Topological Optimization and Optimal Transport In the Applied Sciences
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.
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| Main Authors | , , , , , |
|---|---|
| Format | eBook |
| Language | English |
| Published |
Germany
De Gruyter
2017
Walter de Gruyter GmbH |
| Edition | 1 |
| Series | Radon Series on Computational and Applied Mathematics |
| Subjects | |
| Online Access | Get full text |
| ISBN | 9783110430417 311043041X 9783110439267 3110439263 |
| DOI | 10.1515/9783110430417 |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. 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 |
| Author | Champion, Thierry Bergounioux, Maïtine Rumpf, Martin Santambrogio, Filippo Carlier, Guillaume Oudet, Édouard |
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| Contributor | Buet, Blanche Matthes, Daniel Preux, A Masnou, Simon Benamou, Jean-David Carlier, Guillaume Hatchi, Roméo Hintermüller, M Gerolin, Augusto Fragalà, Ilaria Laborde, Maxime Peters, M. D Kovtunenko, Victor A Osberger, Horst Toader, Anca-Maria Maury, B Reda, F. Al Froese, Brittany D Marino, Simone Di Pegon, Paul Leonardi, Gian Paolo Nenna, Luca Barbarosie, Cristian Champion, Thierry Bretin, Elie Crasta, Graziano Santambrogio, Filippo Wegner, D Harbrecht, H |
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| DOI | 10.1515/9783110430417 |
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| Editor | Bergounioux, Maïtine Rumpf, Martin Carlier, Guillaume Oudet, Édouard |
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| Keywords | optimal transport Shape representations shape optimization relaxation theory |
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| PublicationDate | 2017 [2017] 2017-08-07 |
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| PublicationPlace | Germany |
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| PublicationSeriesTitle | Radon Series on Computational and Applied Mathematics |
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| SubjectTerms | Bildverarbeitung Control theory Mathematical optimization Mathematics MATHEMATICS / Optimization optimal transport Optimierung Partielle Differentialgleichung relaxation theory shape optimization Shape representations Topology Transportation problems (Programming) |
| Subtitle | In the Applied Sciences |
| TableOfContents | Intro -- Contents -- Part I -- 1. Geometric issues in PDE problems related to the infinity Laplace operator -- 2. Solution of free boundary problems in the presence of geometric uncertainties -- 3. Distributed and boundary control problems for the semidiscrete Cahn-Hilliard/Navier-Stokes system with nonsmooth Ginzburg-Landau energies -- 4. High-order topological expansions for Helmholtz problems in 2D -- 5. On a new phase field model for the approximation of interfacial energies of multiphase systems -- 6. Optimization of eigenvalues and eigenmodes by using the adjoint method -- 7. Discrete varifolds and surface approximation -- Part II -- Preface -- 8. Weak Monge-Ampère solutions of the semi-discrete optimal transportation problem -- 9. Optimal transportation theory with repulsive costs -- 10. Wardrop equilibria: long-term variant, degenerate anisotropic PDEs and numerical approximations -- 11. On the Lagrangian branched transport model and the equivalence with its Eulerian formulation -- 12. On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows -- 13. Pressureless Euler equations with maximal density constraint: a time-splitting scheme -- 14. Convergence of a fully discrete variational scheme for a thin-film equation -- 15. Interpretation of finite volume discretization schemes for the Fokker-Planck equation as gradient flows for the discrete Wasserstein distance -- Index Contents -- Preface -- Part II -- 2. Solution of free boundary problems in the presence of geometric uncertainties -- Index 5. On a new phase field model for the approximation of interfacial energies of multiphase systems -- 9. Optimal transportation theory with repulsive costs -- 14. Convergence of a fully discrete variational scheme for a thin-film equation -- 3. Distributed and boundary control problems for the semidiscrete Cahn–Hilliard/Navier–Stokes system with nonsmooth Ginzburg–Landau energies -- 6. Optimization of eigenvalues and eigenmodes by using the adjoint method -- Part I -- Frontmatter -- 1. Geometric issues in PDE problems related to the infinity Laplace operator -- 8. Weak Monge–Ampère solutions of the semi-discrete optimal transportation problem -- 10. Wardrop equilibria: long-term variant, degenerate anisotropic PDEs and numerical approximations -- 11. On the Lagrangian branched transport model and the equivalence with its Eulerian formulation -- 13. Pressureless Euler equations with maximal density constraint: a time-splitting scheme -- 15. Interpretation of finite volume discretization schemes for the Fokker–Planck equation as gradient flows for the discrete Wasserstein distance -- 12. On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows -- 4. High-order topological expansions for Helmholtz problems in 2D -- 7. Discrete varifolds and surface approximation -- |
| Title | Topological Optimization and Optimal Transport |
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