Using exact geometry information in finite element computations
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The traditional workflow in continuum mechanics simulations is that a geometry description – obtained using Constructive Solid Geometry or Computer Aided Design tools – forms the input for a mesh generator. The mesh is then used as the sole input for the finite element, finite volume, and finite difference solver, which at this point no longer has access to the original geometry. However, many more modern techniques – for example, adaptive mesh refinement and the use of higher order geometry approximation methods – really do need information about the underlying geometry to realize their full potential. We have undertaken an exhaustive study of where typical finite element codes use geometry information, with the goal of determining what information geometry tools would have to provide. Our study shows that all geometry needs inside the simulators can be satisfied by just two “primitives”: elementary queries posed by the simulation software to the geometry description. We then show that it is possible to provide these primitives in all of the commonly used ways in which geometries are described in common industrial workflows. We illustrate our solutions using examples from adaptive mesh refinement for complex geometries.
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