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Pregled bibliografske jedinice broj: 903066

A class of renormalised meshless Laplacians for boundary value problems


Bašić, Josip; Degiuli, Nastia; Ban, Dario
A class of renormalised meshless Laplacians for boundary value problems // Journal of computational physics, 354 (2018), 269-287 doi:10.1016/j.jcp.2017.11.003 (međunarodna recenzija, članak, znanstveni)


Naslov
A class of renormalised meshless Laplacians for boundary value problems

Autori
Bašić, Josip ; Degiuli, Nastia ; Ban, Dario

Izvornik
Journal of computational physics (0021-9991) 354 (2018); 269-287

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Laplace operator ; Laplacian ; meshless method ; mesh-free PDE ; Poisson equation

Sažetak
A meshless approach to approximating spatial derivatives on scattered point arrangements is presented in this paper. Three various derivations of approximate discrete Laplace operator formulations are produced using the Taylor series expansion and renormalised least-squares correction of the first spatial derivatives. Numerical analyses are performed for the introduced Laplacian formulations, and their convergence rate and computational efficiency are examined. The tests are conducted on regular and highly irregular scattered point arrangements. The results are compared to those obtained by the smoothed particle hydrodynamics method and the finite differences method on a regular grid. Finally, the strong form of various Poisson and diffusion equations with Dirichlet or Robin boundary conditions are solved in two and three dimensions by making use of the introduced operators in order to examine their stability and accuracy for boundary value problems. The introduced Laplacian operators perform well for highly irregular point distribution and offer adequate accuracy for mesh and mesh-free numerical methods that require frequent movement of the grid or point cloud.

Izvorni jezik
Engleski



POVEZANOST RADA


Ustanove
Fakultet elektrotehnike, strojarstva i brodogradnje, Split,
Fakultet strojarstva i brodogradnje, Zagreb

Časopis indeksira:


  • Current Contents Connect (CCC)
  • Web of Science Core Collection (WoSCC)
    • Science Citation Index Expanded (SCI-EXP)
  • Scopus


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