Fast and accurate interpolation of large scattered data sets on the sphere

Cavoretto, Roberto; Rossi, Alessandra De

doi:10.1016/j.cam.2010.02.031

Cited by 32 publications

(36 citation statements)

References 25 publications

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“…Note that the paper [10] follows preceding works, where efficient searching procedures based on the partition of the domain in strips or spherical zones are considered (see [1,7,8,10]). …”

Section: I(xmentioning

confidence: 99%

A Trivariate Interpolation Algorithm Using a Cube-Partition Searching Procedure

Cavoretto

Rossi

2015

SIAM J. Sci. Comput.

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Abstract. In this paper we propose a fast algorithm for trivariate interpolation, which is based on the partition of unity method for constructing a global interpolant by blending local radial basis function interpolants and using locally supported weight functions. The partition of unity algorithm is efficiently implemented and optimized by connecting the method with an effective cube-partition searching procedure. More precisely, we construct a cube structure, which partitions the domain and strictly depends on the size of its subdomains, so that the new searching procedure and, accordingly, the resulting algorithm enable us to efficiently deal with a large number of nodes. Complexity analysis and numerical experiments show high efficiency and accuracy of the proposed interpolation algorithm.

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“…Note that the paper [10] follows preceding works, where efficient searching procedures based on the partition of the domain in strips or spherical zones are considered (see [1,7,8,10]). …”

Section: I(xmentioning

confidence: 99%

A Trivariate Interpolation Algorithm Using a Cube-Partition Searching Procedure

Cavoretto

Rossi

2015

SIAM J. Sci. Comput.

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“…In exploring alternative methods for the present study, we also experimented with techniques similar to a modified spherical Shepard's interpolant [10] and various planar multiquadric methods [11]. These families of interpolation techniques can produce seemingly realistic fills at modest computational expense, but we are here interested in presenting and exploring advantages of fills based on solutions to partial differential equations.…”

Section: Formulation Of Data Fill Modelmentioning

confidence: 99%

Filling the Polar Data Gap in Sea Ice Concentration Fields Using Partial Differential Equations

Strong

Golden

2016

Remote Sensing

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Abstract:The "polar data gap" is a region around the North Pole where satellite orbit inclination and instrument swath for SMMR and SSM/I-SSMIS satellites preclude retrieval of sea ice concentrations. Data providers make the irregularly shaped data gap round by centering a circular "pole hole mask" over the North Pole. The area within the pole hole mask has conventionally been assumed to be ice-covered for the purpose of sea ice extent calculations, but recent conditions around the perimeter of the mask indicate that this assumption may already be invalid. Here we propose an objective, partial differential equation based model for estimating sea ice concentrations within the area of the pole hole mask. In particular, the sea ice concentration field is assumed to satisfy Laplace's equation with boundary conditions determined by observed sea ice concentrations on the perimeter of the gap region. This type of idealization in the concentration field has already proved to be quite useful in establishing an objective method for measuring the "width" of the marginal ice zone-a highly irregular, annular-shaped region of the ice pack that interacts with the ocean, and typically surrounds the inner core of most densely packed sea ice. Realistic spatial heterogeneity in the idealized concentration field is achieved by adding a spatially autocorrelated stochastic field with temporally varying standard deviation derived from the variability of observations around the mask. To test the model, we examined composite annual cycles of observation-model agreement for three circular regions adjacent to the pole hole mask. The composite annual cycle of observation-model correlation ranged from approximately 0.6 to 0.7, and sea ice concentration mean absolute deviations were of order 10 −2 or smaller. The model thus provides a computationally simple approach to solving the increasingly important problem of how to fill the polar data gap. Moreover, this approach based on solving an elliptic partial differential equation with given boundary conditions has sufficient generality to also provide more sophisticated models which could potentially be more accurate than the Laplace equation version. Such generalizations and potential validation opportunities are discussed.

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“…In a work still in progress, we are going to apply Lobachevsky splines in local methods for fast computation in multivariate and spherical interpolation (see, e.g., [2,9,10,11]). …”

Section: Discussionmentioning

confidence: 99%

“…In Table 1 we show the behavior of Lobachevsky spline integration errors for 3 ≤ d ≤ 6 by varying the value of the shape parameter α ∈ [1,9]. Numerical results highlight that the variation of α may greatly influence the quality of approximation results, though the behavior of such errors turns out to be uniform for any d. In particular, we remark that the best level of accuracy is reached when α ∈ [1,4].…”

Section: Numerical Experimentsmentioning

confidence: 98%

Multidimensional Lobachevsky Spline Integration on Scattered Data

Allasia

Cavoretto

Rossi

2014

Appl. Math. Inf. Sci.

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This paper deals with the topic of numerical integration on scattered data in R d , d ≤ 10, by a class of spline functions, called Lobachevsky splines. Precisely, we propose new integration formulas based on Lobachevsky spline interpolants, which take advantage of being expressible in the multivariate setting as a product of univariate integrals. Theoretically, Lobachevsky spline integration formulas have meaning for any d ∈ N, but numerical results appear quite satisfactory for d ≤ 10, showing good accuracy and stability. Some comparisons are given with radial Gaussian integration formulas and a quasi-Monte Carlo method using Halton data points sets.

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Fast and accurate interpolation of large scattered data sets on the sphere

Cited by 32 publications

References 25 publications

A Trivariate Interpolation Algorithm Using a Cube-Partition Searching Procedure

A Trivariate Interpolation Algorithm Using a Cube-Partition Searching Procedure

Filling the Polar Data Gap in Sea Ice Concentration Fields Using Partial Differential Equations

Multidimensional Lobachevsky Spline Integration on Scattered Data

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