Propagating geometry information to finite element computations

TL;DR

This paper investigates how to effectively incorporate underlying geometric information into finite element simulations, demonstrating that simple primitive queries can satisfy most geometric needs in modern computational mechanics workflows.

Contribution

It identifies two key primitives for geometry access and shows how to implement them across common industrial geometry representations.

Findings

Nearly all geometry needs in finite element codes can be met by two primitive queries.

Proposed primitives are compatible with various geometry description methods.

Examples demonstrate practical implementation of the primitives.

Abstract

The traditional workflow in continuum mechanics simulations is that a geometry description -- for example 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, "underlying" geometry. However, many 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 nearly all geometry-related 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 frequently used ways in which geometries are described in common industrial workflows, and illustrate our solutions using a number of examples.