A Boundary Integral Equation on the Sphere for High-Precision Geodesy

  • Ernst P. Stephan
  • Thanh Tran
  • Adrian Costea
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 1)


Spherical radial basis functions are used to approximate the solution of a boundary integral equation on the unit sphere which is a reformulation of a geodetic boundary value problem. The approximate solution is computed with a corresponding meshless Galerkin scheme using scattered data from satellites. Numerical experiments show that this meshless method is superior to standard boundary element computations with piecewise constants. If we increase the element order, BEM might be competitive but then we also have to approximate appropriately the surface otherwise the convergence rate will be spoiled.


Radial Basis Function Boundary Integral Equation Pseudodifferential Operator Meshless Method Side Condition 
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Copyright information

© Springer Berlin Heidelberg 2010

Authors and Affiliations

  • Ernst P. Stephan
    • 1
  • Thanh Tran
    • 2
  • Adrian Costea
    • 1
  1. 1.Institute for Applied MathematicsLeibniz University HannoverHannoverGermany
  2. 2.School of Mathematics and StatisticsSydneyAustralia

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