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Authors: Carlos Argáez 1 ; Sigurdur Hafstein 1 and Peter Giesl 2

Affiliations: 1 University of Iceland, Iceland ; 2 University of Sussex, United Kingdom

ISBN: 978-989-758-265-3

Keyword(s): Radial Basis Functions, Wendland Functions, Compact Support.

Related Ontology Subjects/Areas/Topics: Dynamical Systems Models and Methods ; Formal Methods ; Mathematical Simulation ; Non-Linear Systems ; Simulation and Modeling

Abstract: In this paper we present a code in C++ to compute Wendland functions for arbitrary smoothness parameters. Wendland functions are compactly supported Radial Basis Functions that are used for interpolation of data or solving Partial Differential Equations with mesh-free collocation. For the computations of Lyapunov functions using Wendland functions their derivatives are also needed so we include this in the code. Wendland functions with a few fixed smoothness parameters are included in some C++ libraries, but for the general case the only code freely available was implemented in MAPLE taking advantage of the computer algebra system. The aim of this contribution is to allow scientists to use Wendland functions in their C++ code without having to implement them themselves. The computed Wendland functions are polynomials and their coefficients are computed and stored in a vector, which allows for efficient computation of their values using the Horner scheme.

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Paper citation in several formats:
Argáez C., Hafstein S. and Giesl P. (2017). Wendland Functions - A C++ Code to Compute Them.In Proceedings of the 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH, ISBN 978-989-758-265-3, pages 323-330. DOI: 10.5220/0006441303230330

@conference{simultech17,
author={Carlos Argáez and Sigurdur Hafstein and Peter Giesl},
title={Wendland Functions - A C++ Code to Compute Them},
booktitle={Proceedings of the 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,},
year={2017},
pages={323-330},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0006441303230330},
isbn={978-989-758-265-3},
}

TY - CONF

JO - Proceedings of the 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,
TI - Wendland Functions - A C++ Code to Compute Them
SN - 978-989-758-265-3
AU - Argáez C.
AU - Hafstein S.
AU - Giesl P.
PY - 2017
SP - 323
EP - 330
DO - 10.5220/0006441303230330

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