INVESTIGATION OF FINITE ELEMENT REPRESENTATIONS OF THE GEOPOTENTIAL.
As alternatives to lengthy series expansions for globally valid approximations of the earth's gravity field, piecewise approximation methods are evaluated. A single global equation is retained only for the point mass and second zonal terms of the geopotential, all finer structure undulations are modeled by a global family of locally valid functions. A degree 23 spherical harmonic series for the geopotential is replaced by finite element approximations within the spherical shell out to 1. 2 earth radii; this example application demonstrates conclusively the feasibility and desirability of the finite element approach. An order of magnitude reduction in the calculation time for gravitational acceleration is realized over conventional calculations with spherical harmonic recursions.
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