Spectral properties of the SPH Laplacian operator. (15th May 2018)

• Record Type: Journal Article
• Authors: Violeau, Damien; Leroy, Agnès; Joly, Antoine; Hérault, Alexis
• Is Part Of: Computers & mathematics with applications. Volume 75:issue 10(2018)
• Page Start: 3649
• Page End: 3662
• Publication Date: 2018-05-15
• Subjects: SPH -- Laplacian -- Eigenvalues -- Spectrum -- Conditioning; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2018.02.023
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In order to address the question of the SPH (Smoothed Particle Hydrodynamics) Laplacian conditioning, a spectral analysis of this discrete operator is performed. In the case of periodic Cartesian particle network, the eigenfunctions and eigenvalues of the SPH Laplacian are found on theoretical grounds. The theory agrees well with numerical eigenvalues. The effects of particle disorder and non-periodicity conditions are then investigated from numerical viewpoint. It is found that the matrix condition number is proportional to the square of the particle number per unit length, irrespective of the space dimension and kernel choice.