Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fast MATLAB evaluation of nonlinear energies using FEM in 2D and 3D:
  nodal elements   Nonlinear energy functionals appearing in the calculus of variations can be
discretized by the finite element (FE) method and formulated as a sum of energy
contributions from local elements. A fast evaluation of energy functionals
containing the first order gradient terms is a central part of this
contribution. We describe a vectorized implementation using the simplest P1
elements in which all energy contributions are evaluated all at once without
the loop over triangular or tetrahedral elements. Furthermore, in connection to
the first-order optimization methods, the discrete gradient of the energy
functional is assembled in a way that gradient components are evaluated over
all degrees of freedom all at once. The key ingredient is the vectorization of
exact or approximate energy gradients over nodal patches. It leads to a
time-efficient implementation at higher memory-cost. Provided codes in MATLAB
related to 2D/3D hyperelasticity and 2D p-Laplacian problem are available for
download and structured in a way it can be easily extended to other types of
vector or scalar forms of energies.

2
The categories of this paper are: math
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat