A set of level 3 basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Spectral methods on triangles and other domains
Journal of Scientific Computing
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
Algorithm 839: FIAT, a new paradigm for computing finite element basis functions
ACM Transactions on Mathematical Software (TOMS)
The science of deriving dense linear algebra algorithms
ACM Transactions on Mathematical Software (TOMS)
A compiler for variational forms
ACM Transactions on Mathematical Software (TOMS)
Efficient compilation of a class of variational forms
ACM Transactions on Mathematical Software (TOMS)
Singularity-free evaluation of collapsed-coordinate orthogonal polynomials
ACM Transactions on Mathematical Software (TOMS)
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
Efficient Assembly of $H(\mathrm{div})$ and $H(\mathrm{curl})$ Conforming Finite Elements
SIAM Journal on Scientific Computing
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Our previous work on FIAT (Finite Element Automatic Tabulator) developed a “computational representation theory ” that allowed us to construct arbitrary order instances of a wide range of finite elements, many of which are infrequently used owing to their associated code complexity. In our present work, we further hone this theory by rephrasing most of the internal operations as linear transformations over finite-dimensional Banach spaces. This additional insight has led to increased code granularity and allowed the use of level 3 BLAS operations. This is both a conceptual and a practical development; as the run-time performance of FIAT has been improved multiple orders of magnitude.