State of the art of meshless methods for implicit structural modeling

Julien Renaudeau and Emmanuel Malvesin and Frantz Maerten and Guillaume Caumon. ( 2016 )
in: 2016 RING Meeting, ASGA

Abstract

Structural model construction algorithms use field data to automatically reconstruct sub-surface structures. The most popular ones are mesh based. Once the mesh is created, these methods are stable and computationally fast to solve the problem. The major drawback is the creation of the mesh, which can be expensive in computational time, storage and may require heavy user interventions. To overcome these meshing related issues, recent methods have been developed where the mesh is not necessary. A direct link between geostatistical data correlations and a so-called meshless method named Radial Basis Functions (RBF) was established. The major counterparts of this method are that the system to solve is dense and that discontinuities and heterogeneous data are not easily handled. The strong theoretical background given by the geostatistics is the reason why meshless geo- modeling has been restricted to RBF algorithms. However, the last three decades were very fruitful in developing alternative meshless techniques. While their convergence still has not been formally proven, they show pratical applications in many areas. In this article, we review meshless methods and their potential applications to structural mod- eling. Our goal is to give information on every choice in the creation of a meshless method and to discuss the adaptability of these choices regarding the stability and efficiency of the method, the capability to honor discontinuities and different type of data.

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BibTeX Reference

@INPROCEEDINGS{,
    author = { Renaudeau, Julien and Malvesin, Emmanuel and Maerten, Frantz and Caumon, Guillaume },
     title = { State of the art of meshless methods for implicit structural modeling },
 booktitle = { 2016 RING Meeting },
      year = { 2016 },
 publisher = { ASGA },
  abstract = { Structural model construction algorithms use field data to automatically reconstruct sub-surface
structures. The most popular ones are mesh based. Once the mesh is created, these methods are
stable and computationally fast to solve the problem. The major drawback is the creation of
the mesh, which can be expensive in computational time, storage and may require heavy user
interventions.
To overcome these meshing related issues, recent methods have been developed where the mesh
is not necessary. A direct link between geostatistical data correlations and a so-called meshless
method named Radial Basis Functions (RBF) was established. The major counterparts of this
method are that the system to solve is dense and that discontinuities and heterogeneous data are
not easily handled.
The strong theoretical background given by the geostatistics is the reason why meshless geo-
modeling has been restricted to RBF algorithms. However, the last three decades were very fruitful
in developing alternative meshless techniques. While their convergence still has not been formally
proven, they show pratical applications in many areas.
In this article, we review meshless methods and their potential applications to structural mod-
eling. Our goal is to give information on every choice in the creation of a meshless method and to
discuss the adaptability of these choices regarding the stability and efficiency of the method, the
capability to honor discontinuities and different type of data. }
}