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Type: Journal article
Title: Subdomain Chebyshev spectral method for 2D and 3D numerical differentiations in a curved coordinate system
Author: Zhou, B.
Heinson, G.
Rivera-Rios, A.
Citation: Journal of Applied Mathematics and Physics, 2015; 03(03):358-370
Publisher: Scientific Research Publishing
Issue Date: 2015
ISSN: 2327-4352
Statement of
Bing Zhou, Graham Heinson, Aixa Rivera-Rios
Abstract: A new numerical approach, called the “subdomain Chebyshev spectral method” is presented for calculation of the spatial derivatives in a curved coordinate system, which may be employed for numerical solutions of partial differential equations defined in a 2D or 3D geological model. The new approach refers to a “strong version” against the “weak version” of the subspace spectral method based on the variational principle or Galerkin’s weighting scheme. We incorporate local nonlinear transformations and global spline interpolations in a curved coordinate system and make the discrete grid exactly matches geometry of the model so that it is achieved to convert the global domain into subdomains and apply Chebyshev points to locally sampling physical quantities and globally computing the spatial derivatives. This new approach not only remains exponential convergence of the standard spectral method in subdomains, but also yields a sparse assembled matrix when applied for the global domain simulations. We conducted 2D and 3D synthetic experiments and compared accuracies of the numerical differentiations with traditional finite difference approaches. The results show that as the points of differentiation vector are larger than five, the subdomain Chebyshev spectral method significantly improve the accuracies of the finite difference approaches.
Keywords: Numerical Differentiation; Chebyshev Spectral Method; Curved Coordinate System; Arbitrary Topography
Rights: Copyright © 2015 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY).
RMID: 0030031664
DOI: 10.4236/jamp.2015.33047
Grant ID:
Appears in Collections:Physics publications

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