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// $Id: grid_generator.h 31932 2013-12-08 02:15:54Z heister $
//
// Copyright (C) 1999 - 2013 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 __deal2__grid_generator_h
#define __deal2__grid_generator_h
#include <deal.II/base/config.h>
#include <deal.II/base/exceptions.h>
#include <deal.II/base/point.h>
#include <deal.II/base/table.h>
#include <deal.II/grid/tria.h>
#include <map>
DEAL_II_NAMESPACE_OPEN
template <int dim, int spacedim> class Triangulation;
template <typename number> class Vector;
template <typename number> class SparseMatrix;
/**
* This namespace provides a collection of functions for generating
* triangulations for some basic geometries.
*
* Some of these functions receive a flag @p colorize. If this is
* set, parts of the boundary receive different boundary indicators
* (@ref GlossBoundaryIndicator),
* allowing them to be distinguished for the purpose of attaching geometry
* objects and evaluating different boundary conditions.
*
* This namespace also provides a function
* GridGenerator::laplace_transformation that smoothly transforms a domain
* into another one. This can be used to
* transform basic geometries to more complicated ones, like a
* shell to a grid of an airfoil, for example.
*
* @ingroup grid
*/
namespace GridGenerator
{
/**
* Initialize the given triangulation with a hypercube (line in 1D, square
* in 2D, etc) consisting of exactly one cell. The hypercube volume is the
* tensor product interval <i>[left,right]<sup>dim</sup></i> in the present
* number of dimensions, where the limits are given as arguments. They
* default to zero and unity, then producing the unit hypercube. All
* boundary indicators are set to zero ("not colorized") for 2d and 3d. In
* 1d the indicators are colorized, see hyper_rectangle().
*
* @image html hyper_cubes.png
*
* See also subdivided_hyper_cube() for a coarse mesh consisting of several
* cells. See hyper_rectangle(), if different lengths in different ordinate
* directions are required.
*
* @note The triangulation needs to be void upon calling this function.
*/
template <int dim, int spacedim>
void hyper_cube (Triangulation<dim,spacedim> &tria,
const double left = 0.,
const double right= 1.);
/**
* Same as hyper_cube(), but with the difference that not only one cell is
* created but each coordinate direction is subdivided into @p repetitions
* cells. Thus, the number of cells filling the given volume is
* <tt>repetitions<sup>dim</sup></tt>.
*
* If spacedim=dim+1 the same mesh as in the case spacedim=dim is created,
* but the vertices have an additional coordinate =0. So, if dim=1 one
* obtains line along the x axis in the xy plane, and if dim=3 one obtains a
* square in lying in the xy plane in 3d space.
*
* @note The triangulation needs to be void upon calling this function.
*/
template <int dim>
void subdivided_hyper_cube (Triangulation<dim> &tria,
const unsigned int repetitions,
const double left = 0.,
const double right= 1.);
/**
* Create a coordinate-parallel brick from the two diagonally opposite
* corner points @p p1 and @p p2.
*
* If the @p colorize flag is set, the @p boundary_indicators of the
* surfaces are assigned, such that the lower one in @p x-direction is 0,
* the upper one is 1. The indicators for the surfaces in @p y-direction are
* 2 and 3, the ones for @p z are 4 and 5. Additionally, material ids are
* assigned to the cells according to the octant their center is in: being
* in the right half plane for any coordinate direction <i>x<sub>i</sub></i>
* adds 2<sup>i</sup>. For instance, the center point (1,-1,1) yields a
* material id 5.
*
* @note The triangulation needs to be void upon calling this function.
*/
template <int dim, int spacedim>
void hyper_rectangle (Triangulation<dim,spacedim> &tria,
const Point<spacedim> &p1,
const Point<spacedim> &p2,
const bool colorize = false);
/**
* Create a coordinate-parallel parallelepiped from the two diagonally
* opposite corner points @p p1 and @p p2. In dimension @p i,
* <tt>repetitions[i]</tt> cells are generated.
*
* To get cells with an aspect ratio different from that of the domain, use
* different numbers of subdivisions in different coordinate directions. The
* minimum number of subdivisions in each direction is 1. @p repetitions is
* a list of integers denoting the number of subdivisions in each coordinate
* direction.
*
* If the @p colorize flag is set, the @p boundary_indicators of the
* surfaces are assigned, such that the lower one in @p x-direction is 0,
* the upper one is 1 (the left and the right vertical face). The indicators
* for the surfaces in @p y-direction are 2 and 3, the ones for @p z are 4
* and 5. Additionally, material ids are assigned to the cells according to
* the octant their center is in: being in the right half plane for any
* coordinate direction <i>x<sub>i</sub></i> adds 2<sup>i</sup>. For
* instance, the center point (1,-1,1) yields a material id 5 (this means
* that in 2d only material ids 0,1,2,3 are assigned independent from the
* number of repetitions).
*
* Note that the @p colorize flag is ignored in 1d and is assumed to always
* be true. That means the boundary indicator is 0 on the left and 1 on the
* right. See step-15 for details.
*
* @note The triangulation needs to be void upon calling this function.
*
* @note For an example of the use of this function see the step-28 tutorial
* program.
*/
template <int dim>
void
subdivided_hyper_rectangle (Triangulation<dim> &tria,
const std::vector<unsigned int> &repetitions,
const Point<dim> &p1,
const Point<dim> &p2,
const bool colorize=false);
/**
* Like the previous function. However, here the second argument does not
* denote the number of subdivisions in each coordinate direction, but a
* sequence of step sizes for each coordinate direction. The domain will
* therefore be subdivided into <code>step_sizes[i].size()</code> cells in
* coordinate direction <code>i</code>, with widths
* <code>step_sizes[i][j]</code> for the <code>j</code>th cell.
*
* This function is therefore the right one to generate graded meshes where
* cells are concentrated in certain areas, rather than a uniformly
* subdivided mesh as the previous function generates.
*
* The step sizes have to add up to the dimensions of the hyper rectangle
* specified by the points @p p1 and @p p2.
*/
template <int dim>
void
subdivided_hyper_rectangle (Triangulation<dim> &tria,
const std::vector<std::vector<double> > &step_sizes,
const Point<dim> &p_1,
const Point<dim> &p_2,
const bool colorize);
/**
* Like the previous function, but with the following twist: the @p
* material_id argument is a dim-dimensional array that, for each cell,
* indicates which material_id should be set. In addition, and this is the
* major new functionality, if the material_id of a cell is <tt>(unsigned
* char)(-1)</tt>, then that cell is deleted from the triangulation,
* i.e. the domain will have a void there.
*/
template <int dim>
void
subdivided_hyper_rectangle (Triangulation<dim> &tria,
const std::vector< std::vector<double> > &spacing,
const Point<dim> &p,
const Table<dim,types::material_id> &material_id,
const bool colorize=false);
/**
* A parallelogram. The first corner point is the origin. The <tt>dim</tt>
* adjacent points are the ones given in the second argument and the fourth
* point will be the sum of these two vectors. Colorizing is done in the
* same way as in hyper_rectangle().
*
* @note This function is implemented in 2d only.
*
* @note The triangulation needs to be void upon calling this function.
*/
template <int dim>
void
parallelogram (Triangulation<dim> &tria,
const Point<dim> corners[dim],
const bool colorize=false);
/**
* @deprecated Use the other function of same name.
*/
template <int dim>
void
parallelogram (Triangulation<dim> &tria,
const Tensor<2,dim> &corners,
const bool colorize=false) DEAL_II_DEPRECATED;
/**
* A parallelepiped. The first corner point is the origin. The
* <tt>dim</tt> adjacent points are vectors describing the edges of
* the parallelepiped with respect to the origin. Additional points
* are sums of these dim vectors. Colorizing is done according to
* hyper_rectangle().
*
* @note This function silently reorders the vertices on the cells
* to lexiographic ordering (see
* <code>GridReordering::reorder_grid</code>). In other words, if
* reodering of the vertices does occur, the ordering of vertices in
* the array of <code>corners</code> will no longer refer to the
* same triangulation.
*
* @note The triangulation needs to be void upon calling this
* function.
*/
template <int dim>
void
parallelepiped (Triangulation<dim> &tria,
const Point<dim> (&corners) [dim],
const bool colorize = false);
/**
* A subdivided parallelepiped. The first corner point is the
* origin. The <tt>dim</tt> adjacent points are vectors describing
* the edges of the parallelepiped with respect to the
* origin. Additional points are sums of these dim vectors. The
* variable @p n_subdivisions designates the number of subdivisions
* in each of the <tt>dim</tt> directions. Colorizing is done
* according to hyper_rectangle().
*
* @note The triangulation needs to be void upon calling this
* function.
*/
template <int dim>
void
subdivided_parallelepiped (Triangulation<dim> &tria,
const unsigned int n_subdivisions,
const Point<dim> (&corners) [dim],
const bool colorize = false);
/**
* A subdivided parallelepiped, ie. the same as above, but where the
* number of subdivisions in each of the <tt>dim</tt> directions may
* vary. Colorizing is done according to hyper_rectangle().
*
* @note The triangulation needs to be void upon calling this
* function.
*/
template <int dim>
void
subdivided_parallelepiped (Triangulation<dim> &tria,
const unsigned int (n_subdivisions) [dim],
const Point<dim> (&corners) [dim],
const bool colorize = false);
/**
* Hypercube with a layer of hypercubes around it. The first two parameters
* give the lower and upper bound of the inner hypercube in all coordinate
* directions. @p thickness marks the size of the layer cells.
*
* If the flag colorize is set, the outer cells get material id's according
* to the following scheme: extending over the inner cube in (+/-)
* x-direction: 1/2. In y-direction 4/8, in z-direction 16/32. The cells at
* corners and edges (3d) get these values bitwise or'd.
*
* Presently only available in 2d and 3d.
*
* @note The triangulation needs to be void upon calling this function.
*/
template <int dim>
void enclosed_hyper_cube (Triangulation<dim> &tria,
const double left = 0.,
const double right= 1.,
const double thickness = 1.,
const bool colorize = false);
/**
* Initialize the given triangulation with a hyperball, i.e. a circle or a
* ball around <tt>center</tt> with given <tt>radius</tt>.
*
* In order to avoid degenerate cells at the boundaries, the circle is
* triangulated by five cells, the ball by seven cells. The diameter of the
* center cell is chosen so that the aspect ratio of the boundary cells
* after one refinement is optimized.
*
* This function is declared to exist for triangulations of all space
* dimensions, but throws an error if called in 1d.
*
* @note The triangulation needs to be void upon calling this function.
*/
template <int dim>
void hyper_ball (Triangulation<dim> &tria,
const Point<dim> ¢er = Point<dim>(),
const double radius = 1.);
/**
* This class produces a half hyper-ball around <tt>center</tt>, which
* contains four elements in 2d and 6 in 3d. The cut plane is perpendicular
* to the <i>x</i>-axis.
*
* The boundary indicators for the final triangulation are 0 for the curved
* boundary and 1 for the cut plane.
*
* The appropriate boundary class is HalfHyperBallBoundary, or
* HyperBallBoundary.
*
* @note The triangulation needs to be void upon calling this function.
*/
template <int dim>
void half_hyper_ball (Triangulation<dim> &tria,
const Point<dim> ¢er = Point<dim>(),
const double radius = 1.);
/**
* Create a cylinder around the x-axis. The cylinder extends from
* <tt>x=-half_length</tt> to <tt>x=+half_length</tt> and its projection
* into the @p yz-plane is a circle of radius @p radius.
*
* In two dimensions, the cylinder is a rectangle from
* <tt>x=-half_length</tt> to <tt>x=+half_length</tt> and from
* <tt>y=-radius</tt> to <tt>y=radius</tt>.
*
* The boundaries are colored according to the following scheme: 0 for the
* hull of the cylinder, 1 for the left hand face and 2 for the right hand
* face.
*
* @note The triangulation needs to be void upon calling this function.
*/
template <int dim>
void cylinder (Triangulation<dim> &tria,
const double radius = 1.,
const double half_length = 1.);
/**
* Create a cutted cone around the x-axis. The cone extends from
* <tt>x=-half_length</tt> to <tt>x=half_length</tt> and its projection into
* the @p yz-plane is a circle of radius @p radius_0 at
* <tt>x=-half_length</tt> and a circle of radius @p radius_1 at
* <tt>x=+half_length</tt>. In between the radius is linearly decreasing.
*
* In two dimensions, the cone is a trapezoid from <tt>x=-half_length</tt>
* to <tt>x=+half_length</tt> and from <tt>y=-radius_0</tt> to
* <tt>y=radius_0</tt> at <tt>x=-half_length</tt> and from
* <tt>y=-radius_1</tt> to <tt>y=radius_1</tt> at <tt>x=+half_length</tt>.
* In between the range of <tt>y</tt> is linearly decreasing.
*
* The boundaries are colored according to the following scheme: 0 for the
* hull of the cone, 1 for the left hand face and 2 for the right hand face.
*
* An example of use can be found in the documentation of the ConeBoundary
* class, with which you probably want to associate boundary indicator 0
* (the hull of the cone).
*
* @note The triangulation needs to be void upon calling this function.
*
* @author Markus Bürg, 2009
*/
template <int dim>
void
truncated_cone (Triangulation<dim> &tria,
const double radius_0 = 1.0,
const double radius_1 = 0.5,
const double half_length = 1.0);
/**
* Initialize the given triangulation with a hyper-L consisting of exactly
* <tt>2^dim-1</tt> cells. It produces the hypercube with the interval
* [<i>left,right</i>] without the hypercube made out of the interval
* [<i>(a+b)/2,b</i>].
*
* @image html hyper_l.png
*
* The triangulation needs to be void upon calling this function.
*
* This function is declared to exist for triangulations of all space
* dimensions, but throws an error if called in 1d.
*
* @note The triangulation needs to be void upon calling this function.
*/
template <int dim>
void hyper_L (Triangulation<dim> &tria,
const double left = -1.,
const double right= 1.);
/**
* Initialize the given Triangulation with a hypercube with a slit. In each
* coordinate direction, the hypercube extends from @p left to @p right.
*
* In 2d, the split goes in vertical direction from <tt>x=(left+right)/2,
* y=left</tt> to the center of the square at <tt>x=y=(left+right)/2</tt>.
*
* In 3d, the 2d domain is just extended in the <i>z</i>-direction, such
* that a plane cuts the lower half of a rectangle in two.
* This function is declared to exist for triangulations of all space
* dimensions, but throws an error if called in 1d.
*
* @note The triangulation needs to be void upon calling this function.
*/
template <int dim>
void hyper_cube_slit (Triangulation<dim> &tria,
const double left = 0.,
const double right = 1.,
const bool colorize = false);
/**
* Produce a hyper-shell, the region between two spheres around
* <tt>center</tt>, with given <tt>inner_radius</tt> and
* <tt>outer_radius</tt>. The number <tt>n_cells</tt> indicates the number
* of cells of the resulting triangulation, i.e., how many cells form the
* ring (in 2d) or the shell (in 3d).
*
* If the flag @p colorize is @p true, then the outer boundary will have the
* indicator 1, while the inner boundary has id zero. If the flag is @p
* false, both have indicator zero.
*
* In 2D, the number <tt>n_cells</tt> of elements for this initial
* triangulation can be chosen arbitrarily. If the number of initial cells
* is zero (as is the default), then it is computed adaptively such that the
* resulting elements have the least aspect ratio.
*
* In 3D, only two different numbers are meaningful, 6 for a surface based
* on a hexahedron (i.e. 6 panels on the inner sphere extruded in radial
* direction to form 6 cells) and 12 for the rhombic dodecahedron. These
* give rise to the following meshes upon one refinement:
*
* @image html hypershell3d-6.png
* @image html hypershell3d-12.png
*
* Neither of these meshes is particularly good since one ends up with
* poorly shaped cells at the inner edge upon refinement. For example, this
* is the middle plane of the mesh for the <code>n_cells=6</code>:
*
* @image html hyper_shell_6_cross_plane.png
*
* The mesh generated with <code>n_cells=6</code> is better but still not
* good. As a consequence, you may also specify <code>n_cells=96</code> as a
* third option. The mesh generated in this way is based on a once refined
* version of the one with <code>n_cells=12</code>, where all internal nodes
* are re-placed along a shell somewhere between the inner and outer
* boundary of the domain. The following two images compare half of the
* hyper shell for <code>n_cells=12</code> and <code>n_cells=96</code> (note
* that the doubled radial lines on the cross section are artifacts of the
* visualization):
*
* @image html hyper_shell_12_cut.png
* @image html hyper_shell_96_cut.png
*
* @note This function is declared to exist for triangulations of all space
* dimensions, but throws an error if called in 1d.
*
* @note The triangulation needs to be void upon calling this function.
*/
template <int dim>
void hyper_shell (Triangulation<dim> &tria,
const Point<dim> ¢er,
const double inner_radius,
const double outer_radius,
const unsigned int n_cells = 0,
bool colorize = false);
/**
* Produce a half hyper-shell, i.e. the space between two circles in two
* space dimensions and the region between two spheres in 3d, with given
* inner and outer radius and a given number of elements for this initial
* triangulation. However, opposed to the previous function, it does not
* produce a whole shell, but only one half of it, namely that part for
* which the first component is restricted to non-negative values. The
* purpose of this class is to enable computations for solutions which have
* rotational symmetry, in which case the half shell in 2d represents a
* shell in 3d.
*
* If the number of initial cells is zero (as is the default), then it is
* computed adaptively such that the resulting elements have the least
* aspect ratio.
*
* If colorize is set to true, the inner, outer, left, and right boundary
* get indicator 0, 1, 2, and 3, respectively. Otherwise all indicators are
* set to 0.
*
* @note The triangulation needs to be void upon calling this function.
*/
template <int dim>
void half_hyper_shell (Triangulation<dim> &tria,
const Point<dim> ¢er,
const double inner_radius,
const double outer_radius,
const unsigned int n_cells = 0,
const bool colorize = false);
/**
* Produce a domain that is the intersection between a hyper-shell with
* given inner and outer radius, i.e. the space between two circles in two
* space dimensions and the region between two spheres in 3d, and the
* positive quadrant (in 2d) or octant (in 3d). In 2d, this is indeed a
* quarter of the full annulus, while the function is a misnomer in 3d
* because there the domain is not a quarter but one eighth of the full
* shell.
*
* If the number of initial cells is zero (as is the default), then it is
* computed adaptively such that the resulting elements have the least
* aspect ratio in 2d.
*
* If colorize is set to true, the inner, outer, left, and right boundary
* get indicator 0, 1, 2, and 3 in 2d, respectively. Otherwise all
* indicators are set to 0. In 3d indicator 2 is at the face x=0, 3 at y=0,
* 4 at z=0.
*
* @note The triangulation needs to be void upon calling this function.
*/
template <int dim>
void quarter_hyper_shell (Triangulation<dim> &tria,
const Point<dim> ¢er,
const double inner_radius,
const double outer_radius,
const unsigned int n_cells = 0,
const bool colorize = false);
/**
* Produce a domain that is the space between two cylinders in 3d, with
* given length, inner and outer radius and a given number of elements for
* this initial triangulation. If @p n_radial_cells is zero (as is the
* default), then it is computed adaptively such that the resulting elements
* have the least aspect ratio. The same holds for @p n_axial_cells.
*
* @note Although this function is declared as a template, it does not make
* sense in 1D and 2D.
*
* @note The triangulation needs to be void upon calling this function.
*/
template <int dim>
void cylinder_shell (Triangulation<dim> &tria,
const double length,
const double inner_radius,
const double outer_radius,
const unsigned int n_radial_cells = 0,
const unsigned int n_axial_cells = 0);
/**
* Produce the surface meshing of the torus. The axis of the torus is the
* $y$-axis while the plane of the torus is the $x$-$z$ plane. The boundary
* of this object can be described by the TorusBoundary class.
*
* @param tria The triangulation to be filled.
*
* @param R The radius of the circle, which forms the middle line of the
* torus containing the loop of cells. Must be greater than @p r.
*
* @param r The inner radius of the
* torus.
*/
void torus (Triangulation<2,3> &tria,
const double R,
const double r);
/**
* This class produces a square on the <i>xy</i>-plane with a circular hole
* in the middle. Square and circle are centered at the origin. In 3d, this
* geometry is extruded in $z$ direction to the interval $[0,L]$.
*
* @image html cubes_hole.png
*
* It is implemented in 2d and 3d, and takes the following arguments:
*
* @arg @p inner_radius: radius of the
* internal hole
* @arg @p outer_radius: half of the edge length of the square
* @arg @p L: extension in @p z-direction (only used in 3d)
* @arg @p repetitions: number of subdivisions
* along the @p z-direction
* @arg @p colorize: whether to assign different
* boundary indicators to different faces.
* The colors are given in lexicographic
* ordering for the flat faces (0 to 3 in 2d,
* 0 to 5 in 3d) plus the curved hole
* (4 in 2d, and 6 in 3d).
* If @p colorize is set to false, then flat faces
* get the number 0 and the hole gets number 1.
*/
template<int dim>
void hyper_cube_with_cylindrical_hole (
Triangulation<dim> &triangulation,
const double inner_radius = .25,
const double outer_radius = .5,
const double L = .5,
const unsigned int repetition = 1,
const bool colorize = false);
/**
* Produce a ring of cells in 3D that is cut open, twisted and glued
* together again. This results in a kind of moebius-loop.
*
* @param tria The triangulation to be worked on.
* @param n_cells The number of cells in the loop. Must be greater than 4.
* @param n_rotations The number of rotations (Pi/2 each) to be performed before glueing the loop together.
* @param R The radius of the circle, which forms the middle line of the torus containing the loop of cells. Must be greater than @p r.
* @param r The radius of the cylinder bend together as loop.
*/
void moebius (Triangulation<3,3> &tria,
const unsigned int n_cells,
const unsigned int n_rotations,
const double R,
const double r);
/**
* Given the two triangulations specified as the first two arguments, create
* the triangulation that contains the cells of both triangulation and store
* it in the third parameter. Previous content of @p result will be deleted.
*
* This function is most often used to compose meshes for more complicated
* geometries if the geometry can be composed of simpler parts for which
* functions exist to generate coarse meshes. For example, the channel mesh
* used in step-35 could in principle be created using a mesh created by the
* GridGenerator::hyper_cube_with_cylindrical_hole function and several
* rectangles, and merging them using the current function. The rectangles
* will have to be translated to the right for this, a task that can be done
* using the GridTools::shift function (other tools to transform individual
* mesh building blocks are GridTools::transform, GridTools::rotate, and
* GridTools::scale).
*
* @note The two input triangulations must be coarse meshes that have no
* refined cells.
*
* @note The function copies the material ids of the cells of the two input
* triangulations into the output triangulation but it currently makes no
* attempt to do the same for boundary ids. In other words, if the two
* coarse meshes have anything but the default boundary indicators, then you
* will currently have to set boundary indicators again by hand in the
* output triangulation.
*
* @note For a related operation on refined meshes when both meshes are
* derived from the same coarse mesh, see
* GridTools::create_union_triangulation .
*/
template <int dim, int spacedim>
void
merge_triangulations (const Triangulation<dim, spacedim> &triangulation_1,
const Triangulation<dim, spacedim> &triangulation_2,
Triangulation<dim, spacedim> &result);
/**
* Take a 2d Triangulation that is being extruded in z direction
* by the total height of @p height using @p n_slices slices (minimum is 2).
* The boundary indicators of the faces of @p input are going to be assigned
* to the corresponding side walls in z direction. The bottom and top
* get the next two free boundary indicators.
*/
void
extrude_triangulation (const Triangulation<2, 2> &input,
const unsigned int n_slices,
const double height,
Triangulation<3,3> &result);
/**
* This function transformes the @p Triangulation @p tria smoothly to a
* domain that is described by the boundary points in the map @p
* new_points. This map maps the point indices to the boundary points in the
* transformed domain.
*
* Note, that the @p Triangulation is changed in-place, therefore you don't
* need to keep two triangulations, but the given triangulation is changed
* (overwritten).
*
* In 1d, this function is not currently implemented.
*
* @deprecated This function has been moved to GridTools::laplace_transform
*/
template <int dim>
void laplace_transformation (Triangulation<dim> &tria,
const std::map<unsigned int,Point<dim> > &new_points) DEAL_II_DEPRECATED;
/**
* Exception
*/
DeclException0 (ExcInvalidRadii);
/**
* Exception
*/
DeclException1 (ExcInvalidRepetitions,
int,
<< "The number of repetitions " << arg1
<< " must be >=1.");
/**
* Exception
*/
DeclException1 (ExcInvalidRepetitionsDimension,
int,
<< "The vector of repetitions must have "
<< arg1 <<" elements.");
}
DEAL_II_NAMESPACE_CLOSE
#endif
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