1. bookVolume 32 (2022): Issue 3 (September 2022)
    Recent Advances in Modelling, Analysis and Implementation of Cyber-Physical Systems (Special section, pp. 345-413), Remigiusz Wiśniewski, Luis Gomes and Shaohua Wan (Eds.)
Journal Details
License
Format
Journal
eISSN
2083-8492
First Published
05 Apr 2007
Publication timeframe
4 times per year
Languages
English
Open Access

RBF Based Quadrature on the Sphere

Published Online: 08 Oct 2022
Volume & Issue: Volume 32 (2022) - Issue 3 (September 2022) - Recent Advances in Modelling, Analysis and Implementation of Cyber-Physical Systems (Special section, pp. 345-413), Remigiusz Wiśniewski, Luis Gomes and Shaohua Wan (Eds.)
Page range: 467 - 478
Received: 04 Oct 2021
Accepted: 11 Apr 2022
Journal Details
License
Format
Journal
eISSN
2083-8492
First Published
05 Apr 2007
Publication timeframe
4 times per year
Languages
English

Ahrens, C. and Beylkin, G. (2009). Rotationally invariant quadratures for the sphere, Proceedings of the Royal Society A 465(2110): 3103–3125.10.1098/rspa.2009.0104 Search in Google Scholar

Atkinson, K. (1982). Numerical integration on the sphere, Journal of the Australian Mathematical Society B 23(3): 332–347.10.1017/S0334270000000278 Search in Google Scholar

Bazant, Z. and Oh, B. (1986). Efficient numerical integration on the surface of a sphere, Journal of Applied Mathematics and Mechanics 66(11): 37–49.10.1002/zamm.19860660108 Search in Google Scholar

Beentjes, C. (2015). Quadrature on a spherical surface, https://cbeentjes.github.io/files/Ramblings/QuadratureSphere.pdf. Search in Google Scholar

Bruno, O.P. and Kunyansky, L.A. (2001). A fast, high order algorithm for the solution of surface scattering problems: Basic implementation, tests and applications, Journal of Computational Physics 169(1): 80–110.10.1006/jcph.2001.6714 Search in Google Scholar

Flyer, N. and Fornberg, B. (2011). Radial basis functions: Developments and applications to planetary scale flows, Computers and Fluids 46(1): 23–32.10.1016/j.compfluid.2010.08.005 Search in Google Scholar

Flyer, N., Lehto, E., Blaise, S., Wright, G. and St-Cyr, A. (2012). A guide to RBF-generated finite differences for nonlinear transport: Shallow water simulations on a sphere, Journal of Computational Physics 231(11): 4078–4095.10.1016/j.jcp.2012.01.028 Search in Google Scholar

Flyer, N., Wright, G. and Fornberg, B. (2014). Radial basis function generated finite differences: A mesh-free method for computational geosciences, in M. Freeden et al. (Eds), Handbook of Geomathematics, Springer-Verlag, Berlin, pp. 2535–2669. Search in Google Scholar

Fornberg, B. and Flyer, N. (2015). A Primer on Radial Basis Functions with Applications to the Geosciences, Society for Industrial and Applied Mathematics, Philadelphia.10.1137/1.9781611974041 Search in Google Scholar

Fornberg, B. and Martel, J. (2014). On spherical harmonics based numerical quadrature over the surface of a sphere, Advances in Computational Mathematics 40(5–6): 1169–1184.10.1007/s10444-014-9346-3 Search in Google Scholar

Fornberg, B. and Piret, C. (2007). A stable algorithm for flat radial basis function on a sphere, SIAM Journal on Scientific Computing 30(1): 60–80.10.1137/060671991 Search in Google Scholar

Fornberg, B. and Piret, C. (2008). On choosing a radial basis function and a shape parameter when solving a convective PDE on a sphere, Journal of Computational Physics 227(5): 2758–2780.10.1016/j.jcp.2007.11.016 Search in Google Scholar

Fuselier, E., Hangelbroek, T., Narcowich, F., Ward, J. and Wright, B. (2014). Kernel based quadrature on spheres and other homogeneous spaces, Numerische Mathematik 127(1): 57–92.10.1007/s00211-013-0581-1 Search in Google Scholar

Halton, J. (1960). On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals, Numerische Mathematik 1(1): 84–90.10.1007/BF01386213 Search in Google Scholar

Hesse, K., Sloan, I. and Womersley, R. (2010). Numerical integration on the sphere, in M. Freeden et al. (Eds), Handbook of Geomathematics, Springer-Verlag, Berlin, pp. 1187–1219.10.1007/978-3-642-01546-5_40 Search in Google Scholar

Klöckner, A., Barnett, A., Greengard, L. and O’Neil, M. (2013). Quadrature by expansion: A new method for the evaluation of layer potentials, Journal of Computational Physics 252: 332–349.10.1016/j.jcp.2013.06.027 Search in Google Scholar

Klinteberg, L. and Tornberg, A.K. (2016). A fast integral equation method for solid particles in viscous flow using quadrature by expansion, Journal of Computational Physics 326: 420–445.10.1016/j.jcp.2016.09.006 Search in Google Scholar

Reeger, J. (2015). Spherical Quadrature RBF (Quadrature Nodes), https://es.mathworks.com/matlabcentral/fileexchange/51214. Search in Google Scholar

Reeger, J. and Fornberg, B. (2016). Numerical quadrature over the surface of a sphere, Studies in Applied Mathematics 137(1): 174–188.10.1111/sapm.12106 Search in Google Scholar

Reeger, J., Fornberg, B. and Watts, L. (2016). Numerical quadrature over smooth, closed surfaces, Proceedings of the Royal Society A 472(2194): 20160401.10.1098/rspa.2016.0401509544327843402 Search in Google Scholar

Saff, E. and Kuijlaar, A. (1997). Distributing many points on a sphere, Proceedings of the Royal Society A 19(2): 5–11.10.1007/BF03024331 Search in Google Scholar

Sommariva, A. and Womersley, R. (2005). Integration by RBF over the sphere, Applied Mathematics Report amr05/17, University of New South Wales, Sydney. Search in Google Scholar

Stroud, A. (1971). Approximate Calculation of Multiple Integrals, Prentice-Hall, Englewood Cliffs. Search in Google Scholar

Womersley, R. and Sloan, H. (2003). Interpolation and cubature on the sphere, https://web.maths.unsw.edu.au/~rsw/Sphere/. Search in Google Scholar

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