# Wendland Functions - A C++ Code to Compute Them

### Carlos Argáez, Sigurdur Hafstein, Peter Giesl

#### 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.

Download#### Paper Citation

#### in Harvard Style

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

#### in Bibtex Style

@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},

}

#### in EndNote Style

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