6533b7cffe1ef96bd1258596
RESEARCH PRODUCT
Highlighting numerical insights of an efficient SPH method
Elisa FrancomanoMarta Paliagasubject
Computer scienceApplied MathematicsGaussianComputation010103 numerical & computational mathematicsFunction (mathematics)01 natural sciences010101 applied mathematicsSmoothed-particle hydrodynamicsComputational Mathematicssymbols.namesakeSettore MAT/08 - Analisi NumericaKernel based methods Smoothed Particle Hydrodynamics Accuracy Convergence Improved fast Gaussian transform.Convergence (routing)symbolsTaylor seriesGaussian function0101 mathematicsFocus (optics)Algorithmdescription
Abstract In this paper we focus on two sources of enhancement in accuracy and computational demanding 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-12-01 |