sll_m_sparse_grid_2d Module Reference

Description

Implementation of a 2D sparse grid with interpolation routines.

Author

Katharina Kormann, IPP

Todo:

Implement the optimized interpolation routines for option boundary=1

<DETAILED_DESCRIPTION>

Derived types and interfaces
type	sll_t_sparse_grid_2d
	Sparse grid object for 2d with interpolation routines. More...

Functions/Subroutines
subroutine	interpolate_array_disp_sgfft (interpolator, dim, displacment_in, data_in, data_out)
	Compute value at displaced grid points using trigonometric interpolation (based on SG FFT) More...
subroutine	initialize_sg2d (interpolator, levels, order, interpolation, interpolation_type, eta_min, eta_max, boundary, modified)
	Initialize a 2d sparse grid object. More...
subroutine	set_hierarchy_info (interpolator, counter, cdim, lvecin, kvecin, novecin)
	Helfer function for initialization. Setting all the information needed for node counter of the sparse grid along dimension cdim. More...
subroutine	set_hierarchy_info_boundary (interpolator, counter, cdim, lvecin, kvecin, novecin)
	Same as set_hierarchy_info but for points on the boundary along dimension cdim. More...
real(kind=f64) function	interpolate_value_sg (interpolator, data, eta)
	Value at eta interpolated from the hierarchical surplus data using standard sparse grid interpolation. More...
real(kind=f64) function	interpolate_from_hierarchical_surplus (interpolator, data, eta)
	Implementation of interpolate_value_sg for periodic sparse grid. More...
real(kind=f64) function	interpolate_from_hierarchical_surplus_boundary (interpolator, data, eta)
	Implementation of interpolate_value_sg for sparse grid with boundary. More...
subroutine	interpolate_const_disp (interpolator, dorder, displacement, data_in, data_out, hiera)
	Interpolation function for interpolation at (constantly) displaced grid points; displacement only in dimension dim. It is another implementation of the base-class function "interpolate_disp". The advantage is that we can not revisit nodes as we do in the recursive dimension-independently-programmed version. More...
subroutine	interpolate_disp_nconst_in_1d (interpolator, displacement, dorder, data_in, data_out)
	Functionality: Interpolates the function values for a displacement on in dimension (periodic b.c. i.e. dimension 1 or 2) where the displacement is allowed to be non-constant in one other dimension (Dirichlet b.c. i.e. dimension 3 or 3). More...
subroutine	interpolate_disp_linnconst_in_1d (interpolator, displacement, dorder, data_in, data_out)
	As interpolate_disp_nconst_in_1d but displacement dependent on displacement*coordinate(dorder(2)) More...
subroutine	fg_to_sg (interpolator, fg_values, sg_values)
	Set sparse grid values from fg vector. More...
integer(kind=i32) function, dimension(2)	fg_index (interpolator, sg_index)
	Compute the index of a sparse grid node on level "level" with index "index_on_level" on full grid with of max_level. More...
subroutine	tohierarchical (interpolator, data_in, data_out)
	Compute Fourier coefficient on sparse grid. More...
subroutine	todehi (interpolator, data_array)
subroutine	tohira (interpolator, data_array)
subroutine	tonodal (interpolator, data_in, data_out)
subroutine	displace (interpolator, dim, displacement, data)
	Compute the Fourier coefficients of at displaced grid points from Fourier coefficients. More...
subroutine	spfft (interpolator, data_in, data_out)
	Fourier transform on sparse grid. More...
subroutine	ispfft (interpolator, data_in, data_out)
	Inverse Fourier transform. More...
subroutine	filter_highest (interpolator, data)
subroutine	filter (interpolator, data)
subroutine	linear_filter (interpolator, data, hs, width)

Function/Subroutine Documentation

displace()

subroutine sll_m_sparse_grid_2d::displace ( class(sll_t_sparse_grid_2d), intent(inout)  interpolator, integer(kind=i32), intent(in)  dim, real(kind=f64), intent(in)  displacement, complex(kind=f64), dimension(:), intent(inout)  data  )

private

Compute the Fourier coefficients of at displaced grid points from Fourier coefficients.

Parameters

[in,out]	interpolator	sparse grid object
[in,out]	data	Fourier coefficients of input and output function, respectively
[in]	displacement	The constant displacement along dimension dim
[in]	dim	Dimension along which we displace.

Definition at line 936 of file sll_m_sparse_grid_2d.F90.

fg_index()

integer(kind=i32) function, dimension(2) sll_m_sparse_grid_2d::fg_index ( class(sll_t_sparse_grid_2d), intent(in)  interpolator, integer(kind=i32), intent(in)  sg_index  )

private

Compute the index of a sparse grid node on level "level" with index "index_on_level" on full grid with of max_level.

Parameters

[in]

sg_index

index of point on sparse grid

Returns

vector of full grid indices

Parameters

[in]

interpolator

Sparse grid object

Definition at line 806 of file sll_m_sparse_grid_2d.F90.

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fg_to_sg()

subroutine sll_m_sparse_grid_2d::fg_to_sg ( class(sll_t_sparse_grid_2d), intent(in)  interpolator, real(kind=f64), dimension(:, :), intent(in)  fg_values, real(kind=f64), dimension(:), intent(out)  sg_values  )

private

Set sparse grid values from fg vector.

Parameters

[in]	fg_values	Values of the full grid
[out]	sg_values	Vectro with sparse grid values
[in]	interpolator	sparse grid object

Definition at line 774 of file sll_m_sparse_grid_2d.F90.

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filter()

subroutine sll_m_sparse_grid_2d::filter ( class(sll_t_sparse_grid_2d), intent(inout)  interpolator, real(kind=f64), dimension(:), intent(inout)  data  )

private

Definition at line 1054 of file sll_m_sparse_grid_2d.F90.

filter_highest()

subroutine sll_m_sparse_grid_2d::filter_highest ( class(sll_t_sparse_grid_2d), intent(inout)  interpolator, real(kind=f64), dimension(:), intent(inout)  data  )

private

Definition at line 1023 of file sll_m_sparse_grid_2d.F90.

initialize_sg2d()

subroutine sll_m_sparse_grid_2d::initialize_sg2d ( class(sll_t_sparse_grid_2d), intent(inout)  interpolator, integer(kind=i32), dimension(:), intent(in)  levels, integer(kind=i32), intent(in)  order, integer(kind=i32), intent(in)  interpolation, integer(kind=i32), intent(in)  interpolation_type, real(kind=f64), dimension(:), intent(in)  eta_min, real(kind=f64), dimension(:), intent(in)  eta_max, integer(kind=i32), intent(in)  boundary, integer(kind=i32), intent(in)  modified  )

private

Initialize a 2d sparse grid object.

Parameters

[in,out]	interpolator	sparse grid object
[in]	eta_min	eta_min defines the lower bound of the domain
[in]	eta_max	eta_max defines the upper bound of the domain
[in]	levels	levels defines the maximum level in the sparse grid for each direction
[in]	order	order of the sparse grid functions
[in]	interpolation	order of the interpolator
[in]	interpolation_type	Choose spline (interpolation_type = 0) or Lagrange (interpolation_type = 1) interpolation for the 1D interpolators if not traditional sparse grid interpolation is used.
[in]	modified	modified defines if we have a traditional sparse grid for modified = 0 (then the l_1 norm of the levels is bounded by max(levels) ) or if the boundary is sparsified for modified = 1 (then the l_1 norm of the levels is bounded by max(levels)+1 )
[in]	boundary	boundary defines the boundary conditions: define 0 for periodic boundary conditions and 1 for zero inflow boundaries

Definition at line 81 of file sll_m_sparse_grid_2d.F90.

interpolate_array_disp_sgfft()

subroutine sll_m_sparse_grid_2d::interpolate_array_disp_sgfft ( class(sll_t_sparse_grid_2d), intent(inout)  interpolator, integer(kind=i32), intent(in)  dim, real(kind=f64), intent(in)  displacment_in, complex(kind=f64), dimension(:), intent(inout)  data_in, real(kind=f64), dimension(:), intent(out)  data_out  )

private

Compute value at displaced grid points using trigonometric interpolation (based on SG FFT)

Parameters

[in,out]	interpolator	Sparse grid object
[in]	dim	dimension along which the points should be displaced with displacement_in
[in]	displacment_in	displacement of the data points along dimension dim
[in,out]	data_in	Fourier transformed values on the sparse grid
[out]	data_out	Function values on the sparse grid after displacement

Definition at line 60 of file sll_m_sparse_grid_2d.F90.

interpolate_const_disp()

subroutine sll_m_sparse_grid_2d::interpolate_const_disp ( class(sll_t_sparse_grid_2d), intent(inout)  interpolator, integer(kind=i32), dimension(:), intent(in)  dorder, real(kind=f64), intent(in)  displacement, real(kind=f64), dimension(:), intent(inout)  data_in, real(kind=f64), dimension(:), intent(out)  data_out, logical, intent(in)  hiera  )

private

Interpolation function for interpolation at (constantly) displaced grid points; displacement only in dimension dim. It is another implementation of the base-class function "interpolate_disp". The advantage is that we can not revisit nodes as we do in the recursive dimension-independently-programmed version.

Parameters

[in,out]	interpolator	sparse grid object
[in]	dorder	dorder(1) gives the dimension along which to displace the points, dorder(2) the other dimension
[in,out]	data_in	hierarchical surplus
[out]	data_out	Value of the function or the hierarchical surplus (depending on value of hiera) for the displaced data points.
[in]	displacement	Constant diplacement along dimension dorder(1)
[in]	hiera	If the result should be the hierarchical surplus, define hiera = .TRUE.; if the result should be the function values at the data points give hiera = .FALSE.

Definition at line 565 of file sll_m_sparse_grid_2d.F90.

interpolate_disp_linnconst_in_1d()

subroutine sll_m_sparse_grid_2d::interpolate_disp_linnconst_in_1d ( class(sll_t_sparse_grid_2d), intent(inout)  interpolator, real(kind=f64), intent(in)  displacement, integer(kind=i32), dimension(:), intent(in)  dorder, real(kind=f64), dimension(:), intent(inout)  data_in, real(kind=f64), dimension(:), intent(out)  data_out  )

private

As interpolate_disp_nconst_in_1d but displacement dependent on displacement*coordinate(dorder(2))

Definition at line 698 of file sll_m_sparse_grid_2d.F90.

interpolate_disp_nconst_in_1d()

subroutine sll_m_sparse_grid_2d::interpolate_disp_nconst_in_1d ( class(sll_t_sparse_grid_2d), intent(inout)  interpolator, real(kind=f64), dimension(:), intent(in)  displacement, integer(kind=i32), dimension(:), intent(in)  dorder, real(kind=f64), dimension(:), intent(inout)  data_in, real(kind=f64), dimension(:), intent(out)  data_out  )

private

Functionality: Interpolates the function values for a displacement on in dimension (periodic b.c. i.e. dimension 1 or 2) where the displacement is allowed to be non-constant in one other dimension (Dirichlet b.c. i.e. dimension 3 or 3).

Parameters

[in,out]	interpolator	Sparse grid object
[in,out]	data_in	hierarchical surplus of the present function
[out]	data_out	values of the displaced function
[in]	dorder	Ordering of the dimensions. dorder(1) (=1 or 2) gives the dimension where we want to displace, dorder(2) (=3 or 4) gives the dimension of which the displacement is dependent. dorder(3) = 1 or 2 not dorder(1) and dorder(4) = 3 or 4 not dorder(2).
[in]	displacement	Vector containing the values of the displacement (in hierarchical order, one dimensional)

Definition at line 618 of file sll_m_sparse_grid_2d.F90.

interpolate_from_hierarchical_surplus()

real(kind=f64) function sll_m_sparse_grid_2d::interpolate_from_hierarchical_surplus ( class(sll_t_sparse_grid_2d), intent(inout)  interpolator, real(kind=f64), dimension(:), intent(in)  data, real(kind=f64), dimension(:), intent(in)  eta  )

private

Implementation of interpolate_value_sg for periodic sparse grid.

Definition at line 410 of file sll_m_sparse_grid_2d.F90.

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interpolate_from_hierarchical_surplus_boundary()

real(kind=f64) function sll_m_sparse_grid_2d::interpolate_from_hierarchical_surplus_boundary ( class(sll_t_sparse_grid_2d), intent(inout)  interpolator, real(kind=f64), dimension(:), intent(in)  data, real(kind=f64), dimension(:), intent(in)  eta  )

private

Implementation of interpolate_value_sg for sparse grid with boundary.

Definition at line 466 of file sll_m_sparse_grid_2d.F90.

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interpolate_value_sg()

real(kind=f64) function sll_m_sparse_grid_2d::interpolate_value_sg ( class(sll_t_sparse_grid_2d), intent(inout)  interpolator, real(kind=f64), dimension(:), intent(in)  data, real(kind=f64), dimension(:), intent(in)  eta  )

private

Value at eta interpolated from the hierarchical surplus data using standard sparse grid interpolation.

Parameters

[in,out]	interpolator	Sparse grid object
[in]	data	values of the hierarchical surplus

Returns

result of the interpolation

Parameters

[in]

eta

coordinates of the point where to interpolate

Definition at line 393 of file sll_m_sparse_grid_2d.F90.

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ispfft()

subroutine sll_m_sparse_grid_2d::ispfft ( class(sll_t_sparse_grid_2d), intent(inout)  interpolator, complex(kind=f64), dimension(:), intent(inout)  data_in, real(kind=f64), dimension(:), intent(out)  data_out  )

private

Inverse Fourier transform.

Definition at line 1007 of file sll_m_sparse_grid_2d.F90.

linear_filter()

subroutine sll_m_sparse_grid_2d::linear_filter ( class(sll_t_sparse_grid_2d), intent(inout)  interpolator, real(kind=f64), dimension(:), intent(inout)  data, real(kind=f64), dimension(:), intent(inout)  hs, real(kind=f64), dimension(2), intent(in)  width  )

private

Definition at line 1080 of file sll_m_sparse_grid_2d.F90.

set_hierarchy_info()

subroutine sll_m_sparse_grid_2d::set_hierarchy_info ( class(sll_t_sparse_grid_2d), intent(inout)  interpolator, integer(kind=i32), intent(in)  counter, integer(kind=i32), intent(in)  cdim, integer(kind=i32), dimension(:), intent(in)  lvecin, integer(kind=i32), dimension(:), intent(in)  kvecin, integer(kind=i32), dimension(:), intent(in)  novecin  )

private

Helfer function for initialization. Setting all the information needed for node counter of the sparse grid along dimension cdim.

Parameters

[in]	cdim	current dimension
[in]	lvecin	vector of current levels
[in]	kvecin	vector of current index within level
[in]	novecin	vector with number of points on the current level along each dimension

Definition at line 208 of file sll_m_sparse_grid_2d.F90.

set_hierarchy_info_boundary()

subroutine sll_m_sparse_grid_2d::set_hierarchy_info_boundary ( class(sll_t_sparse_grid_2d), intent(inout)  interpolator, integer(kind=i32), intent(in)  counter, integer(kind=i32), intent(in)  cdim, integer(kind=i32), dimension(:), intent(in)  lvecin, integer(kind=i32), dimension(:), intent(in)  kvecin, integer(kind=i32), dimension(:), intent(in)  novecin  )

private

Same as set_hierarchy_info but for points on the boundary along dimension cdim.

Parameters

[in]	cdim	current dimension
[in]	counter	counter for node

Definition at line 285 of file sll_m_sparse_grid_2d.F90.

spfft()

subroutine sll_m_sparse_grid_2d::spfft ( class(sll_t_sparse_grid_2d), intent(inout)  interpolator, real(kind=f64), dimension(:), intent(in)  data_in, complex(kind=f64), dimension(:), intent(out)  data_out  )

private

Fourier transform on sparse grid.

Definition at line 996 of file sll_m_sparse_grid_2d.F90.

todehi()

subroutine sll_m_sparse_grid_2d::todehi ( class(sll_t_sparse_grid_2d), intent(inout)  interpolator, complex(kind=f64), dimension(:), intent(inout)  data_array  )

private

Parameters

[in,out]	interpolator	Sparse grid object
[in,out]	data_array	on input: hierarchical surplus; on output: function values

Definition at line 857 of file sll_m_sparse_grid_2d.F90.

tohierarchical()

subroutine sll_m_sparse_grid_2d::tohierarchical ( class(sll_t_sparse_grid_2d), intent(inout)  interpolator, real(kind=f64), dimension(:), intent(in)  data_in, complex(kind=f64), dimension(:), intent(out)  data_out  )

private

Compute Fourier coefficient on sparse grid.

Parameters

[in,out]	interpolator	Sparse grid object
[in]	data_in	Values at the sparse grid points
[out]	data_out	Values of the linear hierarchical surplus

Definition at line 831 of file sll_m_sparse_grid_2d.F90.

tohira()

subroutine sll_m_sparse_grid_2d::tohira ( class(sll_t_sparse_grid_2d), intent(inout)  interpolator, complex(kind=f64), dimension(:), intent(inout)  data_array  )

private

Definition at line 883 of file sll_m_sparse_grid_2d.F90.

tonodal()

subroutine sll_m_sparse_grid_2d::tonodal ( class(sll_t_sparse_grid_2d), intent(inout)  interpolator, complex(kind=f64), dimension(:), intent(inout)  data_in, real(kind=f64), dimension(:), intent(out)  data_out  )

private

Definition at line 907 of file sll_m_sparse_grid_2d.F90.