With a goal of efficiently trading higher-memory footprints for faster runtimes, a high-fidelity interpolation method is presented for approximating a scalar quantity and associated gradients in the global three-dimensional domain external to a sphere. The new “Fetch” interpolation model uses the Junkins weighting function strategy to achieve continuity and smoothness. An overlapping grid strategy ensures a singularity-free domain while minimizing associated memory costs. Local interpolating functions are judiciously chosen with a new adaptive order-based selection of local polynomials that minimizes coefficient storage subject to a radially mapped residual tolerance. Analytic inversions of the normal equations associated with each candidate polynomial allow for rapid solutions to the least-squares process without resorting to the conventional numerical linear system solvers. The gradient and higher-order partial derivatives are computed directly with no memory cost, and they are smooth and continuous to a user-specified order. The method is specifically applied to interpolate the GRACE GGM03C geopotential model up to the degree and order of 360. Highly tuned interpolation models of various resolutions are presented and discussed in detail. Released Fetch interpolation models of the geopotential include resolutions of , , , and . The memory requirements span from 120 to 2360 MB, and the expected speedups over spherical harmonics evaluations span from approximately 3- to 800-fold. The minimum break-even resolution for runtime speeds is approximately the degree and order of 13. The models are valid up to an altitude of 60 Earth radii and are globally continuous to order three, and thus may be of interest to a variety of science and engineering applications. The runtime evaluation codes along with model coefficients are available on the Internet.
Efficient Interpolation of High-Fidelity Geopotentials
Journal of Guidance, Control, and Dynamics ; 39 , 1 ; 128-143
2016-01-01
Article (Journal)
Electronic Resource
English
Efficient Interpolation of High-Fidelity Geopotentials
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