Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Orientation-Preservation Conditions on an Iso-parametric FEM in
  Cavitation Computation   The orientation-preservation condition, i.e., the Jacobian determinant of the
deformation gradient $\det \nabla u$ is required to be positive, is a natural
physical constraint in elasticity as well as in many other fields. It is well
known that the constraint can often cause serious difficulties in both
theoretical analysis and numerical computation, especially when the material is
subject to large deformations. In this paper, we derive a set of sufficient and
necessary conditions for the quadratic iso-parametric finite element
interpolation functions of cavity solutions to be orientation preserving on a
class of radially symmetric large expansion accommodating triangulations. The
result provides a practical quantitative guide for meshing in the neighborhood
of a cavity and shows that the orientation-preservation can be achieved with a
reasonable number of total degrees of freedom by the quadratic iso-parametric
finite element method.

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The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th