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Frontiers in PDE-Constrained Optimization

  • Book
  • © 2018

Overview

Editors:
  1. Harbir Antil

    1. Department of Mathematical Sciences, George Mason University, Fairfax, USA

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  2. Drew P. Kouri

    1. Center for Computing Research, Sandia National Laboratories, Albuquerque, USA

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  3. Martin-D. Lacasse

    1. Corporate Strategic Research, ExxonMobil Research and Engineering Company, Annandale, USA

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  4. Denis Ridzal

    1. Center for Computing Research, Sandia National Laboratories, Albuquerque, USA

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  • Provides a comprehensive treatment to inverse problems, in particular, problems arising in the oil and gas industries
  • Includes tutorials targeted towards graduate students and early career researchers who are interested in getting into the field
  • Contains contributions from invited speakers which include the entire spectrum of problems arising in PDE-constrained optimization

Part of the book series: The IMA Volumes in Mathematics and its Applications (IMA, volume 163)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-x
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  2. PDE-Constrained Optimization: Tutorials

    1. Front Matter

      Pages 1-1
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    2. A Brief Introduction to PDE-Constrained Optimization

      • Harbir Antil, Dmitriy Leykekhman
      Pages 3-40

    3. Optimization of PDEs with Uncertain Inputs

      • Drew P. Kouri, Alexander Shapiro
      Pages 41-81

    4. Inexact Trust-Region Methods for PDE-Constrained Optimization

      • Drew P. Kouri, Denis Ridzal
      Pages 83-121

    5. Numerical Optimization Methods for the Optimal Control of Elliptic Variational Inequalities

      • Thomas M. Surowiec
      Pages 123-170

    6. Introduction to PDE-Constrained Optimization in the Oil and Gas Industry

      • Jeremy Brandman, Huseyin Denli, Dimitar Trenev
      Pages 171-203

    7. Full-Wavefield Inversion: An Extreme-Scale PDE-Constrained Optimization Problem

      • Martin-D. Lacasse, Laurent White, Huseyin Denli, Lingyun Qiu
      Pages 205-255

  3. PDE-Constrained Optimization: Applications

    1. Front Matter

      Pages 257-257
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    2. Energetically Optimal Flapping Wing Motions via Adjoint-Based Optimization and High-Order Discretizations

      • Matthew J. Zahr, Per-Olof Persson
      Pages 259-289

    3. Optimization of a Fractional Differential Equation

      • Enrique Otárola, Abner J. Salgado
      Pages 291-316

    4. Sensitivity-Based Topology and Shape Optimization with Application to Electric Motors

      • Peter Gangl
      Pages 317-340

    5. Distributed Parameter Estimation for the Time-Dependent Radiative Transfer Equation

      • Oliver Dorn
      Pages 341-375

    6. 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

    7. 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
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Keywords

About this book

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 inverseproblems 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.

Reviews

“I am deeply impressed by the quality of the contributions both from the mathematical and also from the applications side. I highly recommend this book to newcomers in the field and also to experts who want to broaden their expertise in other directions.” (Ekkehard Sachs, SIAM Review, Vol. 61 (4), December, 2019)

Editors and Affiliations

  • Department of Mathematical Sciences, George Mason University, Fairfax, USA

    Harbir Antil

  • Center for Computing Research, Sandia National Laboratories, Albuquerque, USA

    Drew P. Kouri, Denis Ridzal

  • Corporate Strategic Research, ExxonMobil Research and Engineering Company, Annandale, USA

    Martin-D. Lacasse

Bibliographic Information

  • Book Title: Frontiers in PDE-Constrained Optimization

  • Editors: Harbir Antil, Drew P. Kouri, Martin-D. Lacasse, Denis Ridzal

  • Series Title: The IMA Volumes in Mathematics and its Applications

  • DOI: https://doi.org/10.1007/978-1-4939-8636-1

  • Publisher: Springer New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: National Technology & Engineering Solutions of Sandia, LLC. Under the terms of Contract DE-NA0003525, there is a non-exclusive license for use of this work by or on behalf of the U.S. Government 2018

  • Hardcover ISBN: 978-1-4939-8635-4Published: 13 October 2018

  • Softcover ISBN: 978-1-4939-9349-9Published: 10 December 2019

  • eBook ISBN: 978-1-4939-8636-1Published: 12 October 2018

  • Series ISSN: 0940-6573

  • Series E-ISSN: 2198-3224

  • Edition Number: 1

  • Number of Pages: X, 434

  • Number of Illustrations: 12 b/w illustrations, 72 illustrations in colour

  • Topics: Partial Differential Equations, Mathematics of Planet Earth, Optimization, Topology

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