Topological optimization and optimal transport in the applied sciences / Edited by Maïtine Bergounioux [and five others].

Format:

Book

Contributor:

Bergounioux, Maïtine, editor.

Series:

Radon series on computational and applied mathematics ; Volume 17.

Radon Series on Computational and Applied Mathematics, 1865-3707 ; Volume 17

Language:

English

Subjects (All):

Mathematical optimization.

Physical Description:

1 online resource (430 pages).

Edition:

1st ed.

Place of Publication:

Berlin, [Germany] ; Boston, [Massachusetts] : De Gruyter, 2017.

Language Note:

In English.

Summary:

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. ContentsPart 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

Contents:

Frontmatter

Contents

Part I

1. Geometric issues in PDE problems related to the infinity Laplace operator / Crasta, Graziano / Fragalà, Ilaria

2. Solution of free boundary problems in the presence of geometric uncertainties / Harbrecht, H. / Peters, M. D.

3. Distributed and boundary control problems for the semidiscrete Cahn-Hilliard/Navier-Stokes system with nonsmooth Ginzburg-Landau energies / Hintermüller, M. / Wegner, D.

4. High-order topological expansions for Helmholtz problems in 2D / Kovtunenko, Victor A.

5. On a new phase field model for the approximation of interfacial energies of multiphase systems / Bretin, Elie / Masnou, Simon

6. Optimization of eigenvalues and eigenmodes by using the adjoint method / Toader, Anca-Maria / Barbarosie, Cristian

7. Discrete varifolds and surface approximation / Buet, Blanche / Leonardi, Gian Paolo / Masnou, Simon

Part II

Preface / Carlier, Guillaume / Champion, Thierry / Santambrogio, Filippo

8. Weak Monge-Ampère solutions of the semi-discrete optimal transportation problem / Benamou, Jean-David / Froese, Brittany D.

9. Optimal transportation theory with repulsive costs / Marino, Simone Di / Gerolin, Augusto / Nenna, Luca

10. Wardrop equilibria: long-term variant, degenerate anisotropic PDEs and numerical approximations / Hatchi, Roméo

11. On the Lagrangian branched transport model and the equivalence with its Eulerian formulation / Pegon, Paul

12. On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows / Laborde, Maxime

13. Pressureless Euler equations with maximal density constraint: a time-splitting scheme / Maury, B. / Preux, A.

14. Convergence of a fully discrete variational scheme for a thin-film equation / Osberger, Horst / Matthes, Daniel

15. Interpretation of finite volume discretization schemes for the Fokker-Planck equation as gradient flows for the discrete Wasserstein distance / Reda, F. Al / Maury, B.

Index

Notes:

Includes bibliographical references at the end of each chapters and index.

Description based on online resource; title from PDF title page (ebrary, viewed August 21, 2017).

ISBN:

9783110430509

3110430509

9783110430417

311043041X

OCLC:

1002222178