2018
DOI: 10.1016/j.cam.2017.06.027
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An efficient quadrature rule on the Cubed Sphere

Abstract: A new quadrature rule for functions defined on the sphere is introduced. The nodes are defined as the points of the Cubed Sphere. The associated weights are defined in analogy to the trapezoidal rule on each panel of the Cubed Sphere. The formula enjoys a symmetry property ensuring that a proportion of 7/8 of all Spherical Harmonics is integrated exactly. Based on the remaining Spherical Harmonics, it is possible to define modified weights giving an enhanced quadrature rule. Numerical results show that the new… Show more

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Cited by 7 publications
(12 citation statements)
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“…Corollary 10. The quadrature rule Q N exactly integrates 15 16 of all real Legendre spherical harmonics. More precisely, for all |m| ≤ n,…”
Section: ∀Q ∈ G ∀U ∈ Umentioning
confidence: 99%
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“…Corollary 10. The quadrature rule Q N exactly integrates 15 16 of all real Legendre spherical harmonics. More precisely, for all |m| ≤ n,…”
Section: ∀Q ∈ G ∀U ∈ Umentioning
confidence: 99%
“…The ratio 15/16 of the real Legendre basis is asymptotic. In [7,15], a similar approach based on invariance properties provided an asymptotic ratio of 7/8 of the complex Legendre basis. We observe here that using the real Legendre basis highlights further exact results.…”
Section: ∀Q ∈ G ∀U ∈ Umentioning
confidence: 99%
See 1 more Smart Citation
“…All the integrals in () are evaluated with the integral 𝕊a2f(x)dσ(x) approximated by Q N ( f ), the rule (20) in Portelenelle and Croisille (2018). This rule is defined by QN(f)=a2k=false(Ifalse)false(VIfalse)i,j=prefix−Nfalse/2Nfalse/2αi,jFfalse(si,jkfalse). Portelenelle and Croisille (2018) define the weights αi,j.…”
Section: Conservationmentioning
confidence: 99%
“…All the integrals in (31) are evaluated with the integral ∫ S 2 a f (x) d (x) approximated by Q N (f ), the rule (20) in Portelenelle and Croisille (2018). This rule is defined by…”
Section: Conservation With the Hccs Schemementioning
confidence: 99%