Implicit Structural Modeling by Minimization of the Bending Energy with Moving Least Squares Functions     

Renaudeau  Julien  Malvesin  Emmanuel  Maerten  Frantz  Caumon  Guillaume 《Mathematical Geosciences》2019,51(6):693-724

Mathematical Geosciences - In this paper, an implicit structural modeling method using locally defined moving least squares shape functions is proposed. The continuous bending energy is minimized...  相似文献   

Finite Difference Implicit Structural Modeling of Geological Structures     

Irakarama  Modeste  Laurent  Gautier  Renaudeau  Julien  Caumon  Guillaume 《Mathematical Geosciences》2021,53(5):785-808

We introduce a new method for implicit structural modeling. The main developments in this paper are the new regularization operators we propose by extending inherent properties of the classic one-dimensional discrete second derivative operator to higher dimensions. The proposed regularization operators discretize naturally on the Cartesian grid using finite differences, owing to the highly symmetric nature of the Cartesian grid. Furthermore, the proposed regularization operators do not require any special treatment on boundary nodes, and their generalization to higher dimensions is straightforward. As a result, the proposed method has the advantage of being simple to implement. Numerical examples show that the proposed method is robust and numerically efficient.

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