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Adaptive Gravitational Force Representation for Fast Trajectory Propagation Near Small Bodies

“…III, we give a rough calculation showing that between 6 and 74 petabytes of storage would be required for a uniform grid, depending on the order of interpolation. A nonuniform grid, on the other hand, raises doubts about the existence of an interpolant for arbitrary data [10].…”

“…The forces per unit mass are computed via the polyhedral method, but can be obtained from other sources as well, such as measured gravimetric data or by numerically solving Poisson's equation at the interpolation points. The interpolation error of the above scheme can be quantified via Ciarlet's formula [10], which in our case depends on an integral of derivatives of the components of the force. This suggests that the error will increase as we approach the asteroid (because force depends inversely on the second power of distance) and decrease as the interpolation domain becomes smaller.…”

Interpolating solutions of the Poisson equation in the disk based on Radon projections

“…The present work expands on the earlier articles [7,9], where the Laplace equation was considered, i.e., the homogeneous case f = 0. Therein, first results on interpolation of harmonic functions with harmonic polynomials based on Radon projections along chords of the unit circle were presented.…”

“…For example, the pointwise interpolation by multivariate polynomials is no longer possible for every choice of the nodes. See [6] and the references therein for a survey of multivariate polynomial interpolation. Furthermore, there are many practical problems in which the information about the relevant function comes as a set of functionals which are not point evaluations.…”

On Extrapolated Multirate Methods

“…9.1]. The most economical solution to this set of linear equations is given by the Aitken-Neville formula [Aitken, 1932;Neville, 1934;Gasca and Sauer, 2000]:…”