Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient mass and stiffness matrix assembly via weighted Gaussian
  quadrature rules for B-splines   Calabro et al. (2017) changed the paradigm of the mass and stiffness
computation from the traditional element-wise assembly to a row-wise concept,
showing that the latter one offers integration that may be orders of magnitude
faster. Considering a B-spline basis function as a non-negative measure, each
mass matrix row is integrated by its own quadrature rule with respect to that
measure. Each rule is easy to compute as it leads to a linear system of
equations, however, the quadrature rules are of the Newton-Cotes type, that is,
they require a number of quadrature points that is equal to the dimension of
the spline space. In this work, we propose weighted quadrature rules of
Gaussian type which require the minimum number of quadrature points while
guaranteeing exactness of integration with respect to the weight function. The
weighted Gaussian rules arise as solutions of non-linear systems of equations.
We derive rules for the mass and stiffness matrices for uniform $C^1$ quadratic
and $C^2$ cubic isogeometric discretizations. Our rules further reduce the
number of quadrature points by a factor of $(\frac{p+1}{2p+1})^d$ when compared
to Calabro et al. (2017), $p$ being the polynomial degree and $d$ the dimension
of the problem, and consequently reduce the computational cost of the mass and
stiffness matrix assembly by a similar factor.

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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: atom-ph