Téléchargez le livre : Moving Frames for the Numerical Solution of Partial Differential Equations in Complex Domains

Moving Frames for the Numerical Solution of Partial Differential Equations in Complex Domains

Computation Using Orthonormal Basis Vectors

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Springer


Paru le : 2025-11-24



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Description

This book presents a comprehensive and geometrical approach to solving partial differential equations (PDEs) on complex curved domains using orthonormal moving frames. Rooted in Élie Cartan’s classical theory but adapted for computational practicality, the framework aligns local basis vectors with the intrinsic geometry and anisotropy of the domain, enabling accurate and efficient discretization without requiring explicit metric tensors or Christoffel symbols. Topics include the construction of moving frames on general manifolds, covariant derivatives via connection 1-forms, and frame-based formulations of gradient, divergence, curl, and Laplacian operators. Extensive MATLAB and C++ implementations (via Nektar++) are provided for benchmark problems in diffusion-reaction systems, shallow water equations, and Maxwell’s equations on complex surfaces such as the sphere, pseudosphere, and atrial tissue. Emphasizing clarity and accessibility, the book blends theory, visualization, and numerical practice, making it an essential resource for graduate students and researchers in scientific computing, applied mathematics, and engineering disciplines dealing with PDEs on non-Euclidean domains.
Pages
248 pages
Collection
n.c
Parution
2025-11-24
Marque
Springer
EAN papier
9789819544943
EAN PDF
9789819544950
Informations sur l'ebook
Nombre pages copiables
2
Nombre pages imprimables
24
Taille du fichier
23316 Ko
Ce livre est accessible aux handicaps Voir les informations sur l'accessibilité
Prix
158,24 €
EAN EPUB
9789819544950
Informations sur l'ebook
Nombre pages copiables
2
Nombre pages imprimables
24
Taille du fichier
47258 Ko
Ce livre est accessible aux handicaps Voir les informations sur l'accessibilité
Prix
158,24 €

Sehun Chun is an associate professor of Applied Mathematics at Yonsei University.

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