This special volume focuses on optimization and control of processes governed by partial differential equations. The contributors are mostly participants of the DFG-priority program 1253: Optimization with PDE-constraints which is active since 2006. The book is organized in sections which cover almost the entire spectrum of modern research in this emerging field. Indeed, even though the field of optimal control and optimization for PDE-constrained problems has undergone a dramatic increase of interest during the last four decades, a full theory for nonlinear problems is still lacking. The contributions of this volume, some of which have the character of survey articles, therefore, aim at creating and developing further new ideas for optimization, control and corresponding numerical simulations of systems of possibly coupled nonlinear partial differential equations. The research conducted within this unique network of groups in more than fifteen German universities focuses on novel methods of optimization, control and identification for problems in infinite-dimensional spaces, shape and topology problems, model reduction and adaptivity, discretization concepts and important applications. Besides the theoretical interest, the most prominent question is about the effectiveness of model-based numerical optimization methods for PDEs versus a black-box approach that uses existing codes, often heuristic-based, for optimization.
Author(s): Eberhard Bänsch, Peter Benner (auth.), Günter Leugering, Sebastian Engell, Andreas Griewank, Michael Hinze, Rolf Rannacher, Volker Schulz, Michael Ulbrich, Stefan Ulbrich (eds.)
Series: International Series of Numerical Mathematics 160
Edition: 1
Publisher: Birkhäuser Basel
Year: 2012
Language: English
Pages: 624
City: Basel
Tags: Partial Differential Equations; Optimization; Computational Mathematics and Numerical Analysis
Front Matter....Pages i-xi
Front Matter....Pages 1-3
Stabilization of Incompressible Flow Problems by Riccati-based Feedback....Pages 5-20
Allen-Cahn and Cahn-Hilliard Variational Inequalities Solved with Optimization Techniques....Pages 21-35
On the Connection Between Forward and Optimization Problem in One-shot One-step Methods....Pages 37-49
Generalized Multilevel SQP-methods for PDAE-constrained Optimization Based on Space-Time Adaptive PDAE Solvers....Pages 51-74
Projection Based Model Reduction for Optimal Design of the Time-dependent Stokes System....Pages 75-98
Automated Extension of Fixed Point PDE Solvers for Optimal Design with Bounded Retardation....Pages 99-122
Well-posedness of Networked Hyperbolic Systems of Balance Laws....Pages 123-146
A Space-Time Multigrid Method for Optimal Flow Control....Pages 147-170
A Globalized Semi-smooth Newton Method for Variational Discretization of Control Constrained Elliptic Optimal Control Problems....Pages 171-182
Structure Exploiting Adjoints for Finite Element Discretizations....Pages 183-196
Computing Covariance Matrices for Constrained Nonlinear Large Scale Parameter Estimation Problems Using Krylov Subspace Methods....Pages 197-212
Front Matter....Pages 213-214
On Shape Optimization with Stochastic Loadings....Pages 215-243
Phase-field Approaches to Structural Topology Optimization....Pages 245-256
Advanced Numerical Methods for PDE Constrained Optimization with Application to Optimal Design in Navier Stokes Flow....Pages 257-275
Shape Optimization for Free Boundary Problems – Analysis and Numerics....Pages 277-288
Non-parametric Aerodynamic Shape Optimization....Pages 289-300
Front Matter....Pages 301-302
A Posteriori Error Representations for Elliptic Optimal Control Problems with Control and State Constraints....Pages 303-317
Adaptive Space-Time Finite Element Methods for Parabolic Optimization Problems....Pages 319-348
A Posteriori Error Estimation in PDE-constrained Optimization with Pointwise Inequality Constraints....Pages 349-373
Front Matter....Pages 375-376
A Priori Mesh Grading for Distributed Optimal Control Problems....Pages 377-389
Front Matter....Pages 375-376
Discretization of Optimal Control Problems....Pages 391-430
A Posteriori Error Estimators for Control Constrained Optimal Control Problems....Pages 431-443
A Priori Error Estimates for Space-Time Finite Element Discretization of Parabolic Optimal Control Problems....Pages 445-466
Numerical Analysis of State-constrained Optimal Control Problems for PDEs....Pages 467-482
Front Matter....Pages 483-485
Modeling, Simulation and Optimization of Radio Frequency Ablation....Pages 487-499
Optimization of Electro-mechanical Smart Structures....Pages 501-519
Freezing of Living Cells: Mathematical Models and Design of Optimal Cooling Protocols....Pages 521-540
Model Reduction, Structure-property Relations and Optimization Techniques for the Production of Nanoscale Particles....Pages 541-559
Control of Nanostructures through Electric Fields and Related Free Boundary Problems....Pages 561-572
Optimization of Simulated Moving Bed Processes....Pages 573-596
Optimization and Inverse Problems in Radiative Heat Transfer....Pages 597-609
On the Influence of Constitutive Models on Shape Optimization for Artificial Blood Pumps....Pages 611-622
