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Data for Integration over discrete closed surfaces using the Method of Fundamental Solutions
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Lockerby, Duncan A. (2021) Data for Integration over discrete closed surfaces using the Method of Fundamental Solutions. [Dataset]
Plain Text (Readme file)
readme.txt - Published Version Available under License Creative Commons Attribution 4.0. Download (610b) |
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Archive (ZIP) (Dataset)
data for paper.zip - Published Version Available under License Creative Commons Attribution 4.0. Download (1511Kb) |
Official URL: http://wrap.warwick.ac.uk/161189/
Abstract
The Method of Fundamental Solutions (MFS) is an established technique for solving linear partial different equations. In this paper it is used for a new purpose: the approximation of integrals over closed surfaces from a finite set of known points and values. The MFS is used to fit an implicit surface through the surface points, where the implicit equation is chosen such that a surface integral is provided by summing the weights of the fit. From the divergence theorem, these surface integrals can be related to specific integrals over the enclosed volume. As a demonstration, we calculate the surface area, volume, centroid and radius of gyration, for three solid geometries: a sphere, a torus, and an ellipsoid. Very quick convergence to analytical results is shown. Local surface properties, such as the components of curvature, can also be obtained accurately. The drawbacks and advantages of the method are discussed, and the potential to calculate properties of constant-density rigid bodies (e.g. the moment of inertia tensor) and averages of incompressible flow fields (e.g. average flow velocity and strain rate) is highlighted.
Item Type: | Dataset | |||||||||
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Subjects: | Q Science > QA Mathematics T Technology > TA Engineering (General). Civil engineering (General) |
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Divisions: | Faculty of Science, Engineering and Medicine > Engineering > Engineering | |||||||||
Type of Data: | ascii .m | |||||||||
Library of Congress Subject Headings (LCSH): | Differential equations, Partial, Numerical integration, Surfaces -- Mathematics, Integrals | |||||||||
Publisher: | University of Warwick, School of Engineering | |||||||||
Official Date: | 21 December 2021 | |||||||||
Dates: |
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Status: | Not Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Media of Output (format): | .txt | |||||||||
Access rights to Published version: | Open Access (Creative Commons) | |||||||||
Copyright Holders: | University of Warwick | |||||||||
Description: | paperCode.m is the Matlab script used to generate the results of the paper (also included as an Appendix to the paper). The input files for each geometry (which are loaded by paperCode.m) are contained in the directories 'ellipsoid', 'sphere', 'torus' and 'particle'. The three files needed by paperCode.m are: |
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Date of first compliant deposit: | 21 December 2021 | |||||||||
Date of first compliant Open Access: | 21 December 2021 | |||||||||
RIOXX Funder/Project Grant: |
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Contributors: |
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