Burrage, K, Burrage, PM and Lythe, G orcid.org/0000-0001-7966-5571 (2022) Effective numerical methods for simulating diffusion on a spherical surface in three dimensions. Numerical Algorithms, 91 (4). pp. 1577-1596. ISSN 1017-1398
Abstract
In order to construct an algorithm for homogeneous diffusive motion that lives on a sphere, we consider the equivalent process of a randomly rotating spin vector of constant length. By introducing appropriate sets of random variables based on cross products, we construct families of methods with increasing efficacy that exactly preserve the spin modulus for every realisation. This is done by exponentiating an antisymmetric matrix whose entries are these random variables that are Gaussian in the simplest case.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Crown 2022. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
Keywords: | Brownian motion; Stochastic differential equations; Diffusion on a sphere |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 21 Mar 2023 11:12 |
Last Modified: | 21 Mar 2023 11:12 |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/s11075-022-01315-w |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:197515 |