From c8112f3759a2f4e7ca4001ba804fafff85dbd8f6 Mon Sep 17 00:00:00 2001 From: bangerth Date: Sat, 18 Apr 2009 22:39:02 +0000 Subject: [PATCH] Minor doc updates. git-svn-id: https://svn.dealii.org/trunk@18650 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/base/include/base/quadrature_lib.h | 48 +++++++++++++--------- 1 file changed, 29 insertions(+), 19 deletions(-) diff --git a/deal.II/base/include/base/quadrature_lib.h b/deal.II/base/include/base/quadrature_lib.h index 7bc51dce66..300c7c03f7 100644 --- a/deal.II/base/include/base/quadrature_lib.h +++ b/deal.II/base/include/base/quadrature_lib.h @@ -357,28 +357,28 @@ class QGaussLog : public Quadrature /** * Gauss Quadrature Formula with arbitrary logarithmic weighting * function. This formula is used to to integrate - * ln(|x-x0|/alpha)*f(x) on the interval [0,1], - * where f is a smooth function without singularities, and x0 and - * alpha are given at construction time, and are the location of the - * singularity x0 and an arbitrary scaling factor in the + * $\ln(|x-x_0|/\alpha)\;f(x)$ on the interval $[0,1]$, + * where $f$ is a smooth function without singularities, and $x_0$ and + * $\alpha$ are given at construction time, and are the location of the + * singularity $x_0$ and an arbitrary scaling factor in the * singularity. * - * You have to make sure that the point x0 is not one of the Gauss + * You have to make sure that the point $x_0$ is not one of the Gauss * quadrature points of order $N$, otherwise an exception is thrown, * since the quadrature weights cannot be computed correctly. * * This quadrature formula is rather expensive, since it uses * internally two Gauss quadrature formulas of order n to integrate * the nonsingular part of the factor, and two GaussLog quadrature - * formulas to integrate on the separate segments [0,x0] and - * [x0,1]. If the singularity is one of the extremes and the factor + * formulas to integrate on the separate segments $[0,x_0]$ and + * $[x_0,1]$. If the singularity is one of the extremes and the factor * alpha is 1, then this quadrature is the same as QGaussLog. * * The last argument from the constructor allows you to use this * quadrature rule in one of two possible ways: * \f[ * \int_0^1 g(x) dx = - * int_0^1 f(x) \ln\left(\frac{|x-x_0|}{\alpha}\right) dx + * \int_0^1 f(x) \ln\left(\frac{|x-x_0|}{\alpha}\right) dx * = \sum_{i=0}^N w_i g(q_i) = \sum_{i=0}^N \bar{w}_i f(q_i) * \f] * @@ -398,22 +398,32 @@ class QGaussLog : public Quadrature * */ template -class QGaussLogR : public Quadrature { -public: - /** The constructor takes four arguments: the order of the gauss - * formula on each of the segments [0,x0] and [x0,1], the actual - * location of the singularity, the scale factor inside the - * logarithmic function and a flag that decides wether the - * singularity is left inside the quadrature formula or it is - * factored out, to be included in the integrand. */ +class QGaussLogR : public Quadrature +{ + public: + /** + * The constructor takes four arguments: + * the order of the gauss formula on each + * of the segments $[0,x_0]$ and + * $[x_0,1]$, the actual location of the + * singularity, the scale factor inside + * the logarithmic function and a flag + * that decides wether the singularity is + * left inside the quadrature formula or + * it is factored out, to be included in + * the integrand. + */ QGaussLogR(const unsigned int n, const Point x0 = Point(), const double alpha = 1, const bool factor_out_singular_weight=false); -protected: - /** This is the length of interval (0,origin), or 1 if either of - * the two extremes have been selected. */ + protected: + /** + * This is the length of interval + * $(0,origin)$, or 1 if either of the two + * extremes have been selected. + */ const double fraction; }; -- 2.39.5