An Unconditionally Monotone C2 Quartic Spline Method with Nonoscillation Derivatives
Abstract
Here, a one-dimensional monotone interpolation method based on interface reconstruction with partial volumes in the slope-space utilizing the Hermite cubic-spline, is proposed. The new method is only quartic, however is C2 and unconditionally monotone. A set of control points is employed to constrain the curvature of the interpolation function and to eliminate possible nonphysical oscillations in the slope space. An extension of this method in two-dimensions is also discussed.
- Authors:
-
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Publication Date:
- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1420288
- Report Number(s):
- LLNL-JRNL-742107
Journal ID: ISSN 2160-0368
- Grant/Contract Number:
- AC52-07NA27344
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Advances in Pure Mathematics
- Additional Journal Information:
- Journal Volume: 8; Journal Issue: 1; Journal ID: ISSN 2160-0368
- Publisher:
- Scientific Research Publishing, Inc.
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; Monotone Interpolation; Quartic; Non-Oscillation Derivative; Interface Reconstruction; Slope Space; Hermit Spline
Citation Formats
Yao, Jin, and Nelson, Karl E. An Unconditionally Monotone C2 Quartic Spline Method with Nonoscillation Derivatives. United States: N. p., 2018.
Web. doi:10.4236/apm.2018.81003.
Yao, Jin, & Nelson, Karl E. An Unconditionally Monotone C2 Quartic Spline Method with Nonoscillation Derivatives. United States. https://doi.org/10.4236/apm.2018.81003
Yao, Jin, and Nelson, Karl E. Wed .
"An Unconditionally Monotone C2 Quartic Spline Method with Nonoscillation Derivatives". United States. https://doi.org/10.4236/apm.2018.81003. https://www.osti.gov/servlets/purl/1420288.
@article{osti_1420288,
title = {An Unconditionally Monotone C2 Quartic Spline Method with Nonoscillation Derivatives},
author = {Yao, Jin and Nelson, Karl E.},
abstractNote = {Here, a one-dimensional monotone interpolation method based on interface reconstruction with partial volumes in the slope-space utilizing the Hermite cubic-spline, is proposed. The new method is only quartic, however is C2 and unconditionally monotone. A set of control points is employed to constrain the curvature of the interpolation function and to eliminate possible nonphysical oscillations in the slope space. An extension of this method in two-dimensions is also discussed.},
doi = {10.4236/apm.2018.81003},
journal = {Advances in Pure Mathematics},
number = 1,
volume = 8,
place = {United States},
year = {2018},
month = {1}
}
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