From 6cfb3b85ae2bbf75a36edc3a8bd94424063512b7 Mon Sep 17 00:00:00 2001 From: bangerth Date: Mon, 13 Apr 2009 03:00:26 +0000 Subject: [PATCH] Add a bit to the documentation. git-svn-id: https://svn.dealii.org/trunk@18604 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/base/include/base/quadrature_lib.h | 60 +++++++++++----------- 1 file changed, 31 insertions(+), 29 deletions(-) diff --git a/deal.II/base/include/base/quadrature_lib.h b/deal.II/base/include/base/quadrature_lib.h index bbc088fe4a..b109cd2de4 100644 --- a/deal.II/base/include/base/quadrature_lib.h +++ b/deal.II/base/include/base/quadrature_lib.h @@ -396,33 +396,35 @@ protected: /** - * Gauss Quadrature Formula with 1/R weighting function. This formula - * can be used to to integrate 1/(R)*f(x) on the reference - * element [0,1]^2, where f is a smooth function without - * singularities, and R is the distance from the point x to the vertex - * xi, given at construction time by specifying its index. Notice that + * Gauss Quadrature Formula with $1/R$ weighting function. This formula + * can be used to to integrate $1/R \ f(x)$ on the reference + * element $[0,1]^2$, where $f$ is a smooth function without + * singularities, and $R$ is the distance from the point $x$ to the vertex + * $\xi$, given at construction time by specifying its index. Notice that * this distance is evaluated in the reference element. * * This quadrature formula is obtained from two QGauss quadrature - * formula, upon transforming them into polar coordinate system + * formulas, upon transforming them into polar coordinate system * centered at the singularity, and then again into another reference * element. This allows for the singularity to be cancelled by part of - * the Jacobian of the transformation, which contains R. In practice + * the Jacobian of the transformation, which contains $R$. In practice * the reference element is transformed into a triangle by collapsing - * one of the side adjacent to the singularity. The Jacobian of this - * transformation contains R, which is removed before scaling the + * one of the sides adjacent to the singularity. The Jacobian of this + * transformation contains $R$, which is removed before scaling the * original quadrature, and this process is repeated for the next half * element. * * Upon construction it is possible to specify wether we want the * singularity removed, or not. In other words, this quadrature can be - * used to integrate f(x) = 1/R*g(x), or simply g(x), with the 1/R + * used to integrate $g(x) = 1/R\ f(x)$, or simply $f(x)$, with the $1/R$ * factor already included in the quadrature weights. */ template -class QGaussOneOverR : public Quadrature { -public: - /** The constructor takes three arguments: the order of the gauss +class QGaussOneOverR : public Quadrature +{ + public: + /** + * The constructor takes three arguments: the order of the Gauss * formula, the index of the vertex where the singularity is * located, and whether we include the weighting singular function * inside the quadrature, or we leave it in the user function to @@ -438,22 +440,22 @@ public: * In other words, you can use this function in either of * the following way, obtaining the same result: * - - QGaussOneOverR singular_quad(order, vertex_id, false); - // This will produce the integral of f(x)/R - for(unsigned int i=0; ivertex(vertex_id)).norm(); - integral += f(singular_quad_noR.point(i))*singular_quad_noR.weight(i)/R; - } - + * @code + * QGaussOneOverR singular_quad(order, vertex_id, false); + * // This will produce the integral of f(x)/R + * for(unsigned int i=0; ivertex(vertex_id)).norm(); + * integral += f(singular_quad_noR.point(i))*singular_quad_noR.weight(i)/R; + * } + * @endcode */ QGaussOneOverR(const unsigned int n, const unsigned int vertex_index, -- 2.39.5