sll_m_mapping_3d Module Reference

Description

Module interfaces for coordinate transformation.

xi1, xi2, xi3 are the logical coordinates which are transformed to the physical coordinates x1, x2, x3 The Jacobian matrix is the derivate matrix of the transformation function the determinant of the Jacobian is needed for the transformation theorem the logical paramters are in the interval [0,1]

Author

Benedikt Perse

Derived types and interfaces
interface	sll_i_eval_function
	abstract interface for mapping functions More...
type	matrix_element
type	sll_t_mapping_3d
	type collecting functions for analytical coordinate mapping More...

Functions/Subroutines
real(kind=f64) function	get_x1 (self, xi)
	Compute x1. More...
real(kind=f64) function	get_x2 (self, xi)
	Compute x2. More...
real(kind=f64) function	get_x3 (self, xi)
	Compute x3. More...
real(kind=f64) function, dimension(3)	get_x (self, xi)
	Compute all three components of X. More...
real(kind=f64) function, dimension(3)	get_xi (self, x)
	Compute the logical coordinate vector Xi. More...
real(kind=f64) function	jacobian (self, xi)
	Compute the determinant of the Jacobi matrix. More...
real(kind=f64) function, dimension(3, 3)	jacobian_matrix (self, xi)
	Compute the entries of the Jacobi matrix. More...
real(kind=f64) function, dimension(3, 3)	jacobian_matrix_transposed (self, xi)
	Compute the entries of the transposed Jacobi matrix. More...
real(kind=f64) function, dimension(3, 3)	jacobian_matrix_inverse (self, xi)
	Compute the entries of the inverse Jacobi matrix. More...
real(kind=f64) function, dimension(3, 3)	jacobian_matrix_inverse_transposed (self, xi)
	Compute the entries of the transposed inverse Jacobi matrix. More...
real(kind=f64) function, dimension(3, 3)	metric (self, xi)
	Compute the entries of the metric. More...
real(kind=f64) function	metric_single (self, xi, component1, component2)
	Compute a single entriy of the metric. More...
real(kind=f64) function, dimension(3, 3)	metric_inverse (self, xi)
	Compute the entries of the inverse metric. More...
real(kind=f64) function	metric_inverse_single (self, xi, component1, component2)
	Compute a single entriy of the inverse metric. More...
real(kind=f64) function	metric_single_jacobian (self, xi, component1, component2)
	Compute a single entriy of the metric divided by the jacobian. More...
real(kind=f64) function	metric_inverse_single_jacobian (self, xi, component1, component2)
	Compute a single entriy of the inverse metric multiplied by the jacobian. More...
subroutine	init (self, params, x1_func, x2_func, x3_func, jac11, jac12, jac13, jac21, jac22, jac23, jac31, jac32, jac33, jacob, xi1_func, xi2_func, xi3_func, flag2d, flag3d, n_cells, deg, Lx, volume)
	Initialize the coordinate transformation. More...
subroutine	init_from_file (self, filename)
	Initialize the coordinate transformation from nml file. More...
subroutine	free (self)
	Finalize the coordinate transformation. More...
subroutine	calculate_interpolation_matrix_1d (n_cells, deg, xk, spline, matrix)
	Helper function for spline mapping. More...
subroutine	calculate_interpolation_matrix_1d_periodic (n_cells, deg, spline, matrix)
	Helper function for spline mapping. More...
subroutine	convert_x_to_xbox (self, position, xi, box)
	Helper function to compute xbox. More...

Function/Subroutine Documentation

calculate_interpolation_matrix_1d()

subroutine sll_m_mapping_3d::calculate_interpolation_matrix_1d ( integer(kind=i32), intent(in)  n_cells, integer(kind=i32), intent(in)  deg, real(kind=f64), dimension(:), intent(in)  xk, type( sll_t_spline_pp_1d), intent(in)  spline, type(sll_t_matrix_csr), intent(out)  matrix  )

private

Helper function for spline mapping.

Definition at line 938 of file sll_m_mapping_3d.F90.

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calculate_interpolation_matrix_1d_periodic()

subroutine sll_m_mapping_3d::calculate_interpolation_matrix_1d_periodic ( integer(kind=i32), intent(in)  n_cells, integer(kind=i32), intent(in)  deg, type( sll_t_spline_pp_1d), intent(in)  spline, type(sll_t_matrix_csr), intent(out)  matrix  )

private

Helper function for spline mapping.

Definition at line 1013 of file sll_m_mapping_3d.F90.

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convert_x_to_xbox()

subroutine sll_m_mapping_3d::convert_x_to_xbox ( class(sll_t_mapping_3d), intent(inout)  self, real(kind=f64), dimension(3), intent(in)  position, real(kind=f64), dimension(3), intent(out)  xi, integer(kind=i32), dimension(3), intent(out)  box  )

private

Helper function to compute xbox.

Parameters

[in,out]	self	kernel smoother object
[in]	position	Position of the particle
[out]	xi	Position of the particle
[out]	box	Position of the particle

Definition at line 1088 of file sll_m_mapping_3d.F90.

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free()

subroutine sll_m_mapping_3d::free ( class(sll_t_mapping_3d), intent(inout)  self )

private

Finalize the coordinate transformation.

Definition at line 924 of file sll_m_mapping_3d.F90.

get_x()

real(kind=f64) function, dimension(3) sll_m_mapping_3d::get_x ( class(sll_t_mapping_3d), intent(inout)  self, real(kind=f64), dimension(3), intent(in)  xi  )

private

Compute all three components of X.

Parameters

[in,out]	self	coordinate transformation
[in]	xi	logical coordinates

Returns

physical coordinates

Definition at line 200 of file sll_m_mapping_3d.F90.

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get_x1()

real(kind=f64) function sll_m_mapping_3d::get_x1 ( class(sll_t_mapping_3d), intent(inout)  self, real(kind=f64), dimension(3), intent(in)  xi  )

private

Compute x1.

Parameters

[in,out]	self	coordinate transformation
[in]	xi	logical coordinates

Returns

physical coordinate

Definition at line 143 of file sll_m_mapping_3d.F90.

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get_x2()

real(kind=f64) function sll_m_mapping_3d::get_x2 ( class(sll_t_mapping_3d), intent(inout)  self, real(kind=f64), dimension(3), intent(in)  xi  )

private

Compute x2.

Parameters

[in,out]	self	coordinate transformation
[in]	xi	logical coordinates

Returns

physical coordinate

Definition at line 162 of file sll_m_mapping_3d.F90.

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get_x3()

real(kind=f64) function sll_m_mapping_3d::get_x3 ( class(sll_t_mapping_3d), intent(inout)  self, real(kind=f64), dimension(3), intent(in)  xi  )

private

Compute x3.

Parameters

[in,out]	self	coordinate transformation
[in]	xi	logical coordinates

Returns

physical coordinate

Definition at line 181 of file sll_m_mapping_3d.F90.

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get_xi()

real(kind=f64) function, dimension(3) sll_m_mapping_3d::get_xi ( class(sll_t_mapping_3d), intent(inout)  self, real(kind=f64), dimension(3), intent(in)  x  )

private

Compute the logical coordinate vector Xi.

Parameters

[in,out]	self	coordinate transformation
[in]	x	physical coordinates

Returns

logical coordinates

Definition at line 223 of file sll_m_mapping_3d.F90.

init()

subroutine sll_m_mapping_3d::init ( class(sll_t_mapping_3d), intent(out)  self, real(kind=f64), dimension(:), intent(in)  params, procedure(sll_i_eval_function)  x1_func, procedure(sll_i_eval_function)  x2_func, procedure(sll_i_eval_function)  x3_func, procedure(sll_i_eval_function), optional  jac11, procedure(sll_i_eval_function), optional  jac12, procedure(sll_i_eval_function), optional  jac13, procedure(sll_i_eval_function), optional  jac21, procedure(sll_i_eval_function), optional  jac22, procedure(sll_i_eval_function), optional  jac23, procedure(sll_i_eval_function), optional  jac31, procedure(sll_i_eval_function), optional  jac32, procedure(sll_i_eval_function), optional  jac33, procedure(sll_i_eval_function), optional  jacob, procedure(sll_i_eval_function), optional  xi1_func, procedure(sll_i_eval_function), optional  xi2_func, procedure(sll_i_eval_function), optional  xi3_func, logical, optional  flag2d, logical, optional  flag3d, integer(kind=i32), dimension(3), optional  n_cells, integer(kind=i32), dimension(3), optional  deg, real(kind=f64), dimension(3), optional  Lx, real(kind=f64), optional  volume  )

private

Initialize the coordinate transformation.

Parameters

[out]	self	coordinate transformation
[in]	params	transformation parameters
	x1_func	transformation function
	x2_func	transformation function
	x3_func	transformation function
	jac11	entry of jacobian matrix
	jac12	entry of jacobian matrix
	jac13	entry of jacobian matrix
	jac21	entry of jacobian matrix
	jac22	entry of jacobian matrix
	jac23	entry of jacobian matrix
	jac31	entry of jacobian matrix
	jac32	entry of jacobian matrix
	jac33	entry of jacobian matrix
	jacob	determinant of jacobian matrix
	xi1_func	transformation function
	xi2_func	transformation function
	xi3_func	transformation function
	flag2d	logical flag for mappings mixing the first two logical coordiantes
	flag3d	logical flag for mappings mixing all three logical coordinates
	n_cells	number of cells (and grid points)
	deg	spline deg
	lx	length of the physical domain
	volume	volume of the physical domain

Definition at line 526 of file sll_m_mapping_3d.F90.

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init_from_file()

subroutine sll_m_mapping_3d::init_from_file ( class(sll_t_mapping_3d), intent(out)  self, character(len=*), intent(in)  filename  )

private

Initialize the coordinate transformation from nml file.

Parameters

[out]

self

coordinate transformation

mapping cases defined in sll_m_3d_coordinate_transformations

Definition at line 738 of file sll_m_mapping_3d.F90.

jacobian()

real(kind=f64) function sll_m_mapping_3d::jacobian ( class(sll_t_mapping_3d), intent(inout)  self, real(kind=f64), dimension(3), intent(in)  xi  )

private

Compute the determinant of the Jacobi matrix.

Parameters

[in,out]	self	coordinate transformation
[in]	xi	logical coordinates

Definition at line 235 of file sll_m_mapping_3d.F90.

jacobian_matrix()

real(kind=f64) function, dimension(3,3) sll_m_mapping_3d::jacobian_matrix ( class(sll_t_mapping_3d), intent(inout)  self, real(kind=f64), dimension(3), intent(in)  xi  )

private

Compute the entries of the Jacobi matrix.

Parameters

[in,out]	self	coordinate transformation
[in]	xi	logical coordinates

Returns

jacobian matrix

Definition at line 262 of file sll_m_mapping_3d.F90.

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jacobian_matrix_inverse()

real(kind=f64) function, dimension(3,3) sll_m_mapping_3d::jacobian_matrix_inverse ( class(sll_t_mapping_3d), intent(inout)  self, real(kind=f64), dimension(3), intent(in)  xi  )

private

Compute the entries of the inverse Jacobi matrix.

Parameters

[in,out]	self	coordinate transformation
[in]	xi	logical coordinates

Returns

inverse jacobian matrix

Definition at line 325 of file sll_m_mapping_3d.F90.

jacobian_matrix_inverse_transposed()

real(kind=f64) function, dimension(3,3) sll_m_mapping_3d::jacobian_matrix_inverse_transposed ( class(sll_t_mapping_3d), intent(inout)  self, real(kind=f64), dimension(3), intent(in)  xi  )

private

Compute the entries of the transposed inverse Jacobi matrix.

Parameters

[in,out]	self	coordinate transformation
[in]	xi	logical coordinates

Returns

jacobian matrix

Definition at line 366 of file sll_m_mapping_3d.F90.

jacobian_matrix_transposed()

real(kind=f64) function, dimension(3,3) sll_m_mapping_3d::jacobian_matrix_transposed ( class(sll_t_mapping_3d), intent(inout)  self, real(kind=f64), dimension(3), intent(in)  xi  )

private

Compute the entries of the transposed Jacobi matrix.

Parameters

[in,out]	self	coordinate transformation
[in]	xi	logical coordinates

Returns

transposed jacobian matrix

Definition at line 303 of file sll_m_mapping_3d.F90.

metric()

real(kind=f64) function, dimension(3,3) sll_m_mapping_3d::metric ( class(sll_t_mapping_3d), intent(inout)  self, real(kind=f64), dimension(3), intent(in)  xi  )

private

Compute the entries of the metric.

Parameters

[in,out]	self	coordinate transformation
[in]	xi	logical coordinates

Returns

metric

Definition at line 389 of file sll_m_mapping_3d.F90.

metric_inverse()

real(kind=f64) function, dimension(3,3) sll_m_mapping_3d::metric_inverse ( class(sll_t_mapping_3d), intent(inout)  self, real(kind=f64), dimension(3), intent(in)  xi  )

private

Compute the entries of the inverse metric.

Parameters

[in,out]	self	coordinate transformation
[in]	xi	logical coordinates

Returns

inverse metric

Definition at line 427 of file sll_m_mapping_3d.F90.

metric_inverse_single()

real(kind=f64) function sll_m_mapping_3d::metric_inverse_single ( class(sll_t_mapping_3d), intent(inout)  self, real(kind=f64), dimension(3), intent(in)  xi, integer(kind=i32), intent(in)  component1, integer(kind=i32), intent(in)  component2  )

private

Compute a single entriy of the inverse metric.

Parameters

[in,out]	self	coordinate transformation
[in]	xi	logical coordinates
[in]	component2	components of the wished entry

Returns

single entry of the inverse metric

Definition at line 448 of file sll_m_mapping_3d.F90.

metric_inverse_single_jacobian()

real(kind=f64) function sll_m_mapping_3d::metric_inverse_single_jacobian ( class(sll_t_mapping_3d), intent(inout)  self, real(kind=f64), dimension(3), intent(in)  xi, integer(kind=i32), intent(in)  component1, integer(kind=i32), intent(in)  component2  )

private

Compute a single entriy of the inverse metric multiplied by the jacobian.

Parameters

[in,out]	self	coordinate transformation
[in]	xi	logical coordinates
[in]	component2	components of the wished entry

Returns

single entry of the inverse metric multiplied by the jacobian

Definition at line 493 of file sll_m_mapping_3d.F90.

metric_single()

real(kind=f64) function sll_m_mapping_3d::metric_single ( class(sll_t_mapping_3d), intent(inout)  self, real(kind=f64), dimension(3), intent(in)  xi, integer(kind=i32), intent(in)  component1, integer(kind=i32), intent(in)  component2  )

private

Compute a single entriy of the metric.

Parameters

[in,out]	self	coordinate transformation
[in]	xi	logical coordinates
[in]	component2	components of the wished entry

Returns

single entry of the metric

Definition at line 410 of file sll_m_mapping_3d.F90.

metric_single_jacobian()

real(kind=f64) function sll_m_mapping_3d::metric_single_jacobian ( class(sll_t_mapping_3d), intent(inout)  self, real(kind=f64), dimension(3), intent(in)  xi, integer(kind=i32), intent(in)  component1, integer(kind=i32), intent(in)  component2  )

private

Compute a single entriy of the metric divided by the jacobian.

Parameters

[in,out]	self	coordinate transformation
[in]	xi	logical coordinates
[in]	component2	components of the wished entry

Returns

single entry of the metric divided by the jacobian

Definition at line 464 of file sll_m_mapping_3d.F90.