An Unconditionally Monotone C2 Quartic Spline Method with Nonoscillation Derivatives

Yao, Jin; Nelson, Karl E.

doi:10.4236/apm.2018.81003

Title: An Unconditionally Monotone C² Quartic Spline Method with Nonoscillation Derivatives

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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:

Yao, Jin ^[1]; Nelson, Karl E. ^[1]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Publication Date:: Wed Jan 24 00:00:00 EST 2018

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.

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                    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

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                    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.

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@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         = {Wed Jan 24 00:00:00 EST 2018},

  month        = {Wed Jan 24 00:00:00 EST 2018}

}

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Title: An Unconditionally Monotone C2 Quartic Spline Method with Nonoscillation Derivatives

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Title: An Unconditionally Monotone C² Quartic Spline Method with Nonoscillation Derivatives