Finite element implementation of second order directional derivatives for regularization of implicit modeling of geological structures

Morgan Thierry-Coudon and Modeste Irakarama and Guillaume Caumon and Mustapha Zakari and Pierre Anquez. ( 2019 )
in: 2019 Ring Meeting, ASGA

Abstract

Minimizing second order directional derivatives is one of the many ways of regularizing interpolation problems, such as implicit modeling. This type of regularization was first proposed on cartesian grids using finite differences; here, we focus on its implementation on 3D unstructured meshes using finite elements. Minimizing directional derivatives on boundary vertices leads to isosurfaces that are artificially perpendicular to the boundaries of the model. These artifacts can be removed by omitting the regularisation constraint on boundary vertices. Omitting regularization constraints on each boundaries imposes each boundary node to be connected to at least one internal node. This condition is usually not satisfied by conventional meshing software. We propose a strategy for splitting boundary elements of the mesh to ensure that each boundary vertex is connected to at least one internal node.

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BibTeX Reference

@INPROCEEDINGS{ThierryCoudonRM2019,
    author = { Thierry-Coudon, Morgan and Irakarama, Modeste and Caumon, Guillaume and Zakari, Mustapha and Anquez, Pierre },
     title = { Finite element implementation of second order directional derivatives for regularization of implicit modeling of geological structures },
 booktitle = { 2019 Ring Meeting },
      year = { 2019 },
 publisher = { ASGA },
  abstract = { Minimizing second order directional derivatives is one of the many ways of regularizing interpolation problems, such as implicit modeling. This type of regularization was first proposed on cartesian grids using finite differences; here, we focus on its implementation on 3D unstructured meshes using finite elements. Minimizing directional derivatives on boundary vertices leads to isosurfaces that are artificially perpendicular to the boundaries of the model. These artifacts can be removed by omitting the regularisation constraint on boundary vertices. Omitting regularization constraints on each boundaries imposes each boundary node to be connected to at least one internal node. This condition is usually not satisfied by conventional meshing software. We propose a strategy for splitting boundary elements of the mesh to ensure that each boundary vertex is connected to at least one internal node. }
}