From 0ca0642d7ae78ad3d7499f3f06f9dc716e4e4200 Mon Sep 17 00:00:00 2001 From: Wolfgang Bangerth Date: Sat, 20 Sep 2014 06:47:05 -0500 Subject: [PATCH] Adjust based on Guido's feedback. --- include/deal.II/base/quadrature_lib.h | 46 ++++++++++++++++----------- 1 file changed, 27 insertions(+), 19 deletions(-) diff --git a/include/deal.II/base/quadrature_lib.h b/include/deal.II/base/quadrature_lib.h index dc47d6c60d..38dd8808ee 100644 --- a/include/deal.II/base/quadrature_lib.h +++ b/include/deal.II/base/quadrature_lib.h @@ -27,10 +27,13 @@ DEAL_II_NAMESPACE_OPEN /*@{*/ /** - * Gauss-Legendre quadrature of arbitrary order. + * The Gauss-Legendre family of quadrature rules for numerical + * integration. * - * The coefficients of these quadrature rules are computed by the - * function found in Numerical Recipies. + * The coefficients of these quadrature rules are computed by the function + * described in Numerical + * Recipies. * * @author Guido Kanschat, 2001 */ @@ -50,7 +53,8 @@ public: /** - * The Gauss-Lobatto quadrature rule. + * The Gauss-Lobatto family of quadrature rules for numerical + * integration. * * This modification of the Gauss quadrature uses the two interval end * points as well. Being exact for polynomials of degree 2n-3, @@ -64,7 +68,7 @@ public: * @note This implementation has not been optimized concerning * numerical stability and efficiency. It can be easily adapted * to the general case of Gauss-Lobatto-Jacobi-Bouzitat quadrature - * with arbitrary parameters $\alpha$, $\beta, of which + * with arbitrary parameters $\alpha$, $\beta$, of which * the Gauss-Lobatto-Legendre quadrature ($\alpha = \beta = 0$) * is a special case. * @@ -94,10 +98,10 @@ protected: * equal to the roots of the * corresponding Jacobi * polynomial (specified by @p - * alpha, @p beta). @p q is + * alpha, @p beta). @p q is the * number of points. * - * @return vector containing nodes. + * @return Vector containing nodes. */ std::vector compute_quadrature_points (const unsigned int q, @@ -111,7 +115,8 @@ protected: * related to Jacobi polynomial specified * by @p alpha, @p beta. * @p x denotes the quadrature points. - * @return vector containing weights. + * + * @return Vector containing weights. */ std::vector compute_quadrature_weights (const std::vector &x, @@ -144,8 +149,8 @@ protected: /** - * A quadrature formula implementing the one-point, midpoint quadrature - * rule. This formula is exact for linear polynomials. + * The midpoint rule for numerical quadrature. This one-point formula is exact + * for linear polynomials. */ template class QMidpoint : public Quadrature @@ -156,8 +161,8 @@ public: /** - * A quadrature formula implementing the Simpson quadrature rule (with 3 - * quadrature points). This formula is exact for polynomials of degree 3. + * The Simpson rule for numerical quadrature. This formula with 3 quadrature + * points is exact for polynomials of degree 3. */ template class QSimpson : public Quadrature @@ -167,9 +172,10 @@ public: }; + /** - * A quadrature formula implementing the trapezoidal quadrature rule. This - * formula is exact for linear polynomials. + * The trapezoidal rule for numerical quadrature. This formula with two + * quadrature points is exact for linear polynomials. * * The class is poorly named since the proper name of the quadrature formula * is "trapezoidal rule", or sometimes also called the "trapezoid rule". The @@ -186,8 +192,10 @@ public: QTrapez (); }; + + /** - * A quadrature formula implementing the Milne rule. The Milne rule is a + * The Milne rule for numerical quadrature formula. The Milne rule is a * closed Newton-Cotes formula and is exact for polynomials of degree 5. * * @sa Stoer: Einführung in die Numerische Mathematik I, p. 102 @@ -201,7 +209,7 @@ public: /** - * A quadrature formula implementing the Weddle rule. The Weddle rule is a + * The Weddle rule for numerical quadrature. The Weddle rule is a * closed Newton-Cotes formula and is exact for polynomials of degree 7. * * @sa Stoer: Einführung in die Numerische Mathematik I, p. 102 @@ -216,7 +224,7 @@ public: /** - * A quadrature formula implementing the Gauss quadrature formula with + * A class for Gauss quadrature with * logarithmic weighting function. This * formula is used to integrate $\ln|x|\;f(x)$ on the interval * $[0,1]$, where $f$ is a smooth function without @@ -262,7 +270,7 @@ protected: /** - * Gauss Quadrature Formula with arbitrary logarithmic weighting + * A class for Gauss quadrature with arbitrary logarithmic weighting * function. This formula is used to to integrate * $\ln(|x-x_0|/\alpha)\;f(x)$ on the interval $[0,1]$, * where $f$ is a smooth function without singularities, and $x_0$ and @@ -335,7 +343,7 @@ protected: /** - * Gauss Quadrature Formula with $1/R$ weighting function. This formula + * A class for Gauss quadrature 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 -- 2.39.5