Finite Differences. More...

Detailed Description

template<typename Sys_eqs, typename grid_type>
class FD_scheme< Sys_eqs, grid_type >

Finite Differences.

This class is able to discretize on a Matrix any system of equations producing a linear system of type \(Ax=b\). In order to create a consistent Matrix it is required that each processor must contain a contiguous range on grid points without holes. In order to ensure this, each processor produce a contiguous local labeling of its local points. Each processor also add an offset equal to the number of local points of the processors with id smaller than him, to produce a global and non overlapping labeling. An example is shown in the figures down, here we have a grid 8x6 divided across four processors each processor label locally its grid points

 *
+--------------------------+
| 1   2   3   4| 1  2  3  4|
|              |           |
| 5   6   7   8| 5  6  7  8|
|              |           |
| 9  10  11  12| 9 10 11 12|
+--------------------------+
|13  14  15| 13 14 15 16 17|
|          |               |
|16  17  18| 18 19 20 21 22|
|          |               |
|19  20  21| 23 24 25 26 27|
+--------------------------+

 *
 *
 *

To the local relabelling is added an offset to make the local id global and non overlapping

 *
+--------------------------+
| 1   2   3   4|23 24 25 26|
|              |           |
| 5   6   7   8|27 28 29 30|
|              |           |
| 9  10  12  13|31 32 33 34|
+--------------------------+
|14  15  16| 35 36 37 38 39|
|          |               |
|17  18  19| 40 41 42 43 44|
|          |               |
|20  21  22| 45 46 47 48 49|
+--------------------------+
 *
 *
 *

Template Parameters

Sys_eqs Definition of the system of equations

Examples

Solve lid-driven cavity 2D for incompressible fluid (inertia=0 --> Re=0)

In this case the system of equation to solve is

\( \left\{ \begin{array}{c} \eta\nabla v_x + \partial_x P = 0 \quad Eq1 \\ \eta\nabla v_y + \partial_y P = 0 \quad Eq2 \\ \partial_x v_x + \partial_y v_y = 0 \quad Eq3 \end{array} \right. \)

and boundary conditions

\( \left\{ \begin{array}{c} v_x = 0, v_y = 0 \quad x = 0 \quad B1\\ v_x = 0, v_y = 1.0 \quad x = L \quad B2\\ v_x = 0, v_y = 0 \quad y = 0 \quad B3\\ v_x = 0, v_y = 0 \quad y = L \quad B4\\ \end{array} \right. \)

with \(v_x\) and \(v_y\) the velocity in x and y and \(P\) Pressure

In order to solve such system first we define the general properties of the system

Define the equations of the system

Define the domain and impose the equations

3D

A 3D case is given in the examples

Definition at line 127 of file FD_Solver.hpp.

#include <FD_Solver.hpp>

Data Structures
struct	constant_b
	Encapsulation of the b term as constant. More...

struct	function_b
	Encapsulation of the b term as a function. More...

struct	key_and_eq
	Equation id + space position. More...

struct	variable_b
	Encapsulation of the b term as constant. More...

Public Types
typedef grid_dist_id< Sys_eqs::dims, typename Sys_eqs::stype, aggregate< size_t >, typename grid_type::decomposition::extended_type >	g_map_type
	Distributed grid map.

typedef Sys_eqs	Sys_eqs_typ
	Type that specify the properties of the system of equations.

Public Member Functions
void	setStagPos (comb< Sys_eqs::dims >(&sp)[Sys_eqs::nvar])
	set the staggered position for each property

void	computeStag ()
	compute the staggered position for each property

const Padding< Sys_eqs::dims > &	getPadding ()
	Get the specified padding.

const g_map_type &	getMap ()
	Return the map between the grid index position and the position in the distributed vector.

	FD_scheme (const Ghost< Sys_eqs::dims, long int > &stencil, grid_type &b_g, options_solver opt=options_solver::STANDARD)
	Constructor.

	FD_scheme (Padding< Sys_eqs::dims > &pd, const Ghost< Sys_eqs::dims, long int > &stencil, grid_type &b_g, options_solver opt=options_solver::STANDARD)
	Constructor.

template<typename T >
void	impose (const T &op, const grid_key_dx< Sys_eqs::dims > start_k, const grid_key_dx< Sys_eqs::dims > stop_k, typename Sys_eqs::stype num, eq_id id, comb< Sys_eqs::dims > c_where)
	Impose an operator.

template<typename T , unsigned int prp_id>
void	impose (const T &op, const grid_key_dx< Sys_eqs::dims > start_k, const grid_key_dx< Sys_eqs::dims > stop_k, prop_id< prp_id > num, eq_id id, comb< Sys_eqs::dims > c_where)
	Impose an operator.

template<typename T >
void	impose (const T &op, const grid_key_dx< Sys_eqs::dims > start_k, const grid_key_dx< Sys_eqs::dims > stop_k, const std::function< double(double, double)> &f, eq_id id, comb< Sys_eqs::dims > c_where)
	Impose an operator.

template<typename T >
void	impose (const T &op, const grid_key_dx< Sys_eqs::dims > start_k, const grid_key_dx< Sys_eqs::dims > stop_k, typename Sys_eqs::stype num, eq_id id=eq_id(), bool skip_first=false)
	Impose an operator.

template<typename T , unsigned int prp_id>
void	impose (const T &op, const grid_key_dx< Sys_eqs::dims > start_k, const grid_key_dx< Sys_eqs::dims > stop_k, prop_id< prp_id > num, eq_id id=eq_id(), bool skip_first=false)
	Impose an operator.

template<typename T , typename RHS_type , typename sfinae = typename std::enable_if<!std::is_fundamental<RHS_type>::type::value>::type>
void	impose (const T &op, const grid_key_dx< Sys_eqs::dims > start_k, const grid_key_dx< Sys_eqs::dims > stop_k, const RHS_type &rhs, eq_id id=eq_id(), bool skip_first=false)
	Impose an operator.

template<typename T >
void	impose (const T &op, const grid_key_dx< Sys_eqs::dims > start_k, const grid_key_dx< Sys_eqs::dims > stop_k, const std::function< double(double, double)> &f, eq_id id=eq_id(), bool skip_first=false)
	Impose an operator.

void	new_b ()
	In case we want to impose a new b re-using FD_scheme we have to call This function.

void	new_A ()
	In case we want to impose a new A re-using FD_scheme we have to call This function.

Sys_eqs::SparseMatrix_type &	getA (options_solver opt=options_solver::STANDARD)
	produce the Matrix

Sys_eqs::Vector_type &	getB (options_solver opt=options_solver::STANDARD)
	produce the B vector

template<unsigned int ... pos, typename Vct , typename Grid_dst >
void	copy (Vct &v, const long int(&start)[Sys_eqs_typ::dims], const long int(&stop)[Sys_eqs_typ::dims], Grid_dst &g_dst)
	Copy the vector into the grid.

template<typename ... expr_type>
void	solve (expr_type ... exps)
	Solve an equation.

template<typename SolverType , typename ... expr_type>
void	solve_with_solver (SolverType &solver, expr_type ... exps)
	Solve an equation.

template<typename SolverType , typename ... expr_type>
void	solve_with_constant_nullspace_solver (SolverType &solver, expr_type ... exps)

template<typename SolverType , typename ... expr_type>
void	try_solve_with_solver (SolverType &solver, expr_type ... exps)
	Solve an equation.

template<unsigned int ... pos, typename Vct , typename Grid_dst >
void	copy (Vct &v, Grid_dst &g_dst)
	Copy the vector into the grid.

Data Fields
Sys_eqs::SparseMatrix_type	A
	type of the sparse matrix

Private Types
typedef Sys_eqs::SparseMatrix_type::triplet_type	triplet
	Sparse matrix triplet type.

Private Member Functions
key_and_eq	from_row_to_key (size_t row)
	From the row Matrix position to the spatial position.

const std::vector< size_t >	padding (const size_t(&sz)[Sys_eqs::dims], Padding< Sys_eqs::dims > &pd)
	calculate the mapping grid size with padding

void	consistency ()
	Check if the Matrix is consistent.

template<typename Vct , typename Grid_dst , unsigned int ... pos>
void	copy_staggered (Vct &v, Grid_dst &g_dst)
	Copy a given solution vector in a staggered grid.

template<typename Vct , typename Grid_dst , unsigned int ... pos>
void	copy_normal (Vct &v, Grid_dst &g_dst)
	Copy a given solution vector in a normal grid.

template<typename bop , typename iterator >
void	impose_dit_b (bop num, long int id, const iterator &it_d)
	Impose an operator.

template<typename T , typename col , typename trp , typename iterator , typename cmb , typename Key >
void	impose_git_it (const T &op, col &cols, trp &trpl, long int &id, const iterator &it_d, cmb &c_where, Key &key, grid_key_dx< Sys_eqs::dims > &shift)

template<typename T , typename bop , typename iterator >
void	impose_git (const T &op, bop num, long int id, const iterator &it_d, comb< Sys_eqs::dims > c_where)
	Impose an operator.

void	construct_gmap ()
	Construct the gmap structure.

void	Initialize (const Box< Sys_eqs::dims, typename Sys_eqs::stype > &domain)

template<typename solType , typename expr_type >
void	copy_impl (solType &x, expr_type exp, unsigned int comp)
	Solve an equation.

template<typename solType , typename exp1 , typename ... othersExp>
void	copy_nested (solType &x, unsigned int &comp, exp1 exp, othersExp ... exps)

template<typename solType , typename exp1 >
void	copy_nested (solType &x, unsigned int &comp, exp1 exp)

Private Attributes
grid_type &	grid
	our base grid

Padding< Sys_eqs::dims >	pd
	Padding.

Sys_eqs::Vector_type	b
	Vector b.

const grid_sm< Sys_eqs::dims, void > &	gs
	Domain Grid informations.

Sys_eqs::stype	spacing [Sys_eqs::dims]
	Get the grid spacing.

g_map_type	g_map
	mapping grid

size_t	row
	row of the matrix

size_t	row_b
	row on b

options_solver	opt
	solver options

size_t	tot
	Total number of points.

openfpm::vector< size_t >	pnt
	Grid points that has each processor.

comb< Sys_eqs::dims >	s_pos [Sys_eqs::nvar]
	Staggered position for each property.

size_t	s_pnt

Member Typedef Documentation

◆ g_map_type

template<typename Sys_eqs , typename grid_type >

typedef grid_dist_id<Sys_eqs::dims,typename Sys_eqs::stype,aggregate<size_t>,typename grid_type::decomposition::extended_type> FD_scheme< Sys_eqs, grid_type >::g_map_type

Distributed grid map.

Definition at line 132 of file FD_Solver.hpp.

◆ Sys_eqs_typ

template<typename Sys_eqs , typename grid_type >

typedef Sys_eqs FD_scheme< Sys_eqs, grid_type >::Sys_eqs_typ

Type that specify the properties of the system of equations.

Definition at line 135 of file FD_Solver.hpp.

◆ triplet

template<typename Sys_eqs , typename grid_type >

typedef Sys_eqs::SparseMatrix_type::triplet_type FD_scheme< Sys_eqs, grid_type >::triplet

private

Sparse matrix triplet type.

Definition at line 254 of file FD_Solver.hpp.

Constructor & Destructor Documentation

◆ FD_scheme() [1/2]

template<typename Sys_eqs , typename grid_type >

FD_scheme< Sys_eqs, grid_type >::FD_scheme	(	const Ghost< Sys_eqs::dims, long int > &	stencil,
		grid_type &	b_g,
		options_solver	opt = `options_solver::STANDARD`
	)

inline

Constructor.

The periodicity is given by the grid b_g

Parameters

stencil	maximum extension of the stencil on each directions
domain	the domain
b_g	object grid that will store the solution

Definition at line 867 of file FD_Solver.hpp.

◆ FD_scheme() [2/2]

template<typename Sys_eqs , typename grid_type >

FD_scheme< Sys_eqs, grid_type >::FD_scheme	(	Padding< Sys_eqs::dims > &	pd,
		const Ghost< Sys_eqs::dims, long int > &	stencil,
		grid_type &	b_g,
		options_solver	opt = `options_solver::STANDARD`
	)

inline

Constructor.

The periodicity is given by the grid b_g

Parameters

pd	Padding, how many points out of boundary are present
stencil	maximum extension of the stencil on each directions
domain	the domain
b_g	object grid that will store the solution

Definition at line 885 of file FD_Solver.hpp.

Member Function Documentation

◆ computeStag()

template<typename Sys_eqs , typename grid_type >

void FD_scheme< Sys_eqs, grid_type >::computeStag ( )

inline

compute the staggered position for each property

This is compute from the value_type stored by Sys_eqs::b_grid::value_type the position of the staggered properties

Definition at line 825 of file FD_Solver.hpp.

◆ consistency()

template<typename Sys_eqs , typename grid_type >

void FD_scheme< Sys_eqs, grid_type >::consistency ( )

inlineprivate

Check if the Matrix is consistent.

Definition at line 355 of file FD_Solver.hpp.

◆ construct_gmap()

template<typename Sys_eqs , typename grid_type >

void FD_scheme< Sys_eqs, grid_type >::construct_gmap ( )

inlineprivate

Construct the gmap structure.

Definition at line 680 of file FD_Solver.hpp.

◆ copy() [1/2]

template<typename Sys_eqs , typename grid_type >

template<unsigned int ... pos, typename Vct , typename Grid_dst >

void FD_scheme< Sys_eqs, grid_type >::copy	(	Vct &	v,
		const long int(&)	start[Sys_eqs_typ::dims],
		const long int(&)	stop[Sys_eqs_typ::dims],
		Grid_dst &	g_dst
	)

inline

Copy the vector into the grid.

Copy the solution into the grid

Template Parameters

scheme	Discretization scheme
Grid_dst	type of the target grid
pos	target properties

Parameters

v	Vector that contain the solution of the system
start	point
stop	point
g_dst	Destination grid

Definition at line 1308 of file FD_Solver.hpp.

◆ copy() [2/2]

template<typename Sys_eqs , typename grid_type >

template<unsigned int ... pos, typename Vct , typename Grid_dst >

void FD_scheme< Sys_eqs, grid_type >::copy	(	Vct &	v,
		Grid_dst &	g_dst
	)

inline

Copy the vector into the grid.

Copy the solution into the grid

Template Parameters

scheme	Discretization scheme
Grid_dst	type of the target grid
pos	target properties

Parameters

v	Vector that contain the solution of the system
g_dst	Destination grid

Definition at line 1438 of file FD_Solver.hpp.

◆ copy_impl()

template<typename Sys_eqs , typename grid_type >

template<typename solType , typename expr_type >

void FD_scheme< Sys_eqs, grid_type >::copy_impl	(	solType &	x,
		expr_type	exp,
		unsigned int	comp
	)

inlineprivate

Solve an equation.

Warning: exp must be a scalar type

Parameters

exp	where to store the result

Definition at line 757 of file FD_Solver.hpp.

◆ copy_nested() [1/2]

template<typename Sys_eqs , typename grid_type >

template<typename solType , typename exp1 >

void FD_scheme< Sys_eqs, grid_type >::copy_nested	(	solType &	x,
		unsigned int &	comp,
		exp1	exp
	)

inlineprivate

Definition at line 798 of file FD_Solver.hpp.

◆ copy_nested() [2/2]

template<typename Sys_eqs , typename grid_type >

template<typename solType , typename exp1 , typename ... othersExp>

void FD_scheme< Sys_eqs, grid_type >::copy_nested	(	solType &	x,
		unsigned int &	comp,
		exp1	exp,
		othersExp ...	exps
	)

inlineprivate

Definition at line 788 of file FD_Solver.hpp.

◆ copy_normal()

template<typename Sys_eqs , typename grid_type >

template<typename Vct , typename Grid_dst , unsigned int ... pos>

void FD_scheme< Sys_eqs, grid_type >::copy_normal	(	Vct &	v,
		Grid_dst &	g_dst
	)

inlineprivate

Copy a given solution vector in a normal grid.

Template Parameters

Vct	Vector type
Grid_dst	target grid
pos	set of property

Parameters

v	Vector
g_dst	target normal grid

Definition at line 461 of file FD_Solver.hpp.

◆ copy_staggered()

template<typename Sys_eqs , typename grid_type >

template<typename Vct , typename Grid_dst , unsigned int ... pos>

void FD_scheme< Sys_eqs, grid_type >::copy_staggered	(	Vct &	v,
		Grid_dst &	g_dst
	)

inlineprivate

Copy a given solution vector in a staggered grid.

Template Parameters

Vct	Vector type
Grid_dst	target grid
pos	set of properties

Parameters

v	Vector
g_dst	target staggered grid

Definition at line 411 of file FD_Solver.hpp.

◆ from_row_to_key()

template<typename Sys_eqs , typename grid_type >

key_and_eq FD_scheme< Sys_eqs, grid_type >::from_row_to_key ( size_t row )

inlineprivate

From the row Matrix position to the spatial position.

Parameters

row	Matrix row

Returns: spatial position + equation id

Definition at line 311 of file FD_Solver.hpp.

◆ getA()

template<typename Sys_eqs , typename grid_type >

Sys_eqs::SparseMatrix_type & FD_scheme< Sys_eqs, grid_type >::getA ( options_solver opt = options_solver::STANDARD )

inline

produce the Matrix

Returns: the Sparse matrix produced

Definition at line 1193 of file FD_Solver.hpp.

◆ getB()

template<typename Sys_eqs , typename grid_type >

Sys_eqs::Vector_type & FD_scheme< Sys_eqs, grid_type >::getB ( options_solver opt = options_solver::STANDARD )

inline

produce the B vector

Returns: the vector produced

Definition at line 1275 of file FD_Solver.hpp.

◆ getMap()

template<typename Sys_eqs , typename grid_type >

const g_map_type & FD_scheme< Sys_eqs, grid_type >::getMap ( )

inline

Return the map between the grid index position and the position in the distributed vector.

It is the map explained in the intro of the FD_scheme

Returns: the map

Definition at line 853 of file FD_Solver.hpp.

◆ getPadding()

template<typename Sys_eqs , typename grid_type >

const Padding< Sys_eqs::dims > & FD_scheme< Sys_eqs, grid_type >::getPadding ( )

inline

Get the specified padding.

Returns: the padding specified

Definition at line 841 of file FD_Solver.hpp.

◆ impose() [1/7]

template<typename Sys_eqs , typename grid_type >

template<typename T , typename RHS_type , typename sfinae = typename std::enable_if<!std::is_fundamental<RHS_type>::type::value>::type>

void FD_scheme< Sys_eqs, grid_type >::impose	(	const T &	op,
		const grid_key_dx< Sys_eqs::dims >	start_k,
		const grid_key_dx< Sys_eqs::dims >	stop_k,
		const RHS_type &	rhs,
		eq_id	id = `eq_id()`,
		bool	skip_first = `false`
	)

inline

Impose an operator.

This function impose an operator on a box region to produce the system

Ax = b

Stokes equation, lid driven cavity with one splipping wall

Parameters

op	Operator to impose (A term)
num	right hand side of the term (b term)
id	Equation id in the system that we are imposing
start	starting point of the box
stop	stop point of the box
skip_first	skip the first point

Definition at line 1097 of file FD_Solver.hpp.

◆ impose() [2/7]

template<typename Sys_eqs , typename grid_type >

template<typename T >

void FD_scheme< Sys_eqs, grid_type >::impose	(	const T &	op,
		const grid_key_dx< Sys_eqs::dims >	start_k,
		const grid_key_dx< Sys_eqs::dims >	stop_k,
		const std::function< double(double, double)> &	f,
		eq_id	id,
		comb< Sys_eqs::dims >	c_where
	)

inline

Impose an operator.

This function impose an operator on a box region to produce the system

Ax = b

Parameters

op	Operator to impose (A term)
f	right hand side of the term (b term)
id	Equation id in the system that we are imposing
start	starting point of the box
stop	stop point of the box
skip_first	skip the first point

Definition at line 971 of file FD_Solver.hpp.

◆ impose() [3/7]

template<typename Sys_eqs , typename grid_type >

template<typename T >

void FD_scheme< Sys_eqs, grid_type >::impose	(	const T &	op,
		const grid_key_dx< Sys_eqs::dims >	start_k,
		const grid_key_dx< Sys_eqs::dims >	stop_k,
		const std::function< double(double, double)> &	f,
		eq_id	id = `eq_id()`,
		bool	skip_first = `false`
	)

inline

Impose an operator.

This function impose an operator on a box region to produce the system

Ax = b

Parameters

op	Operator to impose (A term)
f	right hand side of the term (b term)
id	Equation id in the system that we are imposing
start	starting point of the box
stop	stop point of the box
skip_first	skip the first point

Definition at line 1141 of file FD_Solver.hpp.

◆ impose() [4/7]

template<typename Sys_eqs , typename grid_type >

template<typename T , unsigned int prp_id>

void FD_scheme< Sys_eqs, grid_type >::impose	(	const T &	op,
		const grid_key_dx< Sys_eqs::dims >	start_k,
		const grid_key_dx< Sys_eqs::dims >	stop_k,
		prop_id< prp_id >	num,
		eq_id	id,
		comb< Sys_eqs::dims >	c_where
	)

inline

Impose an operator.

This function impose an operator on a box region to produce the system

Ax = b

Stokes equation, lid driven cavity with one splipping wall

Parameters

op	Operator to impose (A term)
num	right hand side of the term (b term)
id	Equation id in the system that we are imposing
start	starting point of the box
stop	stop point of the box
skip_first	skip the first point

Definition at line 942 of file FD_Solver.hpp.

◆ impose() [5/7]

template<typename Sys_eqs , typename grid_type >

template<typename T , unsigned int prp_id>

void FD_scheme< Sys_eqs, grid_type >::impose	(	const T &	op,
		const grid_key_dx< Sys_eqs::dims >	start_k,
		const grid_key_dx< Sys_eqs::dims >	stop_k,
		prop_id< prp_id >	num,
		eq_id	id = `eq_id()`,
		bool	skip_first = `false`
	)

inline

Impose an operator.

This function impose an operator on a box region to produce the system

Ax = b

Stokes equation, lid driven cavity with one splipping wall

Parameters

op	Operator to impose (A term)
num	right hand side of the term (b term)
id	Equation id in the system that we are imposing
start	starting point of the box
stop	stop point of the box
skip_first	skip the first point

Definition at line 1049 of file FD_Solver.hpp.

◆ impose() [6/7]

template<typename Sys_eqs , typename grid_type >

template<typename T >

void FD_scheme< Sys_eqs, grid_type >::impose	(	const T &	op,
		const grid_key_dx< Sys_eqs::dims >	start_k,
		const grid_key_dx< Sys_eqs::dims >	stop_k,
		typename Sys_eqs::stype	num,
		eq_id	id,
		comb< Sys_eqs::dims >	c_where
	)

inline

Impose an operator.

This function impose an operator on a box region to produce the system

Ax = b

Stokes equation, lid driven cavity with one splipping wall

Parameters

op	Operator to impose (A term)
num	right hand side of the term (b term)
id	Equation id in the system that we are imposing
start	starting point of the box
stop	stop point of the box
skip_first	skip the first point

Definition at line 911 of file FD_Solver.hpp.

◆ impose() [7/7]

template<typename Sys_eqs , typename grid_type >

template<typename T >

void FD_scheme< Sys_eqs, grid_type >::impose	(	const T &	op,
		const grid_key_dx< Sys_eqs::dims >	start_k,
		const grid_key_dx< Sys_eqs::dims >	stop_k,
		typename Sys_eqs::stype	num,
		eq_id	id = `eq_id()`,
		bool	skip_first = `false`
	)

inline

Impose an operator.

This function impose an operator on a box region to produce the system

Ax = b

Stokes equation, lid driven cavity with one splipping wall

Parameters

op	Operator to impose (A term)
num	right hand side of the term (b term)
id	Equation id in the system that we are imposing
start	starting point of the box
stop	stop point of the box
skip_first	skip the first point

Definition at line 1003 of file FD_Solver.hpp.

◆ impose_dit_b()

template<typename Sys_eqs , typename grid_type >

template<typename bop , typename iterator >

void FD_scheme< Sys_eqs, grid_type >::impose_dit_b	(	bop	num,
		long int	id,
		const iterator &	it_d
	)

inlineprivate

Impose an operator.

This function the RHS no matrix is imposed. This function is usefull if the Matrix has been constructed and only the right hand side b must be changed

Ax = b

Parameters

num	right hand side of the term (b term)
id	Equation id in the system that we are imposing
it_d	iterator that define where you want to impose

Definition at line 518 of file FD_Solver.hpp.

◆ impose_git()

template<typename Sys_eqs , typename grid_type >

template<typename T , typename bop , typename iterator >

void FD_scheme< Sys_eqs, grid_type >::impose_git	(	const T &	op,
		bop	num,
		long int	id,
		const iterator &	it_d,
		comb< Sys_eqs::dims >	c_where
	)

inlineprivate

Impose an operator.

This function impose an operator on a particular grid region to produce the system

Ax = b

Stokes equation 2D, lid driven cavity with one splipping wall

Parameters

op	Operator to impose (A term)
num	right hand side of the term (b term)
id	Equation id in the system that we are imposing
it_d	iterator that define where you want to impose

Definition at line 598 of file FD_Solver.hpp.

◆ impose_git_it()

template<typename Sys_eqs , typename grid_type >

template<typename T , typename col , typename trp , typename iterator , typename cmb , typename Key >

void FD_scheme< Sys_eqs, grid_type >::impose_git_it	(	const T &	op,
		col &	cols,
		trp &	trpl,
		long int &	id,
		const iterator &	it_d,
		cmb &	c_where,
		Key &	key,
		grid_key_dx< Sys_eqs::dims > &	shift
	)

inlineprivate

Definition at line 544 of file FD_Solver.hpp.

◆ Initialize()

template<typename Sys_eqs , typename grid_type >

void FD_scheme< Sys_eqs, grid_type >::Initialize ( const Box< Sys_eqs::dims, typename Sys_eqs::stype > & domain )

inlineprivate

\initialize the object FD_scheme

Parameters

domain simulation domain

Definition at line 728 of file FD_Solver.hpp.

◆ new_A()

template<typename Sys_eqs , typename grid_type >

void FD_scheme< Sys_eqs, grid_type >::new_A ( )

inline

In case we want to impose a new A re-using FD_scheme we have to call This function.

Definition at line 1181 of file FD_Solver.hpp.

◆ new_b()

template<typename Sys_eqs , typename grid_type >

void FD_scheme< Sys_eqs, grid_type >::new_b ( )

inline

In case we want to impose a new b re-using FD_scheme we have to call This function.

Definition at line 1174 of file FD_Solver.hpp.

◆ padding()

template<typename Sys_eqs , typename grid_type >

const std::vector< size_t > FD_scheme< Sys_eqs, grid_type >::padding	(	const size_t(&)	sz[Sys_eqs::dims],
		Padding< Sys_eqs::dims > &	pd
	)

inlineprivate

calculate the mapping grid size with padding

Parameters

sz	original grid size
pd	padding

Returns: padded grid size

Definition at line 342 of file FD_Solver.hpp.

◆ setStagPos()

template<typename Sys_eqs , typename grid_type >

void FD_scheme< Sys_eqs, grid_type >::setStagPos ( comb< Sys_eqs::dims >(&) sp[Sys_eqs::nvar] )

inline

set the staggered position for each property

Parameters

sp	vector containing the staggered position for each property

Definition at line 812 of file FD_Solver.hpp.

◆ solve()

template<typename Sys_eqs , typename grid_type >

template<typename ... expr_type>

void FD_scheme< Sys_eqs, grid_type >::solve ( expr_type ... exps )

inline

Solve an equation.

Warning: exp must be a scalar type

Parameters

exp	where to store the result

Definition at line 1351 of file FD_Solver.hpp.

◆ solve_with_constant_nullspace_solver()

template<typename Sys_eqs , typename grid_type >

template<typename SolverType , typename ... expr_type>

void FD_scheme< Sys_eqs, grid_type >::solve_with_constant_nullspace_solver	(	SolverType &	solver,
		expr_type ...	exps
	)

inline

Definition at line 1389 of file FD_Solver.hpp.

◆ solve_with_solver()

template<typename Sys_eqs , typename grid_type >

template<typename SolverType , typename ... expr_type>

void FD_scheme< Sys_eqs, grid_type >::solve_with_solver	(	SolverType &	solver,
		expr_type ...	exps
	)

inline

Solve an equation.

Warning: exp must be a scalar type

Parameters

exp	where to store the result

Definition at line 1373 of file FD_Solver.hpp.

◆ try_solve_with_solver()

template<typename Sys_eqs , typename grid_type >

template<typename SolverType , typename ... expr_type>

void FD_scheme< Sys_eqs, grid_type >::try_solve_with_solver	(	SolverType &	solver,
		expr_type ...	exps
	)

inline

Solve an equation.

Warning: exp must be a scalar type

Parameters

exp	where to store the result

Definition at line 1412 of file FD_Solver.hpp.

Field Documentation

◆ A

template<typename Sys_eqs , typename grid_type >

Sys_eqs::SparseMatrix_type FD_scheme< Sys_eqs, grid_type >::A

type of the sparse matrix

Definition at line 1186 of file FD_Solver.hpp.

◆ b

template<typename Sys_eqs , typename grid_type >

Sys_eqs::Vector_type FD_scheme< Sys_eqs, grid_type >::b

private

Vector b.

Definition at line 257 of file FD_Solver.hpp.

◆ g_map

template<typename Sys_eqs , typename grid_type >

g_map_type FD_scheme< Sys_eqs, grid_type >::g_map

private

mapping grid

Definition at line 266 of file FD_Solver.hpp.

◆ grid

template<typename Sys_eqs , typename grid_type >

grid_type& FD_scheme< Sys_eqs, grid_type >::grid

private

our base grid

Definition at line 248 of file FD_Solver.hpp.

◆ gs

template<typename Sys_eqs , typename grid_type >

const grid_sm<Sys_eqs::dims,void>& FD_scheme< Sys_eqs, grid_type >::gs

private

Domain Grid informations.

Definition at line 260 of file FD_Solver.hpp.

◆ opt

template<typename Sys_eqs , typename grid_type >

options_solver FD_scheme< Sys_eqs, grid_type >::opt

private

solver options

Definition at line 275 of file FD_Solver.hpp.

◆ pd

template<typename Sys_eqs , typename grid_type >

Padding<Sys_eqs::dims> FD_scheme< Sys_eqs, grid_type >::pd

private

Padding.

Definition at line 251 of file FD_Solver.hpp.

◆ pnt

template<typename Sys_eqs , typename grid_type >

openfpm::vector<size_t> FD_scheme< Sys_eqs, grid_type >::pnt

private

Grid points that has each processor.

Definition at line 281 of file FD_Solver.hpp.

◆ row

template<typename Sys_eqs , typename grid_type >

size_t FD_scheme< Sys_eqs, grid_type >::row

private

row of the matrix

Definition at line 269 of file FD_Solver.hpp.

◆ row_b

template<typename Sys_eqs , typename grid_type >

size_t FD_scheme< Sys_eqs, grid_type >::row_b

private

row on b

Definition at line 272 of file FD_Solver.hpp.

◆ s_pnt

template<typename Sys_eqs , typename grid_type >

size_t FD_scheme< Sys_eqs, grid_type >::s_pnt

private

Each point in the grid has a global id, to decompose correctly the Matrix each processor contain a contiguos range of global id, example processor 0 can have from 0 to 234 and processor 1 from 235 to 512 no processors can have holes in the sequence, this number indicate where the sequence start for this processor

Definition at line 290 of file FD_Solver.hpp.

◆ s_pos

template<typename Sys_eqs , typename grid_type >

comb<Sys_eqs::dims> FD_scheme< Sys_eqs, grid_type >::s_pos[Sys_eqs::nvar]

private

Staggered position for each property.

Definition at line 284 of file FD_Solver.hpp.

◆ spacing

template<typename Sys_eqs , typename grid_type >

Sys_eqs::stype FD_scheme< Sys_eqs, grid_type >::spacing[Sys_eqs::dims]

private

Get the grid spacing.

Definition at line 263 of file FD_Solver.hpp.

◆ tot

template<typename Sys_eqs , typename grid_type >

size_t FD_scheme< Sys_eqs, grid_type >::tot

private

Total number of points.

Definition at line 278 of file FD_Solver.hpp.

The documentation for this class was generated from the following file:

openfpm_numerics/src/FiniteDifference/FD_Solver.hpp

Detailed Description

Examples

Solve lid-driven cavity 2D for incompressible fluid (inertia=0 --> Re=0)

Define the equations of the system

Define the domain and impose the equations

3D

Data Structures

Public Types

Public Member Functions

Data Fields

Private Types

Private Member Functions

Private Attributes

Member Typedef Documentation

◆ g_map_type

◆ Sys_eqs_typ

◆ triplet

Constructor & Destructor Documentation

◆ FD_scheme() [1/2]

◆ FD_scheme() [2/2]

Member Function Documentation

◆ computeStag()

◆ consistency()

◆ construct_gmap()

◆ copy() [1/2]

Copy the solution into the grid

◆ copy() [2/2]

Copy the solution into the grid

◆ copy_impl()

◆ copy_nested() [1/2]

◆ copy_nested() [2/2]

◆ copy_normal()

◆ copy_staggered()

◆ from_row_to_key()

◆ getA()

◆ getB()

◆ getMap()

◆ getPadding()

◆ impose() [1/7]

Stokes equation, lid driven cavity with one splipping wall

◆ impose() [2/7]

◆ impose() [3/7]

◆ impose() [4/7]

Stokes equation, lid driven cavity with one splipping wall

◆ impose() [5/7]

Stokes equation, lid driven cavity with one splipping wall

◆ impose() [6/7]

Stokes equation, lid driven cavity with one splipping wall

◆ impose() [7/7]

Stokes equation, lid driven cavity with one splipping wall

◆ impose_dit_b()

◆ impose_git()

Stokes equation 2D, lid driven cavity with one splipping wall

◆ impose_git_it()

◆ Initialize()

◆ new_A()

◆ new_b()

◆ padding()

◆ setStagPos()

◆ solve()

◆ solve_with_constant_nullspace_solver()

◆ solve_with_solver()

◆ try_solve_with_solver()

Field Documentation

◆ A

◆ b

◆ g_map

◆ grid

◆ gs

◆ opt

◆ pd

◆ pnt

◆ row

◆ row_b

◆ s_pnt

◆ s_pos

◆ spacing

◆ tot