In this paper we focus on two sources of enhancement in accuracy and computational de manding in approximating a function and its derivatives by means of the Smoothed Particle Hydrodynamics method. The approximating power of the standard method is perceived to be poor and improvements can be gained making use of the Taylor series expansion of the kernel approximation of the function and its derivatives. The modified formulation is appealing providing more accurate results of the function and its derivatives simultaneously without changing the kernel function adopted in the computation. The request for greater accuracy needs kernel function derivatives with order up to the desidered accuracy order in approximating the function or higher for the derivatives. In this paper we discuss on the scheme dealing with the infinitely differentiable Gaussian kernel function. Studies on the accuracy, convergency and computational efforts with various sets of data sites are provided. Moreover, to make large scale problems tractable the improved fast Gaussian transform is considered picking up the computational cost at an acceptable level preserving the accuracy of the computation.

Francomano Elisa, Paliaga Marta (2018). Highlighting numerical insights of an efficient SPH method. APPLIED MATHEMATICS AND COMPUTATION, 339, 899-915 [10.1016/j.amc.2018.07.060].

Highlighting numerical insights of an efficient SPH method

Francomano Elisa
;
Paliaga Marta
2018-01-01

Abstract

In this paper we focus on two sources of enhancement in accuracy and computational de manding in approximating a function and its derivatives by means of the Smoothed Particle Hydrodynamics method. The approximating power of the standard method is perceived to be poor and improvements can be gained making use of the Taylor series expansion of the kernel approximation of the function and its derivatives. The modified formulation is appealing providing more accurate results of the function and its derivatives simultaneously without changing the kernel function adopted in the computation. The request for greater accuracy needs kernel function derivatives with order up to the desidered accuracy order in approximating the function or higher for the derivatives. In this paper we discuss on the scheme dealing with the infinitely differentiable Gaussian kernel function. Studies on the accuracy, convergency and computational efforts with various sets of data sites are provided. Moreover, to make large scale problems tractable the improved fast Gaussian transform is considered picking up the computational cost at an acceptable level preserving the accuracy of the computation.
2018
Settore MAT/08 - Analisi Numerica
Francomano Elisa, Paliaga Marta (2018). Highlighting numerical insights of an efficient SPH method. APPLIED MATHEMATICS AND COMPUTATION, 339, 899-915 [10.1016/j.amc.2018.07.060].
File in questo prodotto:
File Dimensione Formato  
AMC_Submission.pdf

accesso aperto

Tipologia: Pre-print
Dimensione 1.92 MB
Formato Adobe PDF
1.92 MB Adobe PDF Visualizza/Apri
Highlighting numerical insights of an efficient SPH method .pdf

Solo gestori archvio

Descrizione: Articolo principale
Tipologia: Versione Editoriale
Dimensione 4.38 MB
Formato Adobe PDF
4.38 MB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/295644
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 17
  • ???jsp.display-item.citation.isi??? 14
social impact