Pencho Petruchev

High Effective Evaluation and Approximation

Many quantities in Geodesy, Geomagnetism, Astrophysics and other sciences are represented in terms of high degree surface or solid spherical or ellipsoidal harmonics. For example, the current NGA Earth Gravitational Model EGM2008 uses spherical harmonics of degree 2190.

This makes the computation of gravimetric quantities at a large number of scattered points in space a very computationally demanding process. This talk will present the development of an algorithm for fast and accurate evaluation of gravimetric quantities, represented in high degree solid spherical harmonics, at arbitrarily scattered points in the space exterior to the surface of the Earth. The new algorithm is based on representation of the quantities of interest in solid ellipsoidal harmonics and application of tensor product trigonometric needlets.

The FORTRAN and MATLAB realizations of the algorithm, for example, are capable of evaluating the disturbing potential, height anomaly, gravity anomaly, gravity disturbance, north-south deflection of the vertical, east-west deflection of the vertical, and the second radial derivative of the disturbing potential in the range from the surface of the Earth up to 544 kilometers above it on a standard PC at speed between 20,000 and 40,000 point evaluations per second with relative error not exceeding 10^{-6} and memory (RAM) use of 9.3 GB.

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