Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A stencil scaling approach for accelerating matrix-free finite element
  implementations   We present a novel approach to fast on-the-fly low order finite element
assembly for scalar elliptic partial differential equations of Darcy type with
variable coefficients optimized for matrix-free implementations. Our approach
introduces a new operator that is obtained by appropriately scaling the
reference stiffness matrix from the constant coefficient case. Assuming
sufficient regularity, an a priori analysis shows that solutions obtained by
this approach are unique and have asymptotically optimal order convergence in
the $H^1$- and the $L^2$-norm on hierarchical hybrid grids. For the
pre-asymptotic regime, we present a local modification that guarantees uniform
ellipticity of the operator. Cost considerations show that our novel approach
requires roughly one third of the floating-point operations compared to a
classical finite element assembly scheme employing nodal integration. Our
theoretical considerations are illustrated by numerical tests that confirm the
expectations with respect to accuracy and run-time. A large scale application
with more than a hundred billion ($1.6\cdot10^{11}$) degrees of freedom
executed on 14,310 compute cores demonstrates the efficiency of the new scaling
approach.

5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
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The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga