From 92c2892b9657c80c381d0ea6cc524bff193a5815 Mon Sep 17 00:00:00 2001 From: bangerth Date: Mon, 19 Mar 2012 18:47:19 +0000 Subject: [PATCH] Update mark-up. git-svn-id: https://svn.dealii.org/trunk@25302 0785d39b-7218-0410-832d-ea1e28bc413d --- .../include/deal.II/base/derivative_form.h | 93 +++++++++---------- 1 file changed, 46 insertions(+), 47 deletions(-) diff --git a/deal.II/include/deal.II/base/derivative_form.h b/deal.II/include/deal.II/base/derivative_form.h index 6646475209..d203440d40 100644 --- a/deal.II/include/deal.II/base/derivative_form.h +++ b/deal.II/include/deal.II/base/derivative_form.h @@ -7,19 +7,19 @@ DEAL_II_NAMESPACE_OPEN /** This class represents the (tangential) derivatives of a function - \f f: ${\mathbb R}^{\text{dim}} \rightarrow {\mathbb R}^{\text{spacedim}}\f$. + $ f: {\mathbb R}^{\text{dim}} \rightarrow {\mathbb R}^{\text{spacedim}}$. Such functions are always used to map the reference dim-dimensional cell into spacedim-dimensional space. For such objects, the first derivative of the function is a linear map from - \f${\mathbb R}^{\text{dim}}\f$ to \f${\mathbb R}^{\text{spacedim}}\f$, + ${\mathbb R}^{\text{dim}}$ to ${\mathbb R}^{\text{spacedim}}$, the second derivative a bilinear map - from \f${\mathbb R}^{\text{dim}} \times {\mathbb R}^{\text{dim}}\f$ - to \f${\mathbb R}^{\text{spacedim}}\f$ and so on. - + from ${\mathbb R}^{\text{dim}} \times {\mathbb R}^{\text{dim}}$ + to ${\mathbb R}^{\text{spacedim}}$ and so on. + In deal.II we represent these derivaties using objects of type DerivativeForm<1,dim,spacedim>, DerivativeForm<2,dim,spacedim> and so on. - - + + @author Sebastian Pauletti, 2011 */ @@ -59,7 +59,7 @@ class DerivativeForm * Assignment operator. */ DerivativeForm & operator = (const Tensor<2,dim> &); - + /** * Assignment operator. */ @@ -89,33 +89,33 @@ class DerivativeForm /** Computes the volume element associated with the jacobian of the tranformation F. - That is to say if \f$DF\f$ is square, it computes - \f$\det(DF)\f$, in case DF is not square returns - \f$\sqrt(\det(DF^{t} * DF))\f$. + That is to say if $DF$ is square, it computes + $\det(DF)$, in case DF is not square returns + $\sqrt(\det(DF^{t} * DF))$. */ double determinant () const; - - + + /** Assuming (*this) stores the jacobian of the mapping F, it computes its covariant - matrix, namely \f$DF*G^{-1}\f$, where - \f$G = DF^{t}*DF\f$. + matrix, namely $DF*G^{-1}$, where + $G = DF^{t}*DF$. If $DF$ is square, covariant from - gives \f$DF^{-t}\f$. + gives $DF^{-t}$. */ DerivativeForm<1, dim, spacedim> covariant_form() const; - - - + + + /** * Determine an estimate for the * memory consumption (in bytes) * of this object. */ static std::size_t memory_consumption (); - + /** * Exception. */ @@ -123,7 +123,7 @@ class DerivativeForm int, << "Invalid DerivativeForm index " << arg1); - + private: /** Auxiliary function that computes (*this) * T^{t} */ @@ -137,7 +137,7 @@ class DerivativeForm */ Tensor tensor[spacedim]; - + }; @@ -165,7 +165,7 @@ DerivativeForm::DerivativeForm(const Tensor<2,dim> &T) { Assert( (dim == spacedim) && (order==1), ExcMessage("Only allowed for square tensors.")); - + for (unsigned int j=0; j &ta) { Assert( (dim == spacedim) && (order==1), ExcMessage("Only allowed for square tensors.")); - + for (unsigned int j=0; j &T) { Assert( (1 == spacedim) && (order==1), ExcMessage("Only allowed for spacedim==1 and order==1.")); - + (*this)[0] = T; return *this; @@ -249,7 +249,7 @@ DerivativeForm::operator Tensor<1,dim>() const ExcMessage("Only allowed for spacedim==1.")); return (*this)[0]; - + } @@ -262,12 +262,12 @@ DerivativeForm::operator Tensor<2,dim>() const ExcMessage("Only allowed for square tensors.")); Tensor<2,dim> t; - + for (unsigned int j=0; j tt; - + for (unsigned int i=0; i::determinant () const G[i][j] = DF_t[i] * DF_t[j]; return ( sqrt(dealii::determinant(G)) ); - + } - + } @@ -338,17 +338,17 @@ inline DerivativeForm<1,dim,spacedim> DerivativeForm::covariant_form() const { - + if (dim == spacedim) { - + Tensor<2,dim> DF_t (dealii::transpose(invert( (Tensor<2,dim>)(*this) ))); DerivativeForm<1,dim, spacedim> result = DF_t; return(result); } else { - + DerivativeForm<1,spacedim,dim> DF_t = this->transpose(); Tensor<2, dim> G; //First fundamental form for (unsigned int i=0; i::covariant_form() const G[i][j] = DF_t[i] * DF_t[j]; return (this->times_T_t(invert(G))); - + } - + } @@ -379,17 +379,16 @@ DerivativeForm::memory_consumption () /** One of the uses of DerivativeForm is to apply it as a transformation. This is what this function does. - - If @pT is DerivativeForm<1,dim,1> it computes $DF * T$, - if @pT is DerivativeForm<1,dim,rank> it computes $T*DF^{t}$. + + If @p T is DerivativeForm<1,dim,1> it computes $DF * T$, + if @p T is DerivativeForm<1,dim,rank> it computes $T*DF^{t}$. @relates DerivativeForm @author Sebastian Pauletti, 2011 */ -//rank=1 template inline -Tensor<1, spacedim> +Tensor<1, spacedim> apply_transformation (const DerivativeForm<1,dim,spacedim> &DF, const Tensor<1,dim> &T) { @@ -410,11 +409,11 @@ apply_transformation (const DerivativeForm<1,dim,spacedim> &DF, //rank=2 template inline -DerivativeForm<1, spacedim, dim> +DerivativeForm<1, spacedim, dim> apply_transformation (const DerivativeForm<1,dim,spacedim> &DF, const Tensor<2,dim> &T) { - + DerivativeForm<1, spacedim, dim> dest; for (unsigned int i=0; i &DF1, const DerivativeForm<1,dim,spacedim> &DF2) { Tensor<2, spacedim> dest; - + for (unsigned int i=0; i &DF1, template inline DerivativeForm<1,spacedim,dim> -transpose (const DerivativeForm<1,dim,spacedim> &DF) +transpose (const DerivativeForm<1,dim,spacedim> &DF) { DerivativeForm<1,spacedim,dim> tt; tt = DF.transpose(); -- 2.39.5