From 331c380ef7cc58b7f1787c1fed9ce77158278ff3 Mon Sep 17 00:00:00 2001 From: Luca Heltai Date: Fri, 22 Dec 2017 19:29:30 +0100 Subject: [PATCH] Improved Documentation. --- include/deal.II/base/quadrature_lib.h | 14 +++++++++----- 1 file changed, 9 insertions(+), 5 deletions(-) diff --git a/include/deal.II/base/quadrature_lib.h b/include/deal.II/base/quadrature_lib.h index 6ac9a23e3a..fc8e596912 100644 --- a/include/deal.II/base/quadrature_lib.h +++ b/include/deal.II/base/quadrature_lib.h @@ -763,13 +763,17 @@ public: * \hat x^\beta \hat y * end{pmatrix} * \f] + * * with determinant of the Jacobian equal to $J= \beta \hat \x^{2\beta-1}$. * Such transformation maps the reference square \$[0,1]\times[0,1]$ to the - * reference simplex, by collapsing the left \side of the square and - * squeezing quadrature points towards the orgin, and then shearing the - * resulting triangle to the reference one. This transformation, allows - * one to integrate singularities of order $1/R$ in the origin when $\beta = - * 1$, and higher when $1 < \beta \leq 2$. + * reference simplex, by collapsing the left \side of the square and squeezing + * quadrature points towards the orgin, and then shearing the resulting + * triangle to the reference one. This transformation shows good convergence + * properties when $\beta = 1$ with singularities of order $1/R$ in the origin, + * but different $\beta$ values can be selected to increase convergence and/or + * accuracy when higher order Gauss rules are used (see "Generalized Duffy + * transformation for integrating vertex singularities", S. E. Mousavi, N. + * Sukumar, Computational Mechanics 2009). * * When $\beta = 1$, this transformation is also known as the Lachat-Watson * transformation. -- 2.39.5