Buch, Englisch, 248 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 569 g
Computation Using Orthonormal Basis Vectors
Buch, Englisch, 248 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 569 g
Reihe: Springer Asia Pacific Mathematics Series
ISBN: 978-981-954494-3
Verlag: Springer
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.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
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.
