Moving Frames for the Numerical Solution of Partial Differential Equations in Complex Domains : Computation Using Orthonormal Basis Vectors

Sehun Chun

ISBN 10: 9819544947 / ISBN 13: 9789819544943

Published by Springer, 2025

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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.

Seller Inventory # 9789819544943

Bibliographic Details

• Title: Moving Frames for the Numerical Solution of Partial Differential Equations in Complex Domains : Computation Using Orthonormal Basis Vectors
• Publisher: Springer
• Publication Date: 2025
• Language: English
• ISBN 10: 9819544947
• ISBN 13: 9789819544943
• Binding: Buch
• Condition: Neu
• Dimensions: 241W x 160H x 21D millimeters 241 millimeters width by 160 millimeters height by 21 millimeters depth
• Weight: 569 grams

About this title

Synopsis

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.

About the Author

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