Sinossi
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
Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.
Informazioni sull?autore
M. Bergounioux; É. Oudet; M. Rumpf; G. Carlier; T. Champion; F. Santambrogio.
Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.
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Topological Optimization and Optimal Transport
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Buch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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 432 pp. Englisch. Codice articolo 9783110439267
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Topological Optimization and Optimal Transport: In the Applied Sciences (Radon Series on Computational and Applied Mathematics, 17)
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Buch. Condizione: Neu. Topological Optimization and Optimal Transport | In the Applied Sciences | Maïtine Bergounioux (u. a.) | Buch | XII | Englisch | 2017 | De Gruyter | EAN 9783110439267 | Verantwortliche Person für die EU: Walter de Gruyter GmbH, De Gruyter GmbH, Genthiner Str. 13, 10785 Berlin, productsafety[at]degruyterbrill[dot]com | Anbieter: preigu Print on Demand. Codice articolo 109563934
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De Gruyter, De Gruyter Aug 2017, 2017
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Buch. Condizione: Neu. Neuware -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 operatorSolution of free boundary problems in the presence of geometric uncertaintiesDistributed and boundary control problems for the semidiscrete Cahn Hilliard/Navier Stokes system with nonsmooth Ginzburg Landau energiesHigh-order topological expansions for Helmholtz problems in 2DOn a new phase field model for the approximation of interfacial energies of multiphase systemsOptimization of eigenvalues and eigenmodes by using the adjoint methodDiscrete varifolds and surface approximationPart II Weak Monge Ampere solutions of the semi-discrete optimal transportation problemOptimal transportation theory with repulsive costsWardrop equilibria: long-term variant, degenerate anisotropic PDEs and numerical approximationsOn the Lagrangian branched transport model and the equivalence with its Eulerian formulationOn some nonlinear evolution systems which are perturbations of Wasserstein gradient flowsPressureless Euler equations with maximal density constraint: a time-splitting schemeConvergence of a fully discrete variational scheme for a thin-film equatioInterpretation of finite volume discretization schemes for the Fokker Planck equation as gradient flows for the discrete Wasserstein distanceWalter de Gruyter, Genthiner Straße 13, 10785 Berlin 432 pp. Englisch. Codice articolo 9783110439267
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