Frontiers in PDE-Constrained Optimization

Description

This volume provides a broad and uniform introduction of PDE-constrained optimization as well as to document a number of interesting and challenging applications. Many science and engineering applications necessitate the solution of optimization problems constrained by physical laws that are described by systems of partial differential equations (PDEs)​. As a result, PDE-constrained optimization problems arise in a variety of disciplines including geophysics, earth and climate science, material science, chemical and mechanical engineering, medical imaging and physics. This volume is divided into two parts. The first part provides a comprehensive treatment of PDE-constrained optimization including discussions of problems constrained by PDEs with uncertain inputs and problems constrained by variational inequalities. Special emphasis is placed on algorithm development and numerical computation. In addition, a comprehensive treatment of inverse problems arising in the oil and gas industry is provided. The second part of this volume focuses on the application of PDE-constrained optimization, including problems in optimal control, optimal design, and inverse problems, among other topics. Front Matter ....Pages i-x Front Matter ....Pages 1-1 A Brief Introduction to PDE-Constrained Optimization (Harbir Antil, Dmitriy Leykekhman)....Pages 3-40 Optimization of PDEs with Uncertain Inputs (Drew P. Kouri, Alexander Shapiro)....Pages 41-81 Inexact Trust-Region Methods for PDE-Constrained Optimization (Drew P. Kouri, Denis Ridzal)....Pages 83-121 Numerical Optimization Methods for the Optimal Control of Elliptic Variational Inequalities (Thomas M. Surowiec)....Pages 123-170 Introduction to PDE-Constrained Optimization in the Oil and Gas Industry (Jeremy Brandman, Huseyin Denli, Dimitar Trenev)....Pages 171-203 Full-Wavefield Inversion: An Extreme-Scale PDE-Constrained Optimization Problem (Martin-D. Lacasse, Laurent White, Huseyin Denli, Lingyun Qiu)....Pages 205-255 Front Matter ....Pages 257-257 Energetically Optimal Flapping Wing Motions via Adjoint-Based Optimization and High-Order Discretizations (Matthew J. Zahr, Per-Olof Persson)....Pages 259-289 Optimization of a Fractional Differential Equation (Enrique Otárola, Abner J. Salgado)....Pages 291-316 Sensitivity-Based Topology and Shape Optimization with Application to Electric Motors (Peter Gangl)....Pages 317-340 Distributed Parameter Estimation for the Time-Dependent Radiative Transfer Equation (Oliver Dorn)....Pages 341-375 On the Use of Optimal Transport Distances for a PDE-Constrained Optimization Problem in Seismic Imaging (L. Métivier, A. Allain, R. Brossier, Q. Mérigot, E. Oudet, J. Virieux)....Pages 377-397 Exploiting Sparsity in Solving PDE-Constrained Inverse Problems: Application to Subsurface Flow Model Calibration (Azarang Golmohammadi, M-Reza M. Khaninezhad, Behnam Jafarpour)....Pages 399-434