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See detailSimulations in ambient space : freeing mesh generation techniques from the respect of boundaries in the context of the FEM
Béchet, Eric ULg; Moës, Nicolas; Wolhmuth, Barbara et al

Scientific conference (2009)

Numerical simulations made within the finite element method have been made with increased geometrical and modeling complexity over the decades. To carry out such simulations, mesh generation techniques ... [more ▼]

Numerical simulations made within the finite element method have been made with increased geometrical and modeling complexity over the decades. To carry out such simulations, mesh generation techniques are a key ingredient. With conventional finite element methods, one first need to conform the mesh to the boundaries. The density of the mesh should also be controlled. Altogether, these require tough mesh generation algorithms and often a fair amount of user interaction. In this paper, we present a technique that allows to free mesh generation algorithms from the respect of object boundaries or internal boundaries. First we will show a way to represent the geometry of an object independently of its origin, using multiple level-sets. We will then show how to embed those interfaces in the finite element method without having to conform the mesh. We prove that the numerical results are as accurate as those obtained with conforming boundaries. [less ▲]

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