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High-Accuracy Approximation of High-Rank Derivatives: Isotropic Finite Differences Based on Lattice-Boltzmann Stencils
Joint Authors
Mattila, Keijo Kalervo
Hegele Júnior, Luiz Adolfo
Philippi, Paulo Cesar
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-16, 16 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-01-29
Country of Publication
Egypt
No. of Pages
16
Main Subjects
Medicine
Information Technology and Computer Science
Abstract EN
We propose isotropic finite differences for high-accuracy approximation of high-rank derivatives.
These finite differences are based on direct application of lattice-Boltzmann stencils.
The presented finite-difference expressions are valid in any dimension, particularly in two and three dimensions, and any lattice-Boltzmann stencil isotropic enough can be utilized.
A theoretical basis for the proposed utilization of lattice-Boltzmann stencils in the approximation of high-rank derivatives is established.
In particular, the isotropy and accuracy properties of the proposed approximations are derived directly from this basis.
Furthermore, in this formal development, we extend the theory of Hermite polynomial tensors in the case of discrete spaces and present expressions for the discrete inner products between monomials and Hermite polynomial tensors.
In addition, we prove an equivalency between two approaches for constructing lattice-Boltzmann stencils.
For the numerical verification of the presented finite differences, we introduce 5th-, 6th-, and 8th-order two-dimensional lattice-Boltzmann stencils.
American Psychological Association (APA)
Mattila, Keijo Kalervo& Hegele Júnior, Luiz Adolfo& Philippi, Paulo Cesar. 2014. High-Accuracy Approximation of High-Rank Derivatives: Isotropic Finite Differences Based on Lattice-Boltzmann Stencils. The Scientific World Journal،Vol. 2014, no. 2014, pp.1-16.
https://search.emarefa.net/detail/BIM-1048454
Modern Language Association (MLA)
Mattila, Keijo Kalervo…[et al.]. High-Accuracy Approximation of High-Rank Derivatives: Isotropic Finite Differences Based on Lattice-Boltzmann Stencils. The Scientific World Journal No. 2014 (2014), pp.1-16.
https://search.emarefa.net/detail/BIM-1048454
American Medical Association (AMA)
Mattila, Keijo Kalervo& Hegele Júnior, Luiz Adolfo& Philippi, Paulo Cesar. High-Accuracy Approximation of High-Rank Derivatives: Isotropic Finite Differences Based on Lattice-Boltzmann Stencils. The Scientific World Journal. 2014. Vol. 2014, no. 2014, pp.1-16.
https://search.emarefa.net/detail/BIM-1048454
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1048454