6533b830fe1ef96bd1297a50

RESEARCH PRODUCT

The Poisson problem: A comparison between two approaches based on SPH method

Elena ToscanoA. TortoriciG.m. Di Blasi

subject

Integral representationApplied MathematicsMathematical analysisFunction (mathematics)Domain (software engineering)Smoothed-particle hydrodynamicsSettore MAT/08 - Analisi NumericaComputational MathematicsVariational principleApplied mathematicsPoisson problem Meshless method Smoothed Particle Hydrodynamics Consistency restoring Variational principle Differential methodSmoothing kernelPoisson problemDifferential methodMathematics

description

Abstract In this paper two approaches to solve the Poisson problem are presented and compared. The computational schemes are based on Smoothed Particle Hydrodynamics method which is able to perform an integral representation by means of a smoothing kernel function by involving domain particles in the discrete formulation. The first approach is derived by means of the variational formulation of the Poisson problem, while the second one is a direct differential method. Numerical examples on different domain geometries are implemented to verify and compare the proposed approaches; the computational efficiency of the developed methods is also studied.

yearjournalcountryeditionlanguage
2012-05-01Applied Mathematics and Computation
https://doi.org/10.1016/j.amc.2012.02.049