An Unconditionally Monotone C² Quartic Spline Method with Nonoscillation Derivatives

Journal Article · 24 January 2018 · Advances in Pure Mathematics

DOI: https://doi.org/10.4236/apm.2018.81003 · OSTI ID:1420288

Yao, Jin ^[1]; Nelson, Karl E. ^[1]

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

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.

• Research Organization: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: AC52-07NA27344
• OSTI ID: 1420288
• Report Number(s): LLNL-JRNL-742107
• Journal Information: Advances in Pure Mathematics, Vol. 8, Issue 1; ISSN 2160-0368
• Publisher: Scientific Research Publishing, Inc.Copyright Statement
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
Monotone Interpolation
Quartic
Non-Oscillation Derivative
Interface Reconstruction
Slope Space
Hermit Spline