Arbitrary Manifold Descriptions in Finite Element Codes

Numerical Tools: 

One of the main advantages of using the deal.II library ( when discretising partial differential equations, is the support for adaptively refined grids on high performance infrastructures. Adaptively refining a Finite Element Mesh requires adding new vertices to a triangulation. This is usually done by creating new vertices "in the middle" of the surrounding ones, irrespective of the geometry.When the geometry of the problem is non trivial, adaptive refinement alone is not sufficient to guarantee an accurate solution of the PDE at hand, and one has to ensure that new vertices are created respecting the topology of the underlying geometry. The deal.II library prior to its version 8.2 allowed this type of control only on the boundary of the domain, producing results which where not satisfactory in many industrially relevant cases. We restructured the internal architecture of the deal.II Triangulation class and added a new class, the Manifold description, which makes it possible to describe arbitrary manifolds.For the codimension one case, i.e., when describing the boundary of a domain, we also provided an interface to the OpenCASCADE library ( to describe to the Finite Element Code arbitrary CAD shapes by their STEP or IGES files.