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//
// Copyright (C) 2000 - 2016 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, redistribute
// it, and/or modify it under the terms of the GNU Lesser General
// Public License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE at
// the top level of the deal.II distribution.
//
// ---------------------------------------------------------------------
#ifndef dealii__mapping_q1_h
#define dealii__mapping_q1_h
#include <deal.II/base/derivative_form.h>
#include <deal.II/base/config.h>
#include <deal.II/base/table.h>
#include <deal.II/base/qprojector.h>
#include <deal.II/grid/tria_iterator.h>
#include <deal.II/dofs/dof_accessor.h>
#include <deal.II/fe/mapping_q_generic.h>
#include <cmath>
DEAL_II_NAMESPACE_OPEN
/*!@addtogroup mapping */
/*@{*/
/**
* Implementation of a $d$-linear mapping from the reference cell to a general
* quadrilateral/hexahedron.
*
* The mapping implemented by this class maps the reference (unit) cell to a
* general grid cell with straight lines in $d$ dimensions. (Note, however,
* that in 3D the <i>faces</i> of a general, trilinearly mapped cell may be
* curved, even if the edges are not). This is the standard mapping used for
* polyhedral domains. It is also the mapping used throughout deal.II for many
* functions that come in two variants, one that allows to pass a mapping
* argument explicitly and one that simply falls back to the MappingQ1 class
* declared here. (Or, in fact, to an object of kind MappingQGeneric(1), which
* implements exactly the functionality of this class.)
*
* The shape functions for this mapping are the same as for the finite element
* FE_Q of polynomial degree 1. Therefore, coupling these two yields an
* isoparametric element.
*
* @note This class is, in all reality, nothing more than a different name for
* calling MappingQGeneric with a polynomial degree of one as argument.
*
* @author Guido Kanschat, 2000, 2001; Ralf Hartmann, 2000, 2001, 2005,
* Wolfgang Bangerth, 2015
*/
template <int dim, int spacedim=dim>
class MappingQ1 : public MappingQGeneric<dim,spacedim>
{
public:
/**
* Default constructor.
*/
MappingQ1 ();
// for documentation, see the Mapping base class
virtual
MappingQ1<dim,spacedim> *clone () const;
};
/**
* Many places in the library by default use (bi-,tri-)linear mappings unless
* users explicitly provide a different mapping to use. In these cases, the
* called function has to create a $Q_1$ mapping object, i.e., an object of
* kind MappingQGeneric(1). This is costly. It would also be costly to create
* such objects as static objects in the affected functions, because static
* objects are never destroyed throughout the lifetime of a program, even
* though they only have to be created once the first time code runs through a
* particular function.
*
* In order to avoid creation of (static or dynamic) $Q_1$ mapping objects in
* these contexts throughout the library, this class defines a static $Q_1$
* mapping object. This object can then be used in all of those places where
* such an object is needed.
*/
template <int dim, int spacedim=dim>
struct StaticMappingQ1
{
/**
* The static $Q_1$ mapping object discussed in the documentation of this
* class.
*/
static MappingQGeneric<dim, spacedim> mapping;
};
/*@}*/
DEAL_II_NAMESPACE_CLOSE
#endif
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