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Commit a9ea8f7d authored by Pietro Incardona's avatar Pietro Incardona
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Improving the documentation of numeric

parent 90e8aaa8
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Showing with 667 additions and 282 deletions
src/FiniteDifference/Average.hpp
View file @ a9ea8f7d
......@@ -42,18 +42,28 @@ class Avg
/*! \brief Calculate the position where the derivative is calculated
*
* In case on non staggered case this function just return pos, in case of staggered,
* it calculate where the operator is calculated on a staggered grid
* In case of non staggered case this function just return a null grid_key, in case of staggered,
* it calculate how the operator shift the calculation in the cell
*
* \param position where we are calculating the derivative
* \param gs Grid info
* \param s_pos staggered position of the properties
*
*/
inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos, const grid_sm<Sys_eqs::dims,void> & gs)
inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos, const grid_sm<Sys_eqs::dims,void> & gs, const openfpm::vector<comb<Sys_eqs::dims>> & s_pos = openfpm::vector<comb<Sys_eqs::dims>>())
{
std::cerr << "Error " << __FILE__ << ":" << __LINE__ << " only CENTRAL, FORWARD, BACKWARD derivative are defined";
}
};
/*! \brief Average on direction i
/*! \brief Central average scheme on direction i
*
* \verbatim
*
* +0.5 +0.5
* *---+---*
*
* \endverbatim
*
*/
template<unsigned int d, typename arg, typename Sys_eqs>
......@@ -61,8 +71,20 @@ class Avg<d,arg,Sys_eqs,CENTRAL>
{
public:
/*! \brief fill the row
/*! \brief Calculate which colums of the Matrix are non zero
*
* stub_or_real it is just for change the argument type when testing, in normal
* conditions it is a distributed map
*
* \param g_map It is the map explained in FDScheme
* \param k_map position where the average is calculated
* \param gs Grid info
* \param cols non-zero colums calculated by the function
* \param coeff coefficent (constant in front of the derivative)
*
* ### Example
*
* \snippet FDScheme_unit_tests.hpp Usage of stencil derivative
*
*/
inline static void value(const typename stub_or_real<Sys_eqs,Sys_eqs::dims,typename Sys_eqs::stype,typename Sys_eqs::b_grid::decomposition>::type & g_map, grid_dist_key_dx<Sys_eqs::dims> & kmap , const grid_sm<Sys_eqs::dims,void> & gs, typename Sys_eqs::stype (& spacing )[Sys_eqs::dims] , std::unordered_map<long int,typename Sys_eqs::stype > & cols, typename Sys_eqs::stype coeff)
......@@ -87,43 +109,44 @@ class Avg<d,arg,Sys_eqs,CENTRAL>
}
/*! \brief Calculate the position where the derivative is calculated
/*! \brief Calculate the position where the average is calculated
*
* In case on non staggered case this function just return pos, in case of staggered,
* it calculate where the operator is calculated on a staggered grid
* It follow the same concept of central derivative
*
* \param pos from the position
* \param fld Field we are deriving, if not provided the function just return pos
* \param s_pos position of the properties in the staggered grid
* \param position where we are calculating the derivative
* \param gs Grid info
* \param s_pos staggered position of the properties
*
*/
inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos, long int fld = -1, const openfpm::vector<comb<Sys_eqs::dims>> & s_pos = openfpm::vector<comb<Sys_eqs::dims>>())
inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos, const grid_sm<Sys_eqs::dims,void> & gs, const comb<Sys_eqs::dims> (& s_pos)[Sys_eqs::nvar])
{
auto arg_pos = arg::position(pos,gs,s_pos);
if (is_grid_staggered<Sys_eqs>::value())
{
if (fld == -1)
return pos;
if (s_pos[fld][d] == 1)
if (arg_pos.get(d) == -1)
{
grid_key_dx<Sys_eqs::dims> ret = pos;
ret.set_d(d,0);
return pos;
arg_pos.set_d(d,0);
return arg_pos;
}
else
{
grid_key_dx<Sys_eqs::dims> ret = pos;
ret.set_d(d,1);
return pos;
arg_pos.set_d(d,-1);
return arg_pos;
}
}
return pos;
return arg_pos;
}
};
/*! \brief Average FORWARD on direction i
/*! \brief FORWARD average on direction i
*
* \verbatim
*
* +0.5 0.5
* +------*
*
* \endverbatim
*
*/
template<unsigned int d, typename arg, typename Sys_eqs>
......@@ -131,8 +154,20 @@ class Avg<d,arg,Sys_eqs,FORWARD>
{
public:
/*! \brief fill the row
/*! \brief Calculate which colums of the Matrix are non zero
*
* stub_or_real it is just for change the argument type when testing, in normal
* conditions it is a distributed map
*
* \param g_map It is the map explained in FDScheme
* \param k_map position where the average is calculated
* \param gs Grid info
* \param cols non-zero colums calculated by the function
* \param coeff coefficent (constant in front of the derivative)
*
* ### Example
*
* \snippet FDScheme_unit_tests.hpp Usage of stencil derivative
*
*/
inline static void value(const typename stub_or_real<Sys_eqs,Sys_eqs::dims,typename Sys_eqs::stype,typename Sys_eqs::b_grid::decomposition>::type & g_map, grid_dist_key_dx<Sys_eqs::dims> & kmap , const grid_sm<Sys_eqs::dims,void> & gs, typename Sys_eqs::stype (& spacing )[Sys_eqs::dims] , std::unordered_map<long int,typename Sys_eqs::stype > & cols, typename Sys_eqs::stype coeff)
......@@ -148,24 +183,30 @@ class Avg<d,arg,Sys_eqs,FORWARD>
}
/*! \brief Calculate the position where the derivative is calculated
/*! \brief Calculate the position in the cell where the average is calculated
*
* In case on non staggered case this function just return pos, in case of staggered,
* it calculate where the operator is calculated on a staggered grid
* In case of non staggered case this function just return a null grid_key, in case of staggered,
* the FORWARD scheme return the position of the staggered property
*
* \param pos from the position
* \param fld Field we are deriving, if not provided the function just return pos
* \param s_pos position of the properties in the staggered grid
* \param position where we are calculating the derivative
* \param gs Grid info
* \param s_pos staggered position of the properties
*
*/
inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos, long int fld = -1, const openfpm::vector<comb<Sys_eqs::dims>> & s_pos = openfpm::vector<comb<Sys_eqs::dims>>())
inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos, const grid_sm<Sys_eqs::dims,void> & gs, const comb<Sys_eqs::dims> (& s_pos)[Sys_eqs::nvar])
{
return pos;
return arg::position(pos,gs,s_pos);
}
};
/*! \brief Average BACKWARD on direction i
/*! \brief First order BACKWARD derivative on direction i
*
* \verbatim
*
* +0.5 0.5
* *------+
*
* \endverbatim
*
*/
template<unsigned int d, typename arg, typename Sys_eqs>
......@@ -173,8 +214,20 @@ class Avg<d,arg,Sys_eqs,BACKWARD>
{
public:
/*! \brief fill the row
/*! \brief Calculate which colums of the Matrix are non zero
*
* stub_or_real it is just for change the argument type when testing, in normal
* conditions it is a distributed map
*
* \param g_map It is the map explained in FDScheme
* \param k_map position where the average is calculated
* \param gs Grid info
* \param cols non-zero colums calculated by the function
* \param coeff coefficent (constant in front of the derivative)
*
* ### Example
*
* \snippet FDScheme_unit_tests.hpp Usage of stencil derivative
*
*/
inline static void value(const typename stub_or_real<Sys_eqs,Sys_eqs::dims,typename Sys_eqs::stype,typename Sys_eqs::b_grid::decomposition>::type & g_map, grid_dist_key_dx<Sys_eqs::dims> & kmap , const grid_sm<Sys_eqs::dims,void> & gs, typename Sys_eqs::stype (& spacing )[Sys_eqs::dims], std::unordered_map<long int,typename Sys_eqs::stype > & cols, typename Sys_eqs::stype coeff)
......@@ -189,19 +242,19 @@ class Avg<d,arg,Sys_eqs,BACKWARD>
}
/*! \brief Calculate the position where the derivative is calculated
/*! \brief Calculate the position in the cell where the average is calculated
*
* In case on non staggered case this function just return pos, in case of staggered,
* it calculate where the operator is calculated on a staggered grid
* In case of non staggered case this function just return a null grid_key, in case of staggered,
* the BACKWARD scheme return the position of the staggered property
*
* \param pos from the position
* \param fld Field we are deriving, if not provided the function just return pos
* \param s_pos position of the properties in the staggered grid
* \param position where we are calculating the derivative
* \param gs Grid info
* \param s_pos staggered position of the properties
*
*/
inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos, long int fld = -1, const openfpm::vector<comb<Sys_eqs::dims>> & s_pos = openfpm::vector<comb<Sys_eqs::dims>>())
inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos, const grid_sm<Sys_eqs::dims,void> & gs, const comb<Sys_eqs::dims> (& s_pos)[Sys_eqs::nvar])
{
return pos;
return arg::position(pos,gs,s_pos);
}
};
......
src/FiniteDifference/Derivative.hpp
View file @ a9ea8f7d
......@@ -19,6 +19,7 @@
#include "FiniteDifference/util/common.hpp"
#include "util/util_num.hpp"
/*! \brief Derivative second order on h (spacing)
*
* \tparam d on which dimension derive
......@@ -29,9 +30,16 @@
template<unsigned int d, typename Field, typename Sys_eqs, unsigned int impl=CENTRAL>
class D
{
/*! \brief Create the row of the Matrix
/*! \brief Calculate which colums of the Matrix are non zero
*
* \param pos position where the derivative is calculated
* \param gs Grid info
* \param cols non-zero colums calculated by the function
* \param coeff coefficent (constant in front of the derivative)
*
* \tparam ord
* ### Example
*
* \snippet FDScheme_unit_tests.hpp Usage of stencil derivative
*
*/
inline static void value(const grid_key_dx<Sys_eqs::dims> & pos, const grid_sm<Sys_eqs::dims,void> & gs, std::unordered_map<long int,typename Sys_eqs::stype > & cols, typename Sys_eqs::stype coeff)
......@@ -41,18 +49,28 @@ class D
/*! \brief Calculate the position where the derivative is calculated
*
* In case on non staggered case this function just return pos, in case of staggered,
* it calculate where the operator is calculated on a staggered grid
* In case of non staggered case this function just return a null grid_key, in case of staggered,
* it calculate how the operator shift the calculation in the cell
*
* \param position where we are calculating the derivative
* \param gs Grid info
* \param s_pos staggered position of the properties
*
*/
inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos, const grid_sm<Sys_eqs::dims,void> & gs)
inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos, const grid_sm<Sys_eqs::dims,void> & gs, const comb<Sys_eqs::dims> (& s_pos)[Sys_eqs::nvar])
{
std::cerr << "Error " << __FILE__ << ":" << __LINE__ << " only CENTRAL, FORWARD, BACKWARD derivative are defined";
}
};
/*! \brief Derivative on direction i
/*! \brief Second order central Derivative scheme on direction i
*
* \verbatim
*
* -1 +1
* *---+---*
*
* \endverbatim
*
*/
template<unsigned int d, typename arg, typename Sys_eqs>
......@@ -60,8 +78,16 @@ class D<d,arg,Sys_eqs,CENTRAL>
{
public:
/*! \brief fill the row
/*! \brief Calculate which colums of the Matrix are non zero
*
* \param pos position where the derivative is calculated
* \param gs Grid info
* \param cols non-zero colums calculated by the function
* \param coeff coefficent (constant in front of the derivative)
*
* ### Example
*
* \snippet FDScheme_unit_tests.hpp Usage of stencil derivative
*
*/
inline static void value(const typename stub_or_real<Sys_eqs,Sys_eqs::dims,typename Sys_eqs::stype,typename Sys_eqs::b_grid::decomposition>::type & g_map, grid_dist_key_dx<Sys_eqs::dims> & kmap , const grid_sm<Sys_eqs::dims,void> & gs, typename Sys_eqs::stype (& spacing )[Sys_eqs::dims] , std::unordered_map<long int,typename Sys_eqs::stype > & cols, typename Sys_eqs::stype coeff)
......@@ -88,42 +114,78 @@ class D<d,arg,Sys_eqs,CENTRAL>
/*! \brief Calculate the position where the derivative is calculated
*
* In case on non staggered case this function just return pos, in case of staggered,
* it calculate where the operator is calculated on a staggered grid
* In case on non staggered case this function just return a null grid_key, in case of staggered,
* it calculate how the operator shift in the cell
*
\verbatim
+--$--+
| |
# * #
| |
0--$--+
# = velocity(y)
$ = velocity(x)
* = pressure
\endverbatim
*
* Consider this 2D staggered cell and a second order central derivative scheme, this lead to
*
* \param pos from the position
* \param fld Field we are deriving, if not provided the function just return pos
* \param s_pos position of the properties in the staggered grid
* \f$ \frac{\partial v_y}{\partial x} \f$ is calculated on position (*), so the function return the grid_key {0,0}
*
* \f$ \frac{\partial v_y}{\partial y} \f$ is calculated on position (0), so the function return the grid_key {-1,-1}
*
* \f$ \frac{\partial v_x}{\partial x} \f$ is calculated on position (0), so the function return the grid_key {-1,-1}
*
* \f$ \frac{\partial v_x}{\partial y} \f$ is calculated on position (*), so the function return the grid_key {0,0}
*
* \param position where we are calculating the derivative
* \param gs Grid info
* \param s_pos staggered position of the properties
*
*/
inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos, long int fld = -1, const openfpm::vector<comb<Sys_eqs::dims>> & s_pos = openfpm::vector<comb<Sys_eqs::dims>>())
inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos, const grid_sm<Sys_eqs::dims,void> & gs, const comb<Sys_eqs::dims> (& s_pos)[Sys_eqs::nvar])
{
auto arg_pos = arg::position(pos,gs,s_pos);
if (is_grid_staggered<Sys_eqs>::value())
{
if (fld == -1)
return pos;
if (s_pos[fld][d] == 1)
if (arg_pos.get(d) == -1)
{
grid_key_dx<Sys_eqs::dims> ret = pos;
ret.set_d(d,0);
return pos;
arg_pos.set_d(d,0);
return arg_pos;
}
else
{
grid_key_dx<Sys_eqs::dims> ret = pos;
ret.set_d(d,1);
return pos;
arg_pos.set_d(d,-1);
return arg_pos;
}
}
return pos;
return arg_pos;
}
};
/*! \brief Derivative on direction i
/*! \brief Second order one sided Derivative scheme on direction i
*
* \verbatim
*
* -1.5 2.0 -0.5
* +------*------*
*
* or
*
* -0.5 2.0 -1.5
* *------*------+
*
* in the bulk
*
* -1 +1
* *---+---*
*
* \endverbatim
*
*/
template<unsigned int d, typename arg, typename Sys_eqs>
......@@ -131,15 +193,23 @@ class D<d,arg,Sys_eqs,CENTRAL_B_ONE_SIDE>
{
public:
/*! \brief fill the row
/*! \brief Calculate which colums of the Matrix are non zero
*
* \param pos position where the derivative is calculated
* \param gs Grid info
* \param cols non-zero colums calculated by the function
* \param coeff coefficent (constant in front of the derivative)
*
* ### Example
*
* \snippet FDScheme_unit_tests.hpp Usage of stencil derivative
*
*/
static void value(const typename stub_or_real<Sys_eqs,Sys_eqs::dims,typename Sys_eqs::stype,typename Sys_eqs::b_grid::decomposition>::type & g_map, grid_dist_key_dx<Sys_eqs::dims> & kmap , const grid_sm<Sys_eqs::dims,void> & gs, typename Sys_eqs::stype (& spacing )[Sys_eqs::dims] , std::unordered_map<long int,typename Sys_eqs::stype > & cols, typename Sys_eqs::stype coeff)
{
#ifdef SE_CLASS1
if (Sys_eqs::boundary[d] == PERIODIC)
std::cerr << __FILE__ << ":" << __LINE__ << " error, it make no sense use one sided derivation with periodic boundary\n";
std::cerr << __FILE__ << ":" << __LINE__ << " error, it make no sense use one sided derivation with periodic boundary, please use CENTRAL\n";
#endif
grid_key_dx<Sys_eqs::dims> pos = g_map.getGKey(kmap);
......@@ -188,47 +258,64 @@ public:
/*! \brief Calculate the position where the derivative is calculated
*
* In case on non staggered case this function just return pos, in case of staggered,
* it calculate where the operator is calculated on a staggered grid
* In case on non staggered case this function just return a null grid_key, in case of staggered,
* it calculate how the operator shift in the cell
*
*/
inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos, long int fld = 0, const openfpm::vector<comb<Sys_eqs::dims>> & s_pos = openfpm::vector<comb<Sys_eqs::dims>>())
{
if (is_grid_staggered<Sys_eqs>::value())
{
if (fld == -1)
return pos;
\verbatim
if (s_pos[fld][d] == 1)
{
grid_key_dx<Sys_eqs::dims> ret = pos;
ret.set_d(d,0);
return pos;
}
else
{
grid_key_dx<Sys_eqs::dims> ret = pos;
ret.set_d(d,1);
return pos;
}
}
+--$--+
| |
# * #
| |
0--$--+
return pos;
# = velocity(y)
$ = velocity(x)
* = pressure
\endverbatim
*
* In the one side stencil the cell position depend if you are or not at the boundary.
* outside the boundary is simply the central scheme, at the boundary it is simply the
* staggered position of the property
*
* \param position where we are calculating the derivative
* \param gs Grid info
* \param s_pos staggered position of the properties
*
*/
inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos, const grid_sm<Sys_eqs::dims,void> & gs, const comb<Sys_eqs::dims> (& s_pos)[Sys_eqs::nvar])
{
return arg::position(pos,gs,s_pos);
}
};
/*! \brief Derivative FORWARD on direction i
/*! \brief First order FORWARD derivative on direction i
*
* \verbatim
*
* -1.0 1.0
* +------*
*
* \endverbatim
*
*g
*/
template<unsigned int d, typename arg, typename Sys_eqs>
class D<d,arg,Sys_eqs,FORWARD>
{
public:
/*! \brief fill the row
/*! \brief Calculate which colums of the Matrix are non zero
*
* \param pos position where the derivative is calculated
* \param gs Grid info
* \param cols non-zero colums calculated by the function
* \param coeff coefficent (constant in front of the derivative)
*
* ### Example
*
* \snippet FDScheme_unit_tests.hpp Usage of stencil derivative
*
*/
inline static void value(const typename stub_or_real<Sys_eqs,Sys_eqs::dims,typename Sys_eqs::stype,typename Sys_eqs::b_grid::decomposition>::type & g_map, grid_dist_key_dx<Sys_eqs::dims> & kmap , const grid_sm<Sys_eqs::dims,void> & gs, typename Sys_eqs::stype (& spacing )[Sys_eqs::dims] ,std::unordered_map<long int,typename Sys_eqs::stype > & cols, typename Sys_eqs::stype coeff)
......@@ -246,31 +333,45 @@ class D<d,arg,Sys_eqs,FORWARD>
/*! \brief Calculate the position where the derivative is calculated
*
* In case on non staggered case this function just return pos, in case of staggered,
* it calculate where the operator is calculated on a staggered grid
* In case of non staggered case this function just return a null grid_key, in case of staggered,
* the FORWARD scheme return the position of the staggered property
*
* \param pos from the position
* \param fld Field we are deriving, if not provided the function just return pos
* \param s_pos position of the properties in the staggered grid
* \param position where we are calculating the derivative
* \param gs Grid info
* \param s_pos staggered position of the properties
*
*/
inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos, long int fld = -1, const openfpm::vector<comb<Sys_eqs::dims>> & s_pos = openfpm::vector<comb<Sys_eqs::dims>>())
inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos, const grid_sm<Sys_eqs::dims,void> & gs, const comb<Sys_eqs::dims> (& s_pos)[Sys_eqs::nvar])
{
return pos;
return arg::position(pos,gs,s_pos);
}
};
/*! \brief Derivative BACKWARD on direction i
/*! \brief First order BACKWARD derivative on direction i
*
* \verbatim
*
* -1.0 1.0
* *------+
*
* \endverbatim
*
*g
*/
template<unsigned int d, typename arg, typename Sys_eqs>
class D<d,arg,Sys_eqs,BACKWARD>
{
public:
/*! \brief fill the row
/*! \brief Calculate which colums of the Matrix are non zero
*
* \param pos position where the derivative is calculated
* \param gs Grid info
* \param cols non-zero colums calculated by the function
* \param coeff coefficent (constant in front of the derivative)
*
* ### Example
*
* \snippet FDScheme_unit_tests.hpp Usage of stencil derivative
*
*/
inline static void value(const typename stub_or_real<Sys_eqs,Sys_eqs::dims,typename Sys_eqs::stype,typename Sys_eqs::b_grid::decomposition>::type & g_map, grid_dist_key_dx<Sys_eqs::dims> & kmap , const grid_sm<Sys_eqs::dims,void> & gs, typename Sys_eqs::stype (& spacing )[Sys_eqs::dims], std::unordered_map<long int,typename Sys_eqs::stype > & cols , typename Sys_eqs::stype coeff)
......@@ -288,17 +389,17 @@ class D<d,arg,Sys_eqs,BACKWARD>
/*! \brief Calculate the position where the derivative is calculated
*
* In case on non staggered case this function just return pos, in case of staggered,
* it calculate where the operator is calculated on a staggered grid
* In case of non staggered case this function just return a null grid_key, in case of staggered,
* the BACKWARD scheme return the position of the staggered property
*
* \param pos from the position
* \param fld Field we are deriving, if not provided the function just return pos
* \param s_pos position of the properties in the staggered grid
* \param position where we are calculating the derivative
* \param gs Grid info
* \param s_pos staggered position of the properties
*
*/
inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos, long int fld = -1, const openfpm::vector<comb<Sys_eqs::dims>> & s_pos = openfpm::vector<comb<Sys_eqs::dims>>())
inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos, const grid_sm<Sys_eqs::dims,void> & gs, const comb<Sys_eqs::dims> (& s_pos)[Sys_eqs::nvar])
{