2026-10-11T05:57:57Z https://api.figshare.com/v2/oai

oai:figshare.com:article/33835447 2026-09-16T08:59:06Z portal_1197 item_type_3 month_year_09_2026

Data for Integration over discrete closed surfaces using the Method of Fundamental Solutions Duncan A. Lockerby (11114529) Differential equations, Partial Numerical integration Surfaces -- Mathematics Integrals Migrated from ePrints 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.<br><br>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: ri_[geometry]_[resolution].txt (positions of the surface points) rvj_[geometry]_[resolution].txt (positions of the volume points), and ni_[geometry]_[resolution].txt (outward-facing normal vectors at surface points) The resolutions are labelled, F (for fine), C (for Coarse), etc. 2021-12-21T00:00:00Z Dataset Dataset 10.82444/warw.33835447.v1 https://figshare.com/articles/dataset/Data_for_Integration_over_discrete_closed_surfaces_using_the_Method_of_Fundamental_Solutions/33835447 CC BY 4.0