Wendland functions A C++ code to compute them

Carlos Argaez; Sigurdur Hafstein; Peter Giesl

doi:10.5220/0006441303230330

Wendland functions A C++ code to compute them

Carlos Argaez, Sigurdur Hafstein, Peter Giesl

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

7 Citations (Scopus)

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 usingWendland 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.

Original language	English
Title of host publication	SIMULTECH 2017 - Proceedings of the 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications
Editors	Floriano De Rango, Tuncer Oren, Mohammad S. Obaidat
Publisher	SciTePress
Pages	323-330
Number of pages	8
ISBN (Electronic)	9789897582653
DOIs	https://doi.org/10.5220/0006441303230330
Publication status	Published - 2017
Event	7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications, SIMULTECH 2017 - Madrid, Spain Duration: 26 Jul 2017 → 28 Jul 2017

Publication series

Name	SIMULTECH 2017 - Proceedings of the 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

Conference

Conference	7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications, SIMULTECH 2017
Country/Territory	Spain
City	Madrid
Period	26/07/17 → 28/07/17

Bibliographical note

Publisher Copyright:
© Copyright 2017 by SCITEPRESS - Science and Technology Publications, Lda. All rights reserved.

Other keywords

Compact Support
Radial Basis Functions
Wendland Functions

Access to Document

10.5220/0006441303230330

Cite this

Argaez, C., Hafstein, S., & Giesl, P. (2017). Wendland functions A C++ code to compute them. In F. De Rango, T. Oren, & M. S. Obaidat (Eds.), SIMULTECH 2017 - Proceedings of the 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (pp. 323-330). (SIMULTECH 2017 - Proceedings of the 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications). SciTePress. https://doi.org/10.5220/0006441303230330

Argaez, Carlos ; Hafstein, Sigurdur ; Giesl, Peter. / Wendland functions A C++ code to compute them. SIMULTECH 2017 - Proceedings of the 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications. editor / Floriano De Rango ; Tuncer Oren ; Mohammad S. Obaidat. SciTePress, 2017. pp. 323-330 (SIMULTECH 2017 - Proceedings of the 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications).

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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 usingWendland 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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author = "Carlos Argaez and Sigurdur Hafstein and Peter Giesl",

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year = "2017",

doi = "10.5220/0006441303230330",

language = "English",

series = "SIMULTECH 2017 - Proceedings of the 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications",

publisher = "SciTePress",

pages = "323--330",

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Argaez, C, Hafstein, S & Giesl, P 2017, Wendland functions A C++ code to compute them. in F De Rango, T Oren & MS Obaidat (eds), SIMULTECH 2017 - Proceedings of the 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications. SIMULTECH 2017 - Proceedings of the 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications, SciTePress, pp. 323-330, 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications, SIMULTECH 2017, Madrid, Spain, 26/07/17. https://doi.org/10.5220/0006441303230330

Wendland functions A C++ code to compute them. / Argaez, Carlos; Hafstein, Sigurdur; Giesl, Peter.
SIMULTECH 2017 - Proceedings of the 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications. ed. / Floriano De Rango; Tuncer Oren; Mohammad S. Obaidat. SciTePress, 2017. p. 323-330 (SIMULTECH 2017 - Proceedings of the 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Argaez C, Hafstein S, Giesl P. Wendland functions A C++ code to compute them. In De Rango F, Oren T, Obaidat MS, editors, SIMULTECH 2017 - Proceedings of the 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications. SciTePress. 2017. p. 323-330. (SIMULTECH 2017 - Proceedings of the 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications). doi: 10.5220/0006441303230330

Wendland functions A C++ code to compute them

Abstract

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Conference

Bibliographical note

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