sll_m_coordinate_transformations_2d Module Reference

Description

Analytic coordinate transformation.

There are two main types of coordinate transformations: analytic and discrete. In the first case the transformation can be specified analytically, through the two functions:

\[ \begin{matrix} x_1 = x_1(\eta_1,\eta_2) \\\\ x_2 = x_2(\eta_1,\eta_2) \end{matrix} \]

Where both, eta1 and eta2 should be defined on the intervals that define the extent of the logical mesh (default values in logical mesh are [0,1]. The same transformation can be specified by the set of transformed points \(x_1(i,j), x_2(i,j),\) as two 2D arrays or 1D arrays that describe the transformation on each direction.

The transformation is also represented by the Jacobian matrix:

\[ J(\eta_1,\eta_2) = \begin{bmatrix} \partial x_1(\eta_1,\eta_2) / \partial \eta_1 & \partial x_1(\eta_1,\eta_2) / \partial \eta_2 \\\\ \partial x_2(\eta_1,\eta_2) / \partial \eta_1 & \partial x_2(\eta_1,\eta_2) / \partial \eta_2 \end{bmatrix} \]

Derived types and interfaces
interface	j_matrix_f_nopass
type	jacobian_matrix_element
	Functions array. More...
type	sll_t_coordinate_transformation_2d_analytic
	Analytic transformation. More...
type	sll_t_coordinate_transformation_2d_discrete
interface	sll_o_delete
	Deallocate. More...

Functions/Subroutines
type(sll_t_coordinate_transformation_2d_analytic) function, pointer, public	sll_f_new_coordinate_transformation_2d_analytic (label, mesh_2d, x1_func, x2_func, j11_func, j12_func, j21_func, j22_func, params)
	Create the analytic coordinate transformation. More...
subroutine, public	sll_s_coordinate_transformation_2d_analytic_init (transf, label, mesh_2d, x1_func, x2_func, j11_func, j12_func, j21_func, j22_func, params)
subroutine	delete_transformation_2d_analytic (transf)
class(sll_t_cartesian_mesh_2d) function, pointer	get_cartesian_mesh_analytic (transf)
real(kind=f64) function	jacobian_2d_analytic (transf, eta1, eta2)
real(kind=f64) function, dimension(1:2, 1:2)	jacobian_matrix_2d_analytic (transf, eta1, eta2)
real(kind=f64) function, dimension(1:2, 1:2)	inverse_jacobian_matrix_2d_analytic (transf, eta1, eta2)
real(kind=f64) function	x1_analytic (transf, eta1, eta2)
real(kind=f64) function	x2_analytic (transf, eta1, eta2)
real(kind=f64) function	x1_node_analytic (transf, i, j)
real(kind=f64) function	x2_node_analytic (transf, i, j)
real(kind=f64) function	x1_cell_analytic (transf, i, j)
real(kind=f64) function	x2_cell_analytic (transf, i, j)
real(kind=f64) function	jacobian_2d_cell_analytic (transf, i, j)
real(kind=f64) function	jacobian_node_analytic (transf, i, j)
subroutine	write_to_file_2d_analytic (transf, output_format)
subroutine	read_from_file_2d_analytic (transf, filename)
class(sll_t_cartesian_mesh_2d) function, pointer	get_cartesian_mesh_discrete (transf)
real(kind=f64) function	x1_node_discrete (transf, i, j)
real(kind=f64) function	x2_node_discrete (transf, i, j)
real(kind=f64) function	x1_cell_discrete (transf, i, j)
real(kind=f64) function	x2_cell_discrete (transf, i, j)
real(kind=f64) function	x1_discrete (transf, eta1, eta2)
real(kind=f64) function	x2_discrete (transf, eta1, eta2)
real(kind=f64) function	jacobian_2d_discrete (transf, eta1, eta2)
real(kind=f64) function	jacobian_2d_cell_discrete (transf, i, j)
real(kind=f64) function, dimension(1:2, 1:2)	jacobian_matrix_2d_discrete (transf, eta1, eta2)
real(kind=f64) function, dimension(1:2, 1:2)	inverse_jacobian_matrix_2d_discrete (transf, eta1, eta2)
type(sll_t_coordinate_transformation_2d_discrete) function, pointer, public	sll_f_new_coordinate_transformation_2d_discrete (mesh_2d, label, x1_interpolator, x2_interpolator, jacobians_n_interpolator, x1_node, x2_node, jacobians_node, x1_cell, x2_cell, jacobians_cell)
	Create a new coordinate transformation object. More...
subroutine, public	sll_s_coordinate_transformation_2d_discrete_init (transf, mesh_2d, label, x1_interpolator, x2_interpolator, jacobians_n_interpolator, x1_node, x2_node, jacobians_node, x1_cell, x2_cell, jacobians_cell)
real(kind=f64) function	transf_2d_jacobian_node_discrete (transf, i, j)
subroutine	write_to_file_2d_discrete (transf, output_format)
subroutine	delete_transformation_2d_discrete (transf)
subroutine	read_from_file_2d_discrete (transf, filename)

Function/Subroutine Documentation

delete_transformation_2d_analytic()

subroutine sll_m_coordinate_transformations_2d::delete_transformation_2d_analytic ( class(sll_t_coordinate_transformation_2d_analytic), intent(inout)  transf )

private

Definition at line 354 of file sll_m_coordinate_transformations_2d.F90.

delete_transformation_2d_discrete()

subroutine sll_m_coordinate_transformations_2d::delete_transformation_2d_discrete ( class(sll_t_coordinate_transformation_2d_discrete), intent(inout)  transf )

private

Definition at line 1224 of file sll_m_coordinate_transformations_2d.F90.

get_cartesian_mesh_analytic()

class(sll_t_cartesian_mesh_2d) function, pointer sll_m_coordinate_transformations_2d::get_cartesian_mesh_analytic ( class(sll_t_coordinate_transformation_2d_analytic), intent(in)  transf )

private

Definition at line 363 of file sll_m_coordinate_transformations_2d.F90.

get_cartesian_mesh_discrete()

class(sll_t_cartesian_mesh_2d) function, pointer sll_m_coordinate_transformations_2d::get_cartesian_mesh_discrete ( class(sll_t_coordinate_transformation_2d_discrete), intent(in)  transf )

private

Definition at line 671 of file sll_m_coordinate_transformations_2d.F90.

inverse_jacobian_matrix_2d_analytic()

real(kind=f64) function, dimension(1:2, 1:2) sll_m_coordinate_transformations_2d::inverse_jacobian_matrix_2d_analytic ( class(sll_t_coordinate_transformation_2d_analytic), intent(inout)  transf, real(kind=f64), intent(in)  eta1, real(kind=f64), intent(in)  eta2  )

private

Definition at line 415 of file sll_m_coordinate_transformations_2d.F90.

inverse_jacobian_matrix_2d_discrete()

real(kind=f64) function, dimension(1:2, 1:2) sll_m_coordinate_transformations_2d::inverse_jacobian_matrix_2d_discrete ( class(sll_t_coordinate_transformation_2d_discrete), intent(inout)  transf, real(kind=f64), intent(in)  eta1, real(kind=f64), intent(in)  eta2  )

private

Definition at line 776 of file sll_m_coordinate_transformations_2d.F90.

jacobian_2d_analytic()

real(kind=f64) function sll_m_coordinate_transformations_2d::jacobian_2d_analytic ( class(sll_t_coordinate_transformation_2d_analytic)  transf, real(kind=f64), intent(in)  eta1, real(kind=f64), intent(in)  eta2  )

private

Definition at line 369 of file sll_m_coordinate_transformations_2d.F90.

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jacobian_2d_cell_analytic()

real(kind=f64) function sll_m_coordinate_transformations_2d::jacobian_2d_cell_analytic ( class(sll_t_coordinate_transformation_2d_analytic)  transf, integer(kind=i32), intent(in)  i, integer(kind=i32), intent(in)  j  )

private

Definition at line 509 of file sll_m_coordinate_transformations_2d.F90.

jacobian_2d_cell_discrete()

real(kind=f64) function sll_m_coordinate_transformations_2d::jacobian_2d_cell_discrete ( class(sll_t_coordinate_transformation_2d_discrete)  transf, integer(kind=i32), intent(in)  i, integer(kind=i32), intent(in)  j  )

private

Definition at line 745 of file sll_m_coordinate_transformations_2d.F90.

jacobian_2d_discrete()

real(kind=f64) function sll_m_coordinate_transformations_2d::jacobian_2d_discrete ( class(sll_t_coordinate_transformation_2d_discrete)  transf, real(kind=f64), intent(in)  eta1, real(kind=f64), intent(in)  eta2  )

private

Definition at line 725 of file sll_m_coordinate_transformations_2d.F90.

jacobian_matrix_2d_analytic()

real(kind=f64) function, dimension(1:2, 1:2) sll_m_coordinate_transformations_2d::jacobian_matrix_2d_analytic ( class(sll_t_coordinate_transformation_2d_analytic), intent(inout)  transf, real(kind=f64), intent(in)  eta1, real(kind=f64), intent(in)  eta2  )

private

Definition at line 392 of file sll_m_coordinate_transformations_2d.F90.

jacobian_matrix_2d_discrete()

real(kind=f64) function, dimension(1:2, 1:2) sll_m_coordinate_transformations_2d::jacobian_matrix_2d_discrete ( class(sll_t_coordinate_transformation_2d_discrete), intent(inout)  transf, real(kind=f64), intent(in)  eta1, real(kind=f64), intent(in)  eta2  )

private

Definition at line 753 of file sll_m_coordinate_transformations_2d.F90.

jacobian_node_analytic()

real(kind=f64) function sll_m_coordinate_transformations_2d::jacobian_node_analytic ( class(sll_t_coordinate_transformation_2d_analytic)  transf, integer(kind=i32), intent(in)  i, integer(kind=i32), intent(in)  j  )

private

Definition at line 534 of file sll_m_coordinate_transformations_2d.F90.

read_from_file_2d_analytic()

subroutine sll_m_coordinate_transformations_2d::read_from_file_2d_analytic ( class(sll_t_coordinate_transformation_2d_analytic), intent(inout)  transf, character(len=*), intent(in)  filename  )

private

Definition at line 654 of file sll_m_coordinate_transformations_2d.F90.

read_from_file_2d_discrete()

subroutine sll_m_coordinate_transformations_2d::read_from_file_2d_discrete ( class(sll_t_coordinate_transformation_2d_discrete), intent(inout)  transf, character(len=*), intent(in)  filename  )

private

Definition at line 1269 of file sll_m_coordinate_transformations_2d.F90.

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sll_f_new_coordinate_transformation_2d_analytic()

type(sll_t_coordinate_transformation_2d_analytic) function, pointer, public sll_m_coordinate_transformations_2d::sll_f_new_coordinate_transformation_2d_analytic	(	character(len=*), intent(in)	label,
		type(sll_t_cartesian_mesh_2d), target	mesh_2d,
		procedure(sll_i_transformation_func_nopass)	x1_func,
		procedure(sll_i_transformation_func_nopass)	x2_func,
		procedure(sll_i_transformation_func_nopass)	j11_func,
		procedure(sll_i_transformation_func_nopass)	j12_func,
		procedure(sll_i_transformation_func_nopass)	j21_func,
		procedure(sll_i_transformation_func_nopass)	j22_func,
		real(kind=f64), dimension(:), intent(in)	params
	)

Create the analytic coordinate transformation.

Definition at line 267 of file sll_m_coordinate_transformations_2d.F90.

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sll_f_new_coordinate_transformation_2d_discrete()

type(sll_t_coordinate_transformation_2d_discrete) function, pointer, public sll_m_coordinate_transformations_2d::sll_f_new_coordinate_transformation_2d_discrete	(	type(sll_t_cartesian_mesh_2d), pointer	mesh_2d,
		character(len=*), intent(in)	label,
		class(sll_c_interpolator_2d), target	x1_interpolator,
		class(sll_c_interpolator_2d), target	x2_interpolator,
		class(sll_c_interpolator_2d), target	jacobians_n_interpolator,
		real(kind=f64), dimension(:, :), intent(in), optional	x1_node,
		real(kind=f64), dimension(:, :), intent(in), optional	x2_node,
		real(kind=f64), dimension(:, :), intent(in), optional	jacobians_node,
		real(kind=f64), dimension(:, :), intent(in), optional	x1_cell,
		real(kind=f64), dimension(:, :), intent(in), optional	x2_cell,
		real(kind=f64), dimension(:, :), intent(in), optional	jacobians_cell
	)

Create a new coordinate transformation object.

Definition at line 802 of file sll_m_coordinate_transformations_2d.F90.

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sll_s_coordinate_transformation_2d_analytic_init()

subroutine, public sll_m_coordinate_transformations_2d::sll_s_coordinate_transformation_2d_analytic_init	(	class(sll_t_coordinate_transformation_2d_analytic), intent(inout)	transf,
		character(len=*), intent(in)	label,
		type(sll_t_cartesian_mesh_2d), target	mesh_2d,
		procedure(sll_i_transformation_func_nopass)	x1_func,
		procedure(sll_i_transformation_func_nopass)	x2_func,
		procedure(sll_i_transformation_func_nopass)	j11_func,
		procedure(sll_i_transformation_func_nopass)	j12_func,
		procedure(sll_i_transformation_func_nopass)	j21_func,
		procedure(sll_i_transformation_func_nopass)	j22_func,
		real(kind=f64), dimension(:), intent(in)	params
	)

Definition at line 307 of file sll_m_coordinate_transformations_2d.F90.

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sll_s_coordinate_transformation_2d_discrete_init()

subroutine, public sll_m_coordinate_transformations_2d::sll_s_coordinate_transformation_2d_discrete_init	(	class(sll_t_coordinate_transformation_2d_discrete)	transf,
		type(sll_t_cartesian_mesh_2d), target	mesh_2d,
		character(len=*), intent(in)	label,
		class(sll_c_interpolator_2d), target	x1_interpolator,
		class(sll_c_interpolator_2d), target	x2_interpolator,
		class(sll_c_interpolator_2d), target	jacobians_n_interpolator,
		real(kind=f64), dimension(:, :), intent(in), optional	x1_node,
		real(kind=f64), dimension(:, :), intent(in), optional	x2_node,
		real(kind=f64), dimension(:, :), intent(in), optional	jacobians_node,
		real(kind=f64), dimension(:, :), intent(in), optional	x1_cell,
		real(kind=f64), dimension(:, :), intent(in), optional	x2_cell,
		real(kind=f64), dimension(:, :), intent(in), optional	jacobians_cell
	)

Definition at line 850 of file sll_m_coordinate_transformations_2d.F90.

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transf_2d_jacobian_node_discrete()

real(kind=f64) function sll_m_coordinate_transformations_2d::transf_2d_jacobian_node_discrete ( class(sll_t_coordinate_transformation_2d_discrete)  transf, integer(kind=i32), intent(in)  i, integer(kind=i32), intent(in)  j  )

private

Definition at line 1112 of file sll_m_coordinate_transformations_2d.F90.

write_to_file_2d_analytic()

subroutine sll_m_coordinate_transformations_2d::write_to_file_2d_analytic ( class(sll_t_coordinate_transformation_2d_analytic), intent(inout)  transf, integer(kind=i32), intent(in), optional  output_format  )

private

Definition at line 566 of file sll_m_coordinate_transformations_2d.F90.

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write_to_file_2d_discrete()

subroutine sll_m_coordinate_transformations_2d::write_to_file_2d_discrete ( class(sll_t_coordinate_transformation_2d_discrete), intent(inout)  transf, integer(kind=i32), intent(in), optional  output_format  )

private

Definition at line 1127 of file sll_m_coordinate_transformations_2d.F90.

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x1_analytic()

real(kind=f64) function sll_m_coordinate_transformations_2d::x1_analytic ( class(sll_t_coordinate_transformation_2d_analytic)  transf, real(kind=f64), intent(in)  eta1, real(kind=f64), intent(in)  eta2  )

private

Definition at line 441 of file sll_m_coordinate_transformations_2d.F90.

x1_cell_analytic()

real(kind=f64) function sll_m_coordinate_transformations_2d::x1_cell_analytic ( class(sll_t_coordinate_transformation_2d_analytic)  transf, integer(kind=i32), intent(in)  i, integer(kind=i32), intent(in)  j  )

private

Definition at line 483 of file sll_m_coordinate_transformations_2d.F90.

x1_cell_discrete()

real(kind=f64) function sll_m_coordinate_transformations_2d::x1_cell_discrete ( class(sll_t_coordinate_transformation_2d_discrete)  transf, integer(kind=i32), intent(in)  i, integer(kind=i32), intent(in)  j  )

private

Definition at line 693 of file sll_m_coordinate_transformations_2d.F90.

x1_discrete()

real(kind=f64) function sll_m_coordinate_transformations_2d::x1_discrete ( class(sll_t_coordinate_transformation_2d_discrete)  transf, real(kind=f64), intent(in)  eta1, real(kind=f64), intent(in)  eta2  )

private

Definition at line 709 of file sll_m_coordinate_transformations_2d.F90.

x1_node_analytic()

real(kind=f64) function sll_m_coordinate_transformations_2d::x1_node_analytic ( class(sll_t_coordinate_transformation_2d_analytic)  transf, integer(kind=i32), intent(in)  i, integer(kind=i32), intent(in)  j  )

private

Definition at line 457 of file sll_m_coordinate_transformations_2d.F90.

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x1_node_discrete()

real(kind=f64) function sll_m_coordinate_transformations_2d::x1_node_discrete ( class(sll_t_coordinate_transformation_2d_discrete)  transf, integer(kind=i32), intent(in)  i, integer(kind=i32), intent(in)  j  )

private

Definition at line 677 of file sll_m_coordinate_transformations_2d.F90.

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x2_analytic()

real(kind=f64) function sll_m_coordinate_transformations_2d::x2_analytic ( class(sll_t_coordinate_transformation_2d_analytic)  transf, real(kind=f64), intent(in)  eta1, real(kind=f64), intent(in)  eta2  )

private

Definition at line 449 of file sll_m_coordinate_transformations_2d.F90.

x2_cell_analytic()

real(kind=f64) function sll_m_coordinate_transformations_2d::x2_cell_analytic ( class(sll_t_coordinate_transformation_2d_analytic)  transf, integer(kind=i32), intent(in)  i, integer(kind=i32), intent(in)  j  )

private

Definition at line 496 of file sll_m_coordinate_transformations_2d.F90.

x2_cell_discrete()

real(kind=f64) function sll_m_coordinate_transformations_2d::x2_cell_discrete ( class(sll_t_coordinate_transformation_2d_discrete)  transf, integer(kind=i32), intent(in)  i, integer(kind=i32), intent(in)  j  )

private

Definition at line 701 of file sll_m_coordinate_transformations_2d.F90.

x2_discrete()

real(kind=f64) function sll_m_coordinate_transformations_2d::x2_discrete ( class(sll_t_coordinate_transformation_2d_discrete)  transf, real(kind=f64), intent(in)  eta1, real(kind=f64), intent(in)  eta2  )

private

Definition at line 717 of file sll_m_coordinate_transformations_2d.F90.

x2_node_analytic()

real(kind=f64) function sll_m_coordinate_transformations_2d::x2_node_analytic ( class(sll_t_coordinate_transformation_2d_analytic)  transf, integer(kind=i32), intent(in)  i, integer(kind=i32), intent(in)  j  )

private

Definition at line 470 of file sll_m_coordinate_transformations_2d.F90.

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x2_node_discrete()

real(kind=f64) function sll_m_coordinate_transformations_2d::x2_node_discrete ( class(sll_t_coordinate_transformation_2d_discrete)  transf, integer(kind=i32), intent(in)  i, integer(kind=i32), intent(in)  j  )

private

Definition at line 685 of file sll_m_coordinate_transformations_2d.F90.

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