A brief overview on the numerical behavior of an implicit meshless method and an outlook to future challenges

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Abstract

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.
Lingua originaleEnglish
Stato di pubblicazionePublished - 2015

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meshfree methods
formulations
preprocessing
mesh
elimination
computer programs
configurations

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cita questo

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title = "A brief overview on the numerical behavior of an implicit meshless method and an outlook to future challenges",
abstract = "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.",
author = "Elisa Francomano and Guido Ala and Marta Paliaga",
year = "2015",
language = "English",

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AU - Francomano, Elisa

AU - Ala, Guido

AU - Paliaga, Marta

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10447/205194

UR - http://scitation.aip.org/content/aip/proceeding/aipcp

M3 - Paper

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