Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A consistent analytical formulation for volume-estimation of geometries
  enclosed by implicitly defined surfaces   We have derived an analytical formulation for estimating the volume of
geometries enclosed by implicitly defined surfaces. The novelty of this work is
due to two aspects. First we provide a general analytical formulation for all
two-dimensional cases, and for elementary three three-dimensional cases by
which the volume of general three-dimensional cases can be computed. Second,
our method addresses the inconsistency issue due to mesh refinement. It is
demonstrated by several two-dimensional and three-dimensional cases that this
analytical formulation exhibits 2nd-order accuracy.

20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn