliminaries
2 An Adaptive Algorithm
2.1 Select Search Directions with a t-Test
2.2 Aggregate Search Directions
3 Numerical Results with FreeFem++ FreeFem and GNU Octave octave
4 Conclusions and Future Work
References
Part II Talks in Minisymposia (MT)
Closed Form Inverse of Local Multi-Trace Operators
1 Introduction
2 Local Multi-Trace Formulation
3 Inverse of the Local Multi-Trace Operator
4 Numerical Experiment
5 Conclusions
References
Schwarz Preconditioning for High Order Edge Element Discretizations of the Time-Harmonic Maxwell's Equations
1 Introduction
2 High Order Edge Finite Elements
3 Schwarz Preconditioning
4 Numerical Results
5 Conclusion
References
On Nilpotent Subdomain Iterations
1 Introduction and Model Problem
2 The Neumann-Neumann Algorithm
3 The Dirichlet-Neumann Algorithm
4 The Optimal Schwarz Algorithm
5 Numerical Experiments
6 Conclusion
References
A Direct Elliptic Solver Based on Hierarchically Low-Rank Schur Complements
1 Introduction
2 Related Work
3 Accelerated Cyclic Reduction
4 Numerical Results in 2D
5 Extensions
6 Concluding Remarks
References
Optimized Schwarz Methods for Heterogeneous Helmholtz and Maxwell's Equations
1 Introduction
2 Optimized Schwarz Methods for Helmholtz and Maxwell's Equations
3 Scaling Results When Controlling the Pollution Effect
4 Conclusions
References
On the Origins of Linear and Non-linear Preconditioning
1 Linear Preconditioning
2 Non-linear Preconditioning
3 Conclusion
References
Time Parallelization for Nonlinear Problems Basedon Diagonalization
1 Introduction
2 Scalar Model Problem
3 A PDE Model Problem
4 Numerical Experiments
5 Conclusion
References
The Effect of Irregular Interfaces on the BDDC Method for the Navier-Stokes Equations
1 Introduction
2 BDDC for Navier-Stokes Equations
3 Mesh Partitioning
4 Numerical Results
5 Conclusion
References
BDDC and FETI-DP Methods with Enriched Coarse Spaces for Elliptic Problems with Oscillatory and High Contrast Coefficients
1 Introduction
2 BDDC and FETI-DP Algorithms
3 Adaptively Enriched Coarse Spaces
4 Condition Number Estimate
References
Adaptive Coarse Spaces for FETI-DP in Three Dimensions with Applications to Heterogeneous Diffusion Problems
1 Introduction
2 FETI-DP with Projector Preconditioning and Balancing
3 Adaptive Constraints and Condition Number Bound
4 Heuristic Modifications
5 Numerical Results
References
Newton-Krylov-FETI-DP with Adaptive Coarse Spaces
1 Introduction
2 Newton-Krylov-FETI-DP
3 Adaptive Coarse Space
4 Numerical Results
5 Conclusion
References
New Nonlinear FETI-DP Methods Based on a Partial Nonlinear Elimination of Variables
1 Introduction
2 Nonlinear FETI-DP Methods
3 Nonlinear FETI-DP Based on Partial Elimination
4 Numerical Results
5 Conclusion
References
Direct and Iterative Methods for Numerical Homogenization
1 Introduction
2 Elliptic Problems with Oscillating Coefficients
3 Direct Homogenization by Localized Orthogonal Decomposition
4 Iterative Homogenization by Subspace Correction
5 Numerical Experiments
References
Nonlinear Multiplicative Schwarz Preconditioning in Natural Convection Cavity Flow
1 Introduction
2 MSPIN
3 Natural Convection Cavity Flow Problem
3.1 Effect of Ordering
3.2 Effect of Grouping
4 Conclusions
References
Treatment of Singular Matrices in the Hybrid Total FETI Method
1 From FETI to HTFETI Method
2 Solving a Singular System via Kernel Detection
3 ExaScale PaRallel FETI SOlver: ESPRESO
4 Numerical Experiments
5 Conclusions
References
From Surface Equivalence Principle to ModularDomain Decomposition
1 Introduction
2 Love's Equivalence Principle
3 Iteration Scheme for Modular Domain Decomposition
4 Investigations
5 Discussion and Conclusion
References
Space-Time CFOSLS Methods with AMGe Upscaling
1 Introduction
2 Space-Time Constrained First Order System Least Squares
3 AMGe Upscaling
4 Parabolic Problem
5 Hyperbolic Problem
References
Scalable BDDC Algorithms for Cardiac Electromechanical Coupling
1 Introduction
2 Cardiac Electromechanical Models
3 Methods
3.1 Iterative Substructuring, Schur Complement System and BDDC Preconditioner
4 Numerical Results
References
A BDDC Algorithm for Weak Galerkin Discretizations
1 Introduction
2 An Elliptic Problem and Its WG Discretization
3 The BDDC Algorithms and Condition Number Bound
4 Condition Number Bound
5 Numerical Experiments
References
Parallel Sums and Adaptive BDDC Deluxe
1 Introduction
2 Equivalence Classes and BDDC Algorithms
2.1 BDDC Deluxe
3 Equivalence Classes with More than Two Elements
References
Adaptive BDDC Deluxe Methods for H(curl)
1 Introduction
2 Adaptive BDDC Deluxe Methods
3 Numerical Experiments
3.1 2D Results
3.2 3D Results
References
Part III Contributed Talks (CT) and Posters
A Study of the Effects of Irregular Subdomain Boundaries on Some Domain Decomposition Algorithms
1 Introduction
2 The Differential Problem
2.1 Assumptions
2.2 The Snowflake Domain
3 Additive Average Schwarz Method
3.1 The Preconditioner
4 Numerical Results
References
On the Definition of Dirichlet and Neumann Conditions for the Biharmonic Equation and Its Impact on Associated Schwarz Methods
1 Introduction
2 Classical Schwarz Methods
3 Optimal and Optimized Schwarz Methods
4 Numerical Results
5 Conclusions
References
SHEM: An Optimal Coarse Space for RAS and Its Multiscale Approximation
1 Introduction and Model Problem
2 Optimal Coarse Space
3 Approximation of the Optimal Coarse Space
4 Numerical Results
5 Conclusions
References
Optimized Schwarz Methods for Domain Decompositions with Parabolic Interfaces
1 Introduction
2 Schwarz Methods with Parabolic Interfaces
3 Optimized Local Transmission Conditions
4 Geometric Characteristics Entering the Optimization
5 Numerical Experiments
6 Conclusion
References
A Mortar Domain Decomposition Method for Quasilinear Problems
1 Introduction
2 Variational Formulation
3 Mortar Finite Element Discretization
4 Numerical Example
References
Deflated Krylov Iterations in Domain Decomposition Methods
1 Introduction
2 Statement of the Problem
3 Deflated DDM in Krylov Subspaces
4 Numerical Experiments
5 Conclusion
References
Parallel Overlapping Schwarz with an Energy-Minimizing Coarse Space
1 Introduction and Description of the Method
2 Model Problems
3 Numerical Results
References
Volume Locking Phenomena Arising in a Hybrid Symmetric Interior Penalty Method with Continuous Numerical Traces
1 Introduction
2 Linear Plane Strain Problem
3 The HSIP-D Method
4 Volume Locking Phenomena in the HSIP-C Method
References
Dual-Primal Domain Decomposition Methods for the Total Variation Minimization
1 Introduction
2 Preliminaries
3 Proposed Algorithms
4 Numerical Results
References
A Parallel Two-Phase Flow Solver on Unstructured Mesh in 3D
1 Mathematical Models and Discretization Schemes
2 Scalable Solvers Based on Domain Decomposition and Algebraic Multigrid Techniques
3 Numerical Experiments
3.1 Parallel Performance
4 Conclusions
References
Two New Enriched Multiscale Coarse Spaces for the Additive Average Schwarz Method
1 Introduction
2 Discrete Problem
3 The Classical Additive Average Schwarz Method
4 Eigenvalue Problems
5 Condition Number Estimates
6 Numerical Experiments
References
Relaxing the Roles of Corners in BDDC by Perturbed Formulation
1 Introduction
2 BDDC Overview
3 Perturbed BDDC
4 Convergence Results
5 Numerical Experiments
References
Simulation of Blood Flow in Patient-specific Cerebral Arteries with a Domain Decomposition Method
1 Introduction
2 Blood Flow Model, Discretization, and Solution Algorithm
3 A Case Study and Discussions
4 Concluding Remarks
References

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Domain Decomposition Methods in Science and Engineering XXIII

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