Optimisations for quadrature representations of finite element tensors through automated code generation. (arXiv:1104.0199v1 [cs.MS])

Optimisations for quadrature representations of finite element tensors through automated code generation. (arXiv:1104.0199v1 [cs.MS]): "

We examine aspects of the computation of finite element matrices and vectors
which are made possible by automated code generation. Given a variational form
in a syntax which resembles standard mathematical notation, the low-level
computer code for building finite element tensors, typically matrices, vectors
and scalars, can be generated automatically via a form compiler. In particular,
the generation of code for computing finite element matrices using a quadrature
approach is addressed. For quadrature representations, a number of optimisation
strategies which are made possible by automated code generation are presented.
The relative performance of two different automatically generated
representations of finite element matrices is examined, with a particular
emphasis on complicated variational forms. It is shown that approaches which
perform best for simple forms are not tractable for more complicated problems
in terms of run time performance, the time required to generate the code or the
size of the generated code. The approach and optimisations elaborated here are
effective for a range of variational forms.

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