/* $Id$ */
/* Version: $Name$ */
/* */
-/* Copyright (C) 2001, 2002, 2003, 2004, 2006 by the deal.II authors */
+/* Copyright (C) 2001, 2002, 2003, 2004, 2006, 2007 by the deal.II authors */
/* */
/* This file is subject to QPL and may not be distributed */
/* without copyright and license information. Please refer */
using namespace dealii;
// Now, as we want to compute the
- // value of pi, we have to compare to
+ // value of $\pi$, we have to compare to
// somewhat. These are the first few
- // digits of pi, which we define
+ // digits of $\pi$, which we define
// beforehand for later use. Since we
// would like to compute the
// difference between two numbers
// which are quite accurate, with the
// accuracy of the computed
- // approximation to pi being in the
+ // approximation to $\pi$ being in the
// range of the number of digits
// which a double variable can hold,
// we rather declare the reference
// Now we proceed with the main part
// of the code, the approximation of
- // pi. The area of a circle is given
- // by pi*radius^2, so having a circle
- // of radius 1, the area represents
- // just the number that is searched
- // for. The numerical computation of
- // the area is performed by
- // integrating the constant function
- // of value 1 over the whole
- // computational domain, i.e. by
- // computing the areas $\int_K 1
- // dx=\int_{\hat K} 1\ \textrm{det}\ J(\hat x)
- // d\hat x \approx \sum_i \textrm{det}\ J(\hat
- // x_i)w(\hat x_i)$, where the sum
- // extends over all quadrature points
- // on all active cells in the
+ // $\pi$. The area of a circle is of
+ // course given by $\pi r^2$, so
+ // having a circle of radius 1, the
+ // area represents just the number
+ // that is searched for. The
+ // numerical computation of the area
+ // is performed by integrating the
+ // constant function of value 1 over
+ // the whole computational domain,
+ // i.e. by computing the areas
+ // $\int_K 1 dx=\int_{\hat K} 1\
+ // \textrm{det}\ J(\hat x) d\hat x
+ // \approx \sum_i \textrm{det}\
+ // J(\hat x_i)w(\hat x_i)$, where the
+ // sum extends over all quadrature
+ // points on all active cells in the
// triangulation, with $w(x_i)$ being
// the weight of quadrature point
// $x_i$. The integrals on each cell
// ConvergenceTable class to
// store all important data
// like the approximated values
- // for pi and the error with
+ // for $\pi$ and the error with
// respect to the true value of
- // pi. We will also use
+ // $\pi$. We will also use
// functions provided by the
// ConvergenceTable class to
// compute convergence rates of
- // the approximations to pi.
+ // the approximations to $\pi$.
ConvergenceTable table;
// Now we loop over several
// The following, second function also
- // computes an approximation of pi
+ // computes an approximation of $\pi$
// but this time via the perimeter
- // 2*pi*radius of the domain instead
+ // $2\pi r$ of the domain instead
// of the area. This function is only
// a variation of the previous
// function. So we will mainly give
projects / dealii-svn.git / commitdiff