Optimizing FIAT with Level 3 BLAS

Robert C. Kirby. 4 May, 2005.
Communicated by Robert Kirby.


The code FIAT (FInite element Automatic Tabulator) provides necessary abstractions to define and tabulate a wide range of different finite elements on a reference element. We show here how the performance of the critical operations in its algorithms may be greatly improved by representing polynomials and linear functionals internally as vectors and hence setting up dense matrix operations. The performance gains are up to three orders of magnitude in cases studied. We also discuss how dimensional independence can be obtained through a use of graded incidence relations and give some applications to Lagrange and Brezzi-Douglas-Marini elements.

Original Document

The original document is available in PDF (uploaded 4 May, 2005 by Robert Kirby).