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

Computation Using Orthonormal Basis Vectors

Sehun Chun (Autor)

Buch | Hardcover

248 Seiten

2025
Springer Verlag, Singapore
978-981-95-4494-3 (ISBN)

Titel nicht im Sortiment

Artikel merken

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.

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

Chapter 1 Introduction.- Chapter 2 Constructing moving frames.- Chapter 3 Covariant Derivative in Moving Frames.- Chapter 4 Differential Operators in Moving Frames.- Chapter 5 Applications to PDEs on Curved Surfaces.- Chapter 6 Relative Acceleration and the Riemann Curvature Tensor.

Erscheinungsdatum	29.11.2025
Reihe/Serie	Springer Asia Pacific Mathematics Series
Zusatzinfo	102 Illustrations, color; 84 Illustrations, black and white
Verlagsort	Singapore
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	curved surfaces • Discontinuous Galerkin method • Method of moving frames • Numerical solution of partial differential equation • spectral method
ISBN-10	981-95-4494-7 / 9819544947
ISBN-13	978-981-95-4494-3 / 9789819544943
Zustand	Neuware