Topological Optimization and Optimal Transport

Published by De Gruyter 2017

Topological Optimization and Optimal Transport

In the Applied Sciences

Edited by: Maïtine Bergounioux, Édouard Oudet, Martin Rumpf, Guillaume Carlier, Thierry Champion and Filippo Santambrogio

Volume 17 in the series Radon Series on Computational and Applied Mathematics

https://doi.org/10.1515/9783110430417

Overview
Contents

About this book

By discussing topics such as shape representations, relaxation theory and optimal transport, trends and synergies of mathematical tools required for optimization of geometry and topology of shapes are explored. Furthermore, applications in science and engineering, including economics, social sciences, biology, physics and image processing are covered.

Contents
Part I

Geometric issues in PDE problems related to the infinity Laplace operator
Solution of free boundary problems in the presence of geometric uncertainties
Distributed and boundary control problems for the semidiscrete Cahn–Hilliard/Navier–Stokes system with nonsmooth Ginzburg–Landau energies
High-order topological expansions for Helmholtz problems in 2D
On a new phase field model for the approximation of interfacial energies of multiphase systems
Optimization of eigenvalues and eigenmodes by using the adjoint method
Discrete varifolds and surface approximation

Part II

Weak Monge–Ampere solutions of the semi-discrete optimal transportation problem
Optimal transportation theory with repulsive costs
Wardrop equilibria: long-term variant, degenerate anisotropic PDEs and numerical approximations
On the Lagrangian branched transport model and the equivalence with its Eulerian formulation
On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows
Pressureless Euler equations with maximal density constraint: a time-splitting scheme
Convergence of a fully discrete variational scheme for a thin-film equatio
Interpretation of finite volume discretization schemes for the Fokker–Planck equation as gradient flows for the discrete Wasserstein distance

Author information

M. Bergounioux; É. Oudet; M. Rumpf; G. Carlier; T. Champion; F. Santambrogio.

Topics

Frontmatter Publicly Available Download PDF	I
Contents Publicly Available Download PDF	V
Part I
1. Geometric issues in PDE problems related to the infinity Laplace operator Graziano Crasta and Ilaria Fragalà Requires Authentication Unlicensed Licensed Download PDF	3
2. Solution of free boundary problems in the presence of geometric uncertainties H. Harbrecht and M. D. Peters Requires Authentication Unlicensed Licensed Download PDF	20
3. Distributed and boundary control problems for the semidiscrete Cahn–Hilliard/Navier–Stokes system with nonsmooth Ginzburg–Landau energies M. Hintermüller and D. Wegner Requires Authentication Unlicensed Licensed Download PDF	40
4. High-order topological expansions for Helmholtz problems in 2D Victor A. Kovtunenko Requires Authentication Unlicensed Licensed Download PDF	64
5. On a new phase field model for the approximation of interfacial energies of multiphase systems Elie Bretin and Simon Masnou Requires Authentication Unlicensed Licensed Download PDF	123
6. Optimization of eigenvalues and eigenmodes by using the adjoint method Anca-Maria Toader and Cristian Barbarosie Requires Authentication Unlicensed Licensed Download PDF	142
7. Discrete varifolds and surface approximation Blanche Buet, Gian Paolo Leonardi and Simon Masnou Requires Authentication Unlicensed Licensed Download PDF	159
Part II
Preface Guillaume Carlier, Thierry Champion and Filippo Santambrogio Requires Authentication Unlicensed Licensed Download PDF	173
8. Weak Monge–Ampère solutions of the semi-discrete optimal transportation problem Jean-David Benamou and Brittany D. Froese Requires Authentication Unlicensed Licensed Download PDF	175
9. Optimal transportation theory with repulsive costs Simone Di Marino, Augusto Gerolin and Luca Nenna Requires Authentication Unlicensed Licensed Download PDF	204
10. Wardrop equilibria: long-term variant, degenerate anisotropic PDEs and numerical approximations Roméo Hatchi Requires Authentication Unlicensed Licensed Download PDF	257
11. On the Lagrangian branched transport model and the equivalence with its Eulerian formulation Paul Pegon Requires Authentication Unlicensed Licensed Download PDF	281
12. On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows Maxime Laborde Requires Authentication Unlicensed Licensed Download PDF	304
13. Pressureless Euler equations with maximal density constraint: a time-splitting scheme B. Maury and A. Preux Requires Authentication Unlicensed Licensed Download PDF	333
14. Convergence of a fully discrete variational scheme for a thin-film equation Horst Osberger and Daniel Matthes Requires Authentication Unlicensed Licensed Download PDF	356
15. Interpretation of finite volume discretization schemes for the Fokker–Planck equation as gradient flows for the discrete Wasserstein distance F. Al Reda and B. Maury Requires Authentication Unlicensed Licensed Download PDF	400
Index Requires Authentication Unlicensed Licensed Download PDF	417

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Researchers in mathematics (especially in optimization), engineering and computer science.
Pages
- Front matter: 12
- Main content: 420
Illustrations
- Illustrations: 105
Keywords: Shape representations; shape optimization; relaxation theory; optimal transport

eBook

Published: August 7, 2017
ISBN: 9783110430417

Hardcover

Published: August 7, 2017
ISBN: 9783110439267