mod_finite_differences_computer Module Reference

Computer for evaluating Finite Difference Schemes. More...

Functions/Subroutines
double precision function	fd_compute_from_values (scheme, steps, values)
	Compute the finite difference via the scheme by giving the associated field values. More...
double precision function	fd_weno_compute_from_values (scheme, step, steps, values)
	Compute the WENO finite difference via the scheme by giving the associated field values. More...
double precision function	fd_compute_from_scheme (scheme, values)
	Compute the finite difference of the scheme by giving the associated field values. More...
double precision function	fd_compute_from_array (scheme, step_array, array, index)
	Compute the finite difference via the scheme by giving the associated array, the step array (see below), the index where to compute the FD. More...
double precision function	fd_compute_from_field (scheme, x_step_array, y_step_array, z_step_array, field, i, j, k, axis)
	Compute the finite difference via the scheme by giving the associated field, the step arrays for each dimension, the indices (position) and the direction (x,y or z). More...
double precision function	fd_compute_from_field_offset (scheme, x_step_array, y_step_array, z_step_array, field, i, j, k, axis, offset)
	Compute the finite difference via the scheme by giving the associated field, the step arrays for each dimension, the indices (position) and the direction (x,y or z). More...
double precision function	fd_weno_compute_from_array (scheme, step, step_array, array, index)
	Compute the WENO finite difference via the scheme by giving the associated array, the step array (see below), the index where to compute the FD. More...
double precision function	fd_weno_compute_from_field (scheme, step, x_step_array, y_step_array, z_step_array, field, i, j, k, axis)
	Compute the WENO finite difference via the scheme by giving the associated field, the step arrays for each dimension, the indices (position) and the direction (x,y or z). More...

Detailed Description

All the methods defined here are used to effectively compute/evaluate finite differences. They take as argument a scheme that is built through the various schemes of the module (see mod_finite_differences_scheme_first_o1 for example).

Function/Subroutine Documentation

fd_compute_from_array()

double precision function mod_finite_differences_computer::fd_compute_from_array	(	class(t_fd_scheme)	scheme,
		double precision, dimension(:), intent(in)	step_array,
		double precision, dimension(:), intent(in)	array,
		integer, intent(in)	index
	)

Parameters

[in]	scheme	the finite difference scheme
[in]	step_array	the discretization step array where step_array(i) is the step between array(i) and array(i+1)
[in]	array	the array \(\phi(i)\) to which apply the scheme at the given indices.
[in]	index	the index where to compute the FD

Returns

the value of the scheme evaluated with the input values

fd_compute_from_field()

double precision function mod_finite_differences_computer::fd_compute_from_field	(	class(t_fd_scheme)	scheme,
		double precision, dimension(:), intent(in)	x_step_array,
		double precision, dimension(:), intent(in)	y_step_array,
		double precision, dimension(:), intent(in)	z_step_array,
		double precision, dimension(:,:,:), intent(in)	field,
		integer, intent(in)	i,
		integer, intent(in)	j,
		integer, intent(in)	k,
		integer, intent(in)	axis
	)

Parameters

[in]	scheme	the finite difference scheme
[in]	x_step_array	the discretization step array in the x direction
[in]	y_step_array	the discretization step array in the y direction
[in]	z_step_array	the discretization step array in the z direction
[in]	field	the field \(\phi(i,j,k)\) to which apply the scheme at the given indices.
[in]	i,j,k	the indices where to compute the FD
[in]	axis	the axis (direction) \(axis={1,2,3}\) for \({x,y,z}\)

Returns

the value of the scheme evaluated with the input values

Warning

This function is not the most efficient, especialy when used in a i,j,k loop, because it switches for each direction!

fd_compute_from_field_offset()

double precision function mod_finite_differences_computer::fd_compute_from_field_offset	(	class(t_fd_scheme)	scheme,
		double precision, dimension(:), intent(in)	x_step_array,
		double precision, dimension(:), intent(in)	y_step_array,
		double precision, dimension(:), intent(in)	z_step_array,
		double precision, dimension(:,:,:), intent(in)	field,
		integer, intent(in)	i,
		integer, intent(in)	j,
		integer, intent(in)	k,
		integer, intent(in)	axis,
		integer, intent(in)	offset
	)

Parameters

[in]	scheme	the finite difference scheme
[in]	x_step_array	the discretization step array in the x direction
[in]	y_step_array	the discretization step array in the y direction
[in]	z_step_array	the discretization step array in the z direction
[in]	field	the field \(\phi(i,j,k)\) to which apply the scheme at the given indices.
[in]	i,j,k	the indices where to compute the FD
[in]	axis	the axis (direction) \(axis={1,2,3}\) for \({x,y,z}\)
[in]	offset	offset the dx

Returns

the value of the scheme evaluated with the input values

Warning

This function is not the most efficient, especialy when used in a i,j,k loop, because it switches for each direction!

fd_compute_from_scheme()

double precision function mod_finite_differences_computer::fd_compute_from_scheme	(	class(t_fd_scheme)	scheme,
		double precision, dimension(:), intent(in)	values
	)

Parameters

[in]	scheme	the finite difference scheme (previously defined)
[in]	values	the field values to which to apply the scheme. They must be of the same dimension as the scheme

Returns

the value of the scheme evaluated with the input values

Precondition

the scheme has already been init and filled!

fd_compute_from_values()

double precision function mod_finite_differences_computer::fd_compute_from_values	(	class(t_fd_scheme)	scheme,
		double precision, dimension(:), intent(in)	steps,
		double precision, dimension(:), intent(in)	values
	)

Parameters

[in]	scheme	the finite difference scheme
[in]	steps	the discretization steps, with size(steps)==size(values)-1
[in]	values	the field values to which to apply the scheme. They must be of the same dimension as the scheme

Returns

the value of the scheme evaluated with the input values

fd_weno_compute_from_array()

double precision function mod_finite_differences_computer::fd_weno_compute_from_array	(	class(t_fd_weno_scheme)	scheme,
		double precision, intent(in)	step,
		double precision, dimension(:), intent(in)	step_array,
		double precision, dimension(:), intent(in)	array,
		integer, intent(in)	index
	)

Parameters

[in]	scheme	the finite difference scheme
[in]	step	the step where to evaluate the scheme (starting from the reference node)
[in]	step_array	the discretization step array where step_array(i) is the step between array(i) and array(i+1)
[in]	array	the array \(\phi(i)\) to which apply the scheme at the given indices.
[in]	index	the index where to compute the FD

Returns

the value of the scheme evaluated with the input values

fd_weno_compute_from_field()

double precision function mod_finite_differences_computer::fd_weno_compute_from_field	(	class(t_fd_weno_scheme)	scheme,
		double precision, intent(in)	step,
		double precision, dimension(:), intent(in)	x_step_array,
		double precision, dimension(:), intent(in)	y_step_array,
		double precision, dimension(:), intent(in)	z_step_array,
		double precision, dimension(:,:,:), intent(in)	field,
		integer, intent(in)	i,
		integer, intent(in)	j,
		integer, intent(in)	k,
		integer, intent(in)	axis
	)

Parameters

[in]	scheme	the finite difference scheme
[in]	step	the step where to evaluate the scheme (starting from the reference node)
[in]	x_step_array	the discretization step array in the x direction
[in]	y_step_array	the discretization step array in the y direction
[in]	z_step_array	the discretization step array in the z direction
[in]	field	the field \(\phi(i,j,k)\) to which apply the scheme at the given indices.
[in]	i,j,k	the indices where to compute the FD
[in]	axis	the axis (direction) \(axis={1,2,3}\) for \({x,y,z}\)

Returns

the value of the scheme evaluated with the input values

Warning

This function is not the most efficient, especialy when used in a i,j,k loop, because it switches for each direction!

fd_weno_compute_from_values()

double precision function mod_finite_differences_computer::fd_weno_compute_from_values	(	class(t_fd_weno_scheme)	scheme,
		double precision, intent(in)	step,
		double precision, dimension(:), intent(in)	steps,
		double precision, dimension(:), intent(in)	values
	)

Parameters

[in]	scheme	the finite difference scheme
[in]	step	the step where to evaluate the scheme (starting from the reference node)
[in]	steps	the discretization steps, with size(steps)==size(values)-1
[in]	values	the field values to which to apply the scheme. They must be of the same dimension as the scheme

Returns

the value of the scheme evaluated with the input values