From d1f861f01498370b54d1f099088463d1630cb3ee Mon Sep 17 00:00:00 2001 From: bangerth Date: Wed, 29 Aug 2007 15:09:58 +0000 Subject: [PATCH] Use formulas instead of plain text git-svn-id: https://svn.dealii.org/trunk@15086 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/examples/step-10/step-10.cc | 49 +++++++++++++++-------------- 1 file changed, 25 insertions(+), 24 deletions(-) diff --git a/deal.II/examples/step-10/step-10.cc b/deal.II/examples/step-10/step-10.cc index ac6c1b53a7..a29e810cb7 100644 --- a/deal.II/examples/step-10/step-10.cc +++ b/deal.II/examples/step-10/step-10.cc @@ -4,7 +4,7 @@ /* $Id$ */ /* 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 */ @@ -44,15 +44,15 @@ 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 @@ -260,21 +260,22 @@ void gnuplot_output() // 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 @@ -420,13 +421,13 @@ void compute_pi_by_area () // 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 @@ -536,9 +537,9 @@ void compute_pi_by_area () // 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 -- 2.39.5