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Table of Contents
Intro
Preface
Background of the Conference Series
About the 26th Conference
Acknowledgments
Contents
List of Contributors
Part I Plenary Talks (PT)
Multiscale Model Reduction for a Class of Optimal Control Problems with Highly Oscillating Coefficients
1 Introduction
2 Method description
2.1 Multiscale basis functions
2.2 The proposed method
2.3 Outline of error analysis
3 Numerical results
References
SeveralWays to Achieve Robustness When SolvingWave Propagation Problems
1 Motivation and challenges
1.1 Why the time-harmonic problem in mid and high frequency is hard
2 What is the best coarse space for Helmholtz?
2.1 Spectral coarse spaces for Helmholtz
2.2 Comparison of coarse spaces
3 Can we improve on the auxiliary subspace preconditioner?
4 General conclusions
References
Scalable Hybrid TFETI-DP Methods for Large Boundary Variational Inequalities
1 Introduction
2 Model problem
3 Domain decomposition and discretization
4 TFETI problem
5 Connecting subdomains into clusters
6 Bounds on the spectrum of H and optimality
7 Numerical experiments
7.1 Comparing estimate and experiments
7.2 Comparing linear unpreconditioned H-TFETI-DP and TFETI
7.3 Model variational inequality and elastic body on rigid obstacle
References
Fundamental Coarse Space Components for Schwarz Methods with Crosspoints
1 Introduction
2 Modal analysis of the Schwarz iteration map
3 The special case of 2 × 2 subdomains
4 A new coarse space for parallel Schwarz methods
5 Numerical experiments
6 A note on the optimized Robin parameter
7 Conclusion
References
Nonoverlapping Domain Decomposition Methods for Time HarmonicWave Problems
1 Elliptic equations versus the Helmholtz equation
2 Impedance-based transmission conditions and related DDM
3 Convergence analysis
4 Construction of appropriate impedance operators
5 The problem of cross points
References
Quantitative Analysis of Nonlinear Multifidelity Optimization for Inverse Electrophysiology
1 Introduction
2 Electrophysiological models
3 Inverse problem of Conductivity Identification
4 Multilevel Quasi-Newton Trust-region Method
Quasi-Newton trust-region method
Recursive multilevel trust-region method
5 Numerical results
5.1 Patient-specific geometry
5.2 Convergence study
6 Conclusion
References
Adaptive Space-Time Finite Element and Isogeometric Analysis
1 Introduction
2 Space-time variational formulations
3 Space-time isogeometric analysis
4 Space-time finite element analysis
5 Space-time optimal control
References
Nonoverlapping Domain Decomposition Methods for Saddle Point Problems
1 Introduction
2 Problem setting
3 Domain decomposition
4 Positive definite formulations
4.1 The primal system (6)
4.2 The dual system (12)
5 Condition number estimates
Preface
Background of the Conference Series
About the 26th Conference
Acknowledgments
Contents
List of Contributors
Part I Plenary Talks (PT)
Multiscale Model Reduction for a Class of Optimal Control Problems with Highly Oscillating Coefficients
1 Introduction
2 Method description
2.1 Multiscale basis functions
2.2 The proposed method
2.3 Outline of error analysis
3 Numerical results
References
SeveralWays to Achieve Robustness When SolvingWave Propagation Problems
1 Motivation and challenges
1.1 Why the time-harmonic problem in mid and high frequency is hard
2 What is the best coarse space for Helmholtz?
2.1 Spectral coarse spaces for Helmholtz
2.2 Comparison of coarse spaces
3 Can we improve on the auxiliary subspace preconditioner?
4 General conclusions
References
Scalable Hybrid TFETI-DP Methods for Large Boundary Variational Inequalities
1 Introduction
2 Model problem
3 Domain decomposition and discretization
4 TFETI problem
5 Connecting subdomains into clusters
6 Bounds on the spectrum of H and optimality
7 Numerical experiments
7.1 Comparing estimate and experiments
7.2 Comparing linear unpreconditioned H-TFETI-DP and TFETI
7.3 Model variational inequality and elastic body on rigid obstacle
References
Fundamental Coarse Space Components for Schwarz Methods with Crosspoints
1 Introduction
2 Modal analysis of the Schwarz iteration map
3 The special case of 2 × 2 subdomains
4 A new coarse space for parallel Schwarz methods
5 Numerical experiments
6 A note on the optimized Robin parameter
7 Conclusion
References
Nonoverlapping Domain Decomposition Methods for Time HarmonicWave Problems
1 Elliptic equations versus the Helmholtz equation
2 Impedance-based transmission conditions and related DDM
3 Convergence analysis
4 Construction of appropriate impedance operators
5 The problem of cross points
References
Quantitative Analysis of Nonlinear Multifidelity Optimization for Inverse Electrophysiology
1 Introduction
2 Electrophysiological models
3 Inverse problem of Conductivity Identification
4 Multilevel Quasi-Newton Trust-region Method
Quasi-Newton trust-region method
Recursive multilevel trust-region method
5 Numerical results
5.1 Patient-specific geometry
5.2 Convergence study
6 Conclusion
References
Adaptive Space-Time Finite Element and Isogeometric Analysis
1 Introduction
2 Space-time variational formulations
3 Space-time isogeometric analysis
4 Space-time finite element analysis
5 Space-time optimal control
References
Nonoverlapping Domain Decomposition Methods for Saddle Point Problems
1 Introduction
2 Problem setting
3 Domain decomposition
4 Positive definite formulations
4.1 The primal system (6)
4.2 The dual system (12)
5 Condition number estimates