THESIS
2022
1 online resource (xii, 54 pages) : illustrations (some color)
Abstract
We proposed a recursive interpolation scheme that gives high order interpolants
called Spherical Interpolation of DEgRee (SIDER in short) on the unit sphere S
^{2}. The idea
generalizes the construction of the Bézier curves in R. We also adopt the philosophy of
Essentially Non-Oscillatory (ENO) schemes from R to S
^{2} to develop Spherical Essentially
Non-Oscillatory (SENO in short) schemes using SIDER as the building pieces. Given
n+1 data points that satisfy certain constraints, there must be one SIDERn that passes
through all the data points with C
^{n} continuity (if n = 2 or 3). When the underlying
curve on S
^{2} has kinks or sharp discontinuity in the higher derivatives, SENO can reduce
spurious oscillations in high order reconstructions....[
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We proposed a recursive interpolation scheme that gives high order interpolants
called Spherical Interpolation of DEgRee (SIDER in short) on the unit sphere S
^{2}. The idea
generalizes the construction of the Bézier curves in R. We also adopt the philosophy of
Essentially Non-Oscillatory (ENO) schemes from R to S
^{2} to develop Spherical Essentially
Non-Oscillatory (SENO in short) schemes using SIDER as the building pieces. Given
n+1 data points that satisfy certain constraints, there must be one SIDERn that passes
through all the data points with C
^{n} continuity (if n = 2 or 3). When the underlying
curve on S
^{2} has kinks or sharp discontinuity in the higher derivatives, SENO can reduce
spurious oscillations in high order reconstructions.
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