Journal of Geodesy

, Volume 90, Issue 7, pp 655–675 | Cite as

Fast computation of general forward gravitation problems

  • Fabien CasenaveEmail author
  • Laurent Métivier
  • Gwendoline Pajot-Métivier
  • Isabelle Panet
Original Article


We consider the well-known problem of the forward computation of the gradient of the gravitational potential generated by a mass density distribution of general 3D geometry. Many methods have been developed for given geometries, and the computation time often appears as a limiting practical issue for considering large or complex problems. In this work, we develop a fast method to carry out this computation, where a tetrahedral mesh is used to model the mass density distribution. Depending on the close- or long-range nature of the involved interactions, the algorithm automatically switches between analytic integration formulae and numerical quadratic formulae, and relies on the Fast Multipole Method to drastically increase the computation speed of the long-range interactions. The parameters of the algorithm are empirically chosen for the computations to be the fastest possible while guarantying a given relative accuracy of the result. Computations that would load many-core clusters for days can now be carried out on a desk computer in minutes. The computation of the contribution of topographical masses to the Earth’s gravitational field at the altitude of the GOCE satellite and over France are proposed as numerical illustrations of the method.


Gravitation General 3D geometry  Fast multipole method 



The authors wish to thank CNES for financial support through the TOSCA Committee, and INRIA for providing the sources of Scalfmm.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Fabien Casenave
    • 1
    • 2
    Email author
  • Laurent Métivier
    • 1
  • Gwendoline Pajot-Métivier
    • 1
  • Isabelle Panet
    • 1
  1. 1.IGN LAREGUniv Paris Diderot, Sorbonne Paris CitéParis Cedex 13France
  2. 2.SafranTechMagny-Les-HameauxFrance

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