Sum-factorization techniques in Isogeometric Analysis
Résumé
The fast assembling of stiffness and mass matrices is a key issue in isogeometric
analysis, particularly if the spline degree is increased. If the assembling is done
in a naive way, the computational complexity grows with the spline degree to a power
of $3d$, where $d$ is the spacial dimension. Recently much progress was achieved
in improving the assembling procedures, particularly in the methods of sum factorization,
low rank assembling, and weighted quadrature. A few years ago, it was shown that the
computational complexity of the sum factorization approach grows with the spline degree
to a power of $2d+1$. We show that it is possible to decrease this to a power of
$d+2$ without loosing generality or accuracy.
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