CBC Talk on Tensor Product Finite Elements, and Other Tales From the World of Firedrake - March 10, 2015

Andrew McRae from Imperial College London will visit CBC and give a talk on "Tensor Product Finite Elements, and Other Tales From the World of Firedrake" in Bakrommet, Tuesday 10/3, 1300-1345

Total number of participants: 8
Total number of guests outside of CBC: 1
Number of different nationalities represented: 5 
Total number of speakers: 1 
Total number of talks: 1


All FEniCS users will be familiar with the FunctionSpace constructor taking three arguments - a mesh, a family, and a degree.  However, it is unreasonable to expect that all valid finite elements can be specified with just the latter two pieces of information.  We have therefore extended parts of the FEniCS toolchain to allow more sophisticated manipulation of finite elements.
Our main application for this is to allow the use of semi-structured, or extruded, meshes.  These are particularly appropriate for geophysical applications, in which both the domain and governing equations may be far from isotropic.  In addition, the introduction of a 'vertical' structure helps to offset the efficiency losses that arise from using an unstructured 'horizontal' mesh.

Geometrically, the local cells are a product of existing cells.  This allows existing finite elements to be combined through a tensor product, in order to build finite elements suitable for an extruded mesh.  A subset of these are also suitable for unstructured quadrilateral meshes, or their extruded (hexahedral) counterparts.

We also have several simpler examples of element manipulation, which provide a way to implement hybridization or flux reconstruction techniques.  These elements are all fully supported within the Firedrake project, which I will naturally talk about briefly.

10/ Mar 2015 13.0013.45



Center for Biomedical Computing (CBC) aims to develop and apply novel simulation technologies to reach new understanding of complex physical processes affecting human health. We target selected medical problems where insight from mathematical modeling can contribute to changing clinical practice.