Error tools

Routines to compute errors ( \(L^p\) norms). More...

Functions
subroutine	mod_compute_error::compute_error_cell (field, reference_field, grid_volume, is_relative_error, mask, error_l1, error_l2, error_linf)
	Compute relative or absolute error of a field defined on cells with respect to a reference field.
subroutine	mod_compute_error::compute_error_face (field, reference_field, grid_volume, is_relative_error, mask, error_l1, error_l1_u, error_l1_v, error_l1_w, error_l2, error_l2_u, error_l2_v, error_l2_w, error_linf, error_linf_u, error_linf_v, error_linf_w)
	Compute error of a field defined on faces with respect to a reference field.
subroutine	mod_compute_error::compute_and_print_error_cell (label, field, reference_field, grid_volume, is_relative_error, mask)
	Compute and print the error of a field defined on cells with respect to a reference field.
subroutine	mod_compute_error::compute_and_print_error_face (label, field, reference_field, grid_volume, is_relative_error, mask)
	Compute and print the error of a field defined on faces with respect to a reference field.
subroutine	mod_compute_error::compute_and_print_l1_error_face (label, field, reference_field, grid_volume, is_relative_error, mask)
	Compute and print the L1 error of a field defined on faces with respect to a reference field.
subroutine	mod_compute_error::compute_and_print_l2_error_face (label, field, reference_field, grid_volume, is_relative_error, mask)
	Compute and print the L2 error of a field defined on faces with respect to a reference field.
subroutine	mod_compute_error::compute_and_print_linf_error_face (label, field, reference_field, grid_volume, is_relative_error, mask)
	Compute and print the Linf error of a field defined on faces with respect to a reference field.
subroutine	mod_compute_error::print_error (label, error_l1, error_l2, error_linf)
	Print the errors with a specific format.
subroutine	mod_compute_error_symmetric_difference::compute_error_symmetric_difference (reference_solution, solution, error, error_symmetric_difference, mask)
	Compute the symmetric difference error of a given phase.
subroutine	mod_compute_l1_norm::compute_l1_norm (l1_norm, field, grid_volume, mask)
	Compute L1 norm of an field defined on cells The field can be defined on cells or one of the faces of the associated volume control. Dimensions of the field is checked to compute the norm on the associated grid.
subroutine	mod_compute_l2_norm::compute_l2_norm (l2_norm, field, grid_volume, mask)
	Compute L2 norm of an field defined on cells The field can be defined on cells or one of the faces of the associated volume control. Dimensions of the field is checked to compute the norm on the associated grid.
subroutine	mod_compute_linf_norm::compute_linf_norm (linf_norm, field, grid_volume, mask)
	Compute Linf norm of an field defined on cells The field can be defined on cells or one of the faces of the associated volume control. Dimensions of the field is checked to compute the norm on the associated grid.
subroutine	mod_compute_reference_solution_error::compute_reference_solution_error ()
	Compute errors according to variables_test_case parameters.

Detailed Description

This module provides low-level routines to compute \(L^1\), \(L^2\), and \(L^\infty\) norms of a field. It also provides higher-level routines to compute the error, i. e. the difference between computed and reference solutions, using the aforementioned norms and printing the result to the log.

Function Documentation

compute_and_print_error_cell()

subroutine mod_compute_error::compute_and_print_error_cell	(	character(len=*), intent(in)	label,
		double precision, dimension(:,:,:), intent(in)	field,
		double precision, dimension(:,:,:), intent(in)	reference_field,
		double precision, dimension(:,:,:), intent(in)	grid_volume,
		logical, intent(in)	is_relative_error,
		logical, dimension(:,:,:), intent(in), optional	mask )

See compute_error_cell.

Parameters

[in]	label	label of the field
[in]	field	cell-centered field
[in]	reference_field	cell-centered field
[in]	grid_volume	volume of the grid where field is defined
[in]	is_relative_error	boolean to compute relative or absolute error
[in]	mask	restrict the sum where mask is .true.

compute_and_print_error_face()

subroutine mod_compute_error::compute_and_print_error_face	(	character(len=*), intent(in)	label,
		type(t_face_field), intent(in)	field,
		type(t_face_field), intent(in)	reference_field,
		type(t_face_field), intent(in)	grid_volume,
		logical, intent(in)	is_relative_error,
		type(t_logical_face_field), intent(in), optional	mask )

See compute_error_face.

Parameters

[in]	label	label of the field
[in]	field	face-centered field
[in]	reference_field	face-centered field
[in]	grid_volume	volume of the grid where field is defined
[in]	is_relative_error	boolean to compute relative or absolute error
[in]	mask	restrict the sum where mask is .true.

compute_and_print_l1_error_face()

subroutine mod_compute_error::compute_and_print_l1_error_face	(	character(len=*), intent(in)	label,
		type(t_face_field), intent(in)	field,
		type(t_face_field), intent(in)	reference_field,
		type(t_face_field), intent(in)	grid_volume,
		logical, intent(in)	is_relative_error,
		type(t_logical_face_field), intent(in), optional	mask )

See compute_error_face.

Parameters

[in]	label	label of the field
[in]	field	face-centered field
[in]	reference_field	face-centered field
[in]	grid_volume	volume of the grid where field is defined
[in]	is_relative_error	boolean to compute relative or absolute error
[in]	mask	restrict the sum where mask is .true.

compute_and_print_l2_error_face()

subroutine mod_compute_error::compute_and_print_l2_error_face	(	character(len=*), intent(in)	label,
		type(t_face_field), intent(in)	field,
		type(t_face_field), intent(in)	reference_field,
		type(t_face_field), intent(in)	grid_volume,
		logical, intent(in)	is_relative_error,
		type(t_logical_face_field), intent(in), optional	mask )

See compute_error_face.

Parameters

[in]	label	label of the field
[in]	field	face-centered field
[in]	reference_field	face-centered field
[in]	grid_volume	volume of the grid where field is defined
[in]	is_relative_error	boolean to compute relative or absolute error
[in]	mask	restrict the sum where mask is .true.

compute_and_print_linf_error_face()

subroutine mod_compute_error::compute_and_print_linf_error_face	(	character(len=*), intent(in)	label,
		type(t_face_field), intent(in)	field,
		type(t_face_field), intent(in)	reference_field,
		type(t_face_field), intent(in)	grid_volume,
		logical, intent(in)	is_relative_error,
		type(t_logical_face_field), intent(in), optional	mask )

See compute_error_face.

Parameters

[in]	label	label of the field
[in]	field	face-centered field
[in]	reference_field	face-centered field
[in]	grid_volume	volume of the grid where field is defined
[in]	is_relative_error	boolean to compute relative or absolute error
[in]	mask	restrict the sum where mask is .true.

compute_error_cell()

subroutine mod_compute_error::compute_error_cell	(	double precision, dimension(:,:,:), intent(in)	field,
		double precision, dimension(:,:,:), intent(in)	reference_field,
		double precision, dimension(:,:,:), intent(in)	grid_volume,
		logical, intent(in)	is_relative_error,
		logical, dimension(:,:,:), intent(in), optional	mask,
		double precision, intent(out), optional	error_l1,
		double precision, intent(out), optional	error_l2,
		double precision, intent(out), optional	error_linf )

The error is computed against the argument reference_field, which must be a cell-centered field.

Parameters

[in]	field	cell-centered field
[in]	reference_field	cell-centered field
[in]	grid_volume	volume of the grid where field is defined
[in]	is_relative_error	boolean to compute relative or absolute error
[in]	mask	restrict the sum where mask is .true.
[out]	error_l1	L1 norm of the error
[out]	error_l2	L2 norm of the error
[out]	error_linf	Linf norm of the error

compute_error_face()

subroutine mod_compute_error::compute_error_face	(	type(t_face_field), intent(in)	field,
		type(t_face_field), intent(in)	reference_field,
		type(t_face_field), intent(in)	grid_volume,
		logical, intent(in)	is_relative_error,
		type(t_logical_face_field), intent(in), optional	mask,
		double precision, intent(out), optional	error_l1,
		double precision, intent(out), optional	error_l1_u,
		double precision, intent(out), optional	error_l1_v,
		double precision, intent(out), optional	error_l1_w,
		double precision, intent(out), optional	error_l2,
		double precision, intent(out), optional	error_l2_u,
		double precision, intent(out), optional	error_l2_v,
		double precision, intent(out), optional	error_l2_w,
		double precision, intent(out), optional	error_linf,
		double precision, intent(out), optional	error_linf_u,
		double precision, intent(out), optional	error_linf_v,
		double precision, intent(out), optional	error_linf_w )

The error is computed against the argument reference_field, which must be a face-centered field.

Parameters

[in]	field	face-centered field
[in]	reference_field	face-centered field
[in]	grid_volume	volume of the grid where field is defined
[in]	is_relative_error	boolean to compute relative or absolute error
[in]	mask	restrict the sum where mask is .true.
[out]	error_l1	L1 norm of the error on all vector components
[out]	error_l1_u	L1 norm of the error in direction _u
[out]	error_l1_v	L1 norm of the error in direction _v
[out]	error_l1_w	L1 norm of the error in direction _w
[out]	error_l2	L2 norm of the error on all vector components
[out]	error_l2_u	L2 norm of the error in direction _u
[out]	error_l2_v	L2 norm of the error in direction _v
[out]	error_l2_w	L2 norm of the error in direction _w
[out]	error_linf	Linf norm of the error on all vector components
[out]	error_linf_u	Linf norm of the error in direction _u
[out]	error_linf_v	Linf norm of the error in direction _v
[out]	error_linf_w	Linf norm of the error in direction _w

compute_error_symmetric_difference()

subroutine mod_compute_error_symmetric_difference::compute_error_symmetric_difference	(	type(t_phase_geometry), intent(in)	reference_solution,
		type(t_phase_geometry), intent(in)	solution,
		double precision, dimension(:,:,:), intent(out)	error,
		double precision, intent(out)	error_symmetric_difference,
		logical, dimension(:,:,:), intent(in), optional	mask )

The symmetric difference error is defined as the area of the symmetric difference between the reconstructed phase \(\omega^\ell\) and a reference phase \(\omega^\star\) divided by the area of the reference phase boundary:

\[ \Delta\Gamma_{avg} = \dfrac{1}{|\partial\omega^\star|}\sum_{i=1}^{n} |\omega^\star_i\triangle\omega^\ell_i| \]

Where \(n\) is the number of cell, \(\omega^\star_i\) and \(\omega^\ell_i\) are the restriction of the phases to the cell \(i\)

This error is also referred as the average deviation.

Here, we do not consider the area of the reference phase boundary. We use the following formula:

\[ \Delta\Gamma_{err} = \sum_{i=1}^{n} (|\omega^\star_i| + |\omega^\ell_i| - 2|\omega^\star_i\cap\omega^\ell_i|) \]

Parameters

[in]	reference_solution	reference phase \(\omega^\star\)
[in]	solution	reconstructed phase \(\omega^\ell\)
[out]	error	cell-wise symmetric difference error
[out]	error_symmetric_difference	symmetric difference error
[in]	mask	mask to compute the error on a portion of the domain

compute_l1_norm()

subroutine mod_compute_l1_norm::compute_l1_norm	(	double precision, intent(out)	l1_norm,
		double precision, dimension(:,:,:), intent(in)	field,
		double precision, dimension(:,:,:), intent(in)	grid_volume,
		logical, dimension(:,:,:), intent(in), optional	mask )

A mask can be apply to compute the error on a part of the domain only.

Parameters

[out]	l1_norm	L1 norm of field
[in]	field	Any field defined on cell or face
[in]	grid_volume	Volume of the grid where field is defined
[in]	mask	Restrict the sum where mask is .true.

compute_l2_norm()

subroutine mod_compute_l2_norm::compute_l2_norm	(	double precision, intent(out)	l2_norm,
		double precision, dimension(:,:,:), intent(in)	field,
		double precision, dimension(:,:,:), intent(in)	grid_volume,
		logical, dimension(:,:,:), intent(in), optional	mask )

A mask can be apply to compute the error on a part of the domain only.

Parameters

[out]	l2_norm	L2 norm of field
[in]	field	Any field defined on cell or face
[in]	grid_volume	Volume of the grid where field is defined
[in]	mask	Restrict the sum where mask is .true.

compute_linf_norm()

subroutine mod_compute_linf_norm::compute_linf_norm	(	double precision, intent(out)	linf_norm,
		double precision, dimension(:,:,:), intent(in)	field,
		double precision, dimension(:,:,:), intent(in)	grid_volume,
		logical, dimension(:,:,:), intent(in), optional	mask )

A mask can be apply to compute the error on a part of the domain only.

The norm is computed where grid_volume > 0

Parameters

[out]	linf_norm	Linf norm of field
[in]	field	Any field defined on cell or face
[in]	grid_volume	Volume of the grid where field is defined
[in]	mask	Restrict the sum where mask is .true.

print_error()

subroutine mod_compute_error::print_error	(	character(len=*), intent(in)	label,
		double precision, intent(in), optional	error_l1,
		double precision, intent(in), optional	error_l2,
		double precision, intent(in), optional	error_linf )

See compute_error_cell and compute_error_face to compute the errors.

Parameters

[in]	label	label of the field
[in]	error_l1	L1 norm of the error
[in]	error_l2	L2 norm of the error
[in]	error_linf	Linf norm of the error