Topological Optimization and Optimal Transport

Topological Optimization and Optimal Transport

Author: Maïtine Bergounioux

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 9783110430509

Category: Mathematics

Page: 432

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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
Topological Optimization and Optimal Transport
Language: en
Pages: 432
Authors: Maïtine Bergounioux, Édouard Oudet, Martin Rumpf, Guillaume Carlier, Thierry Champion, Filippo Santambrogio
Categories: Mathematics
Type: BOOK - Published: 2017-08-07 - Publisher: Walter de Gruyter GmbH & Co KG

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
Geometric Partial Differential Equations - Part 2
Language: en
Pages: 570
Authors: Andrea Bonito, Ricardo Horacio Nochetto
Categories: Mathematics
Type: BOOK - Published: 2021-01-26 - Publisher: Elsevier

Besides their intrinsic mathematical interest, geometric partial differential equations (PDEs) are ubiquitous in many scientific, engineering and industrial applications. They represent an intellectual challenge and have received a great deal of attention recently. The purpose of this volume is to provide a missing reference consisting of self-contained and comprehensive presentations.
Optimal Structural Design
Language: en
Pages: 203
Authors: Nikolay V. Banichuk, Svetlana Yu. Ivanova
Categories: Mathematics
Type: BOOK - Published: 2017-09-11 - Publisher: Walter de Gruyter GmbH & Co KG

This monograph studies optimization problems for rigid punches in elastic media and for high-speed penetration of rigid strikers into deformed elastoplastic, concrete, and composite media using variational calculations, tools from functional analysis, and stochastic and min-max (guaranteed) optimization approaches with incomplete data. The book presents analytical and numerical results developed
Non-Smooth and Complementarity-Based Distributed Parameter Systems
Language: en
Pages:
Authors: Michael Hintermüller
Categories: Mathematics
Type: BOOK - Published: - Publisher: Springer Nature

Books about Non-Smooth and Complementarity-Based Distributed Parameter Systems
Convex and Set-Valued Analysis
Language: en
Pages: 209
Authors: Aram V. Arutyunov, Valeri Obukhovskii
Categories: Mathematics
Type: BOOK - Published: 2016-12-05 - Publisher: Walter de Gruyter GmbH & Co KG

This textbook is devoted to a compressed and self-contained exposition of two important parts of contemporary mathematics: convex and set-valued analysis. In the first part, properties of convex sets, the theory of separation, convex functions and their differentiability, properties of convex cones in finite- and infinite-dimensional spaces are discussed. The