From: Martin Kronbichler Date: Mon, 12 Oct 2020 08:11:13 +0000 (+0200) Subject: Improve documentation of FEEvaluationBaseData::inverse_jacobian X-Git-Tag: v9.3.0-rc1~1012^2 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=refs%2Fpull%2F11037%2Fhead;p=dealii.git Improve documentation of FEEvaluationBaseData::inverse_jacobian --- diff --git a/include/deal.II/matrix_free/fe_evaluation.h b/include/deal.II/matrix_free/fe_evaluation.h index 187f22d840..a05f3db31b 100644 --- a/include/deal.II/matrix_free/fe_evaluation.h +++ b/include/deal.II/matrix_free/fe_evaluation.h @@ -135,10 +135,15 @@ public: JxW(const unsigned int q_point) const; /** - * Return the inverse and transposed version of Jacobian of the mapping - * between the unit to the real cell (representing the covariant - * transformation). This is exactly the matrix used internally to transform - * the unit cell gradients to gradients on the real cell. + * Return the inverse and transposed version $J^{-\mathrm T}$ of the + * Jacobian of the mapping between the unit to the real cell defined as + * $J_{ij} = d x_i / d\hat x_j$. The $(i,j)$ entry of the returned tensor + * contains $d\hat x_j/dx_i$, i.e., columns refer to reference space + * coordinates and rows to real cell coordinates. Thus, the returned tensor + * represents a covariant transformation, which is used in the + * FEEvaluationBase::get_gradient() function to transform the unit cell + * gradients to gradients on the real cell by a multiplication $J^{-\mathrm + * T} \hat{\nabla} u_h$. */ Tensor<2, dim, VectorizedArrayType> inverse_jacobian(const unsigned int q_point) const;