Abstract
This paper is devoted to introducing a nonlinear reconstruction operator, the piecewise polynomial harmonic (PPH), on nonuniform grids. We define this operator and we study its main properties, such as its reproduction of second-degree polynomials, approximation order, and conditions for convexity preservation. In particular, for σ quasi-uniform grids with σ≤4, we get a quasi C3 reconstruction that maintains the convexity properties of the initial data. We give some numerical experiments regarding the approximation order and the convexity preservation.
Highlights
Reconstruction operators are widely used in computer-aided geometric design
We use the definition that we made of the piecewise polynomial harmonic (PPH) reconstruction operator for data over nonuniform grids in [2], and we study some properties of this operator in greater depth
In order to reduce the affected intervals to only one, the one containing the singularity, we introduce a weighted harmonic mean over nonuniform grids, which will be used in the general definition of the PPH reconstruction operator
Summary
Reconstruction operators are widely used in computer-aided geometric design. For simplicity, the functions that are typically used as operators are polynomials. Due to the bad behavior of linear operators in the presence of discontinuities, it has become necessary to design nonlinear operators to overcome this drawback One of these operators was defined in [1] and was called the piecewise polynomial harmonic (PPH). We use the definition that we made of the PPH reconstruction operator for data over nonuniform grids in [2], and we study some properties of this operator in greater depth. The paper is organized as follows: Section 2 is devoted to defining the PPH reconstruction operator over nonuniform grids For this purpose, we will use the weighted harmonic mean with appropriate weights.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
