
Geometric Partial Differential Equations - Part 2
Description
Key Features
- About every aspect of computational geometric PDEs is discussed in this and a companion volume. Topics in this volume include stationary and time-dependent surface PDEs for geometric flows, large deformations of nonlinearly geometric plates and rods, level set and phase field methods and applications, free boundary problems, discrete Riemannian calculus and morphing, fully nonlinear PDEs including Monge-Ampere equations, and PDE constrained optimization
- Each chapter is a complete essay at the research level but accessible to junior researchers and students. The intent is to provide a comprehensive description of algorithms and their analysis for a specific geometric PDE class, starting from basic concepts and concluding with interesting applications. Each chapter is thus useful as an introduction to a research area as well as a teaching resource, and provides numerous pointers to the literature for further reading
- The authors of each chapter are world leaders in their field of expertise and skillful writers. This book is thus meant to provide an invaluable, readable and enjoyable account of computational geometric PDEs
Readership
The targeted audience is mathematically trained research scientists and engineers with basic knowledge in partial differential equations and their numerical approximations.
Table of Contents
1. Shape and topology optimization
Grégoire Allaire, Charles Dapogny, and François Jouve2. Optimal transport: discretization and algorithms
Quentin Mérigot and Boris Thibert3. Optimal control of geometric partial differential equations
Michael Hintermüller and Tobias Keil4. Lagrangian schemes for Wasserstein gradient flows
Jose A. Carrillo, Daniel Matthes, and Marie-Therese Wolfram5. The Q-tensor model with uniaxial constraint
Juan Pablo Borthagaray and Shawn W. Walker6. Approximating the total variation with finite differences or finite elements
Antonin Chambolle and Thomas Pock7. Numerical simulation and benchmarking of drops and bubbles
Stefan Turek and Otto Mierka8. Smooth multi-patch discretizations in isogeometric analysis
Thomas J.R. Hughes, Giancarlo Sangalli, Thomas Takacs, and Deepesh Toshniwal
Product details
- No. of pages: 570
- Language: English
- Copyright: © North Holland 2021
- Published: January 26, 2021
- Imprint: North Holland
- Hardcover ISBN: 9780444643056
- eBook ISBN: 9780444643063
About the Editors
Andrea Bonito
Affiliations and Expertise
Ricardo Nochetto
Affiliations and Expertise
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