6533b85ffe1ef96bd12c125e
RESEARCH PRODUCT
A brief overview on the numerical behavior of an implicit meshless method and an outlook to future challenges
Elisa FrancomanoGuido AlaMarta Paliagasubject
Regularized meshless methodMathematical optimizationComputer sciencemedia_common.quotation_subjectSPHKernel representationSolverMathematics::Numerical AnalysisTask (project management)ADI leapfrog methodPhysics and Astronomy (all)Settore MAT/08 - Analisi NumericaSettore ING-IND/31 - ElettrotecnicaObstaclemeshless methodNode (circuits)Function (engineering)numerical approximationmedia_commondescription
In this paper recent results on a leapfrog ADI meshless formulation are reported and some future challenges are addressed. The method benefits from the elimination of the meshing task from the pre-processing stage in space and it is unconditionally stable in time. Further improvements come from the ease of implementation, which makes computer codes very flexible in contrast to mesh based solver ones. The method requires only nodes at scattered locations and a function and its derivatives are approximated by means of a kernel representation. A perceived obstacle in the implicit formulation is in the second order differentiations which sometimes are eccesively sensitive to the node configurations. Some ideas in approaching the meshless implicit formulation are provided.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-01-01 | AIP Conference Proceedings |