Domain Decomposition Methods in Science and Engineering XXIII 1st Edition by Chang Ock Lee,Xiao Chuan Cai,David Keyes 3319523899 9783319523897

Part I Plenary Talks (PT)

Global Convergence Rates of Some Multilevel Methods for Variational and Quasi-Variational Inequaliti

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 I

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 Domai

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 τ-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 E

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

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

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

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 Numer

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