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Title: An Unconditionally Monotone C 2 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 C 2 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:
 [1];  [1]
  1. 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:
Journal Article: 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. doi:10.4236/apm.2018.81003.
Yao, Jin, and Nelson, Karl E. 2018. "An Unconditionally Monotone C2 Quartic Spline Method with Nonoscillation Derivatives". United States. doi: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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