Sparse grid object for 2d with interpolation routines. More...

Inheritance diagram for sll_t_sparse_grid_2d:

Collaboration diagram for sll_t_sparse_grid_2d:

Private Member Functions
procedure	init => initialize_sg2d

procedure	interpolate_const_disp
	Initialization routine. More...

procedure	interpolate_from_interpolant_value => interpolate_value_sg

procedure	interpolate_disp_nconst_in_1d
	Compute the value of the sparse grid interpolant at position eta. More...

procedure	interpolate_disp_linnconst_in_1d
	Interpolate along one (x)-direction with displacement non-constant in one (v)-direction. More...

procedure	fg_to_sg
	Interpolate along one (x)-direction with displacement non-constant in one (v)-direction. More...

procedure	spfft

procedure	ispfft
	Compute the Sparse grid FFT coefficients. More...

procedure	interpolate_array_disp_sgfft
	Inverse FFT on sparsegrid. More...

procedure	filter_highest
	Compute value at displaced grid points using trigonometric interpolation (based on SG FFT) More...

procedure	filter

procedure	linear_filter

procedure	displace

procedure	set_hierarchy_info

procedure	set_hierarchy_info_boundary

procedure	tohira

procedure	todehi

procedure	tohierarchical

procedure	tonodal

procedure	compute_hierarchical_surplus
	Compute the hierarchical surplus (to the order of the sparse grid) More...

procedure	compute_linear_hierarchical_surplus
	Compute the linear hierarchical surplus. More...

procedure	compute_dehierarchical
	Compute values from (order) hierarchical surplus. More...

procedure	dehierarchical

procedure	dehierarchical_part

procedure	hierarchical_part

procedure	interpolate_disp
	Interpolation function for interpolation at (constantly) displaced grid points; displacement only in dimension dim. More...

procedure	integrate_trapezoidal

procedure	integrate_trapezoidal2

procedure	extract_periodic

procedure	hierarchical_stripe

procedure	dehierarchical_stripe

procedure	insert_periodic

procedure	interpolate_disp_1d_periodic_self

procedure, nopass	basis_function

procedure, nopass	basis_function_derivative

procedure	dehierarchical_part_order

procedure	interpolate_disp_1d_periodic_for_neighbor

procedure	interpolate_disp_1d_periodic

procedure	displace1d

procedure	tonodal1d

procedure	tonodal1d_comp

procedure	todehi1d

procedure	tohira1d

procedure	tohierarchical1d

procedure	tohierarchical1d_comp

procedure	initialize_sg

procedure	hierarchical_part_order

procedure	dehierarchical_order

procedure	free => free_sparse_grid

Private Attributes
integer(kind=i32), dimension(:, :), pointer	index
	2d mapping: for each 2d index l on the sparse grid, index gives the index of the first node belonging to this level More...

integer(kind=i32)	dim
	dim defines the dimension of the sparse grid More...

real(kind=f64), dimension(:), pointer	eta_min
	eta_min defines the lower bound of the computational domain More...

real(kind=f64), dimension(:), pointer	eta_max
	eta_max defines the upper bound of the computational domain More...

real(kind=f64), dimension(:), pointer	length
	length defines the length of the computational domain More...

real(kind=f64)	volume
	volumne defines the volume of the computational domain More...

integer(kind=i32)	max_level
	max_level is the upper bound of the l_infinity norm of the level vector More...

integer(kind=i32), dimension(:), pointer	levels
	levels is the upper bound on the level in each direction More...

integer(kind=i32)	order
	order it the (maximal) order of basis functions More...

integer(kind=i32)	interpolation
	specifies type of interpolation More...

integer(kind=i32)	no_basis_functions
	no_basis_functions is the number of different basis functions More...

integer(kind=i32)	size_basis
	size_basis is the number of grid points More...

integer(kind=i32)	modified
	modified specifies the number of boundary points in sparse grid (0 for usual sparse grid, 1 for as many boundary as middle points) More...

integer(kind=i32)	boundary
	boundary specifies if the boundary is periodic (0) or usual sparse grid (1) More...

class(sparsegrid_node), dimension(:), pointer	hierarchy
	hierarchy is an array containing the nodes More...

class(fft_hierarchical), dimension(:), pointer	fft_object
	fft_object is the object for hierarchical fft More...

real(kind=f64), dimension(:), pointer	stripe

real(kind=f64), dimension(:), pointer	stripe_out
	stripe and stripe are internal arrays to handle the 1d interpolations More...

real(kind=f64), dimension(:), pointer	hs_weights
	hs_weights contains the weights for the computation of the hierarchical surplus More...

integer(kind=i32), dimension(:), pointer	hs_weights_index
	hs_weights_index is the index vector for hs_weights More...

type(sll_t_periodic_interpolator_1d), dimension(:, :), pointer	interp_per
	interp_per is the periodic interpolator object along the stripes More...

type(interpolator_base_ptr), dimension(:, :), pointer	interp
	interp is the interpolator object for the 1d interpolations along the stripes More...

integer(kind=i32), dimension(:), pointer	level_mapping
	level_mapping is an index pointing the the start of each level More...

Detailed Description

Sparse grid object for 2d with interpolation routines.

Definition at line 27 of file sll_m_sparse_grid_2d.F90.

Member Function/Subroutine Documentation

◆ basis_function()

procedure, nopass basis_function

privateinherited

Definition at line 114 of file sll_m_sparse_grid_interpolator.F90.

◆ basis_function_derivative()

procedure, nopass basis_function_derivative

privateinherited

Definition at line 115 of file sll_m_sparse_grid_interpolator.F90.

◆ compute_dehierarchical()

procedure compute_dehierarchical

privateinherited

Compute values from (order) hierarchical surplus.

Definition at line 102 of file sll_m_sparse_grid_interpolator.F90.

◆ compute_hierarchical_surplus()

procedure compute_hierarchical_surplus

privateinherited

Compute the hierarchical surplus (to the order of the sparse grid)

Definition at line 100 of file sll_m_sparse_grid_interpolator.F90.

◆ compute_linear_hierarchical_surplus()

procedure compute_linear_hierarchical_surplus

privateinherited

Compute the linear hierarchical surplus.

Definition at line 101 of file sll_m_sparse_grid_interpolator.F90.

◆ dehierarchical()

procedure dehierarchical

privateinherited

Definition at line 103 of file sll_m_sparse_grid_interpolator.F90.

◆ dehierarchical_order()

procedure dehierarchical_order

privateinherited

Definition at line 128 of file sll_m_sparse_grid_interpolator.F90.

◆ dehierarchical_part()

procedure dehierarchical_part

privateinherited

Definition at line 104 of file sll_m_sparse_grid_interpolator.F90.

◆ dehierarchical_part_order()

procedure dehierarchical_part_order

privateinherited

Definition at line 116 of file sll_m_sparse_grid_interpolator.F90.

◆ dehierarchical_stripe()

procedure dehierarchical_stripe

privateinherited

Definition at line 111 of file sll_m_sparse_grid_interpolator.F90.

◆ displace()

procedure displace

private

Definition at line 45 of file sll_m_sparse_grid_2d.F90.

◆ displace1d()

procedure displace1d

privateinherited

Definition at line 119 of file sll_m_sparse_grid_interpolator.F90.

◆ extract_periodic()

procedure extract_periodic

privateinherited

Definition at line 109 of file sll_m_sparse_grid_interpolator.F90.

◆ fg_to_sg()

procedure fg_to_sg

private

Interpolate along one (x)-direction with displacement non-constant in one (v)-direction.

Definition at line 36 of file sll_m_sparse_grid_2d.F90.

◆ filter()

procedure filter

private

Definition at line 42 of file sll_m_sparse_grid_2d.F90.

◆ filter_highest()

procedure filter_highest

private

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

Definition at line 41 of file sll_m_sparse_grid_2d.F90.

◆ free()

procedure free

privateinherited

Definition at line 129 of file sll_m_sparse_grid_interpolator.F90.

◆ hierarchical_part()

procedure hierarchical_part

privateinherited

Definition at line 105 of file sll_m_sparse_grid_interpolator.F90.

◆ hierarchical_part_order()

procedure hierarchical_part_order

privateinherited

Definition at line 127 of file sll_m_sparse_grid_interpolator.F90.

◆ hierarchical_stripe()

procedure hierarchical_stripe

privateinherited

Definition at line 110 of file sll_m_sparse_grid_interpolator.F90.

◆ init()

procedure init

private

Definition at line 31 of file sll_m_sparse_grid_2d.F90.

◆ initialize_sg()

procedure initialize_sg

privateinherited

Definition at line 126 of file sll_m_sparse_grid_interpolator.F90.

◆ insert_periodic()

procedure insert_periodic

privateinherited

Definition at line 112 of file sll_m_sparse_grid_interpolator.F90.

◆ integrate_trapezoidal()

procedure integrate_trapezoidal

privateinherited

Definition at line 107 of file sll_m_sparse_grid_interpolator.F90.

◆ integrate_trapezoidal2()

procedure integrate_trapezoidal2

privateinherited

Definition at line 108 of file sll_m_sparse_grid_interpolator.F90.

◆ interpolate_array_disp_sgfft()

procedure interpolate_array_disp_sgfft

private

Inverse FFT on sparsegrid.

Definition at line 39 of file sll_m_sparse_grid_2d.F90.

◆ interpolate_const_disp()

procedure interpolate_const_disp

private

Initialization routine.

Definition at line 32 of file sll_m_sparse_grid_2d.F90.

◆ interpolate_disp()

procedure interpolate_disp

privateinherited

Interpolation function for interpolation at (constantly) displaced grid points; displacement only in dimension dim.

Definition at line 106 of file sll_m_sparse_grid_interpolator.F90.

◆ interpolate_disp_1d_periodic()

procedure interpolate_disp_1d_periodic

privateinherited

Definition at line 118 of file sll_m_sparse_grid_interpolator.F90.

◆ interpolate_disp_1d_periodic_for_neighbor()

procedure interpolate_disp_1d_periodic_for_neighbor

privateinherited

Definition at line 117 of file sll_m_sparse_grid_interpolator.F90.

◆ interpolate_disp_1d_periodic_self()

procedure interpolate_disp_1d_periodic_self

privateinherited

Definition at line 113 of file sll_m_sparse_grid_interpolator.F90.

◆ interpolate_disp_linnconst_in_1d()

procedure interpolate_disp_linnconst_in_1d

private

Interpolate along one (x)-direction with displacement non-constant in one (v)-direction.

Definition at line 35 of file sll_m_sparse_grid_2d.F90.

◆ interpolate_disp_nconst_in_1d()

procedure interpolate_disp_nconst_in_1d

private

Compute the value of the sparse grid interpolant at position eta.

Definition at line 34 of file sll_m_sparse_grid_2d.F90.

◆ interpolate_from_interpolant_value()

procedure interpolate_from_interpolant_value

private

Definition at line 33 of file sll_m_sparse_grid_2d.F90.

◆ ispfft()

procedure ispfft

private

Compute the Sparse grid FFT coefficients.

Definition at line 38 of file sll_m_sparse_grid_2d.F90.

◆ linear_filter()

procedure linear_filter

private

Definition at line 43 of file sll_m_sparse_grid_2d.F90.

◆ set_hierarchy_info()

procedure set_hierarchy_info

private

Definition at line 46 of file sll_m_sparse_grid_2d.F90.

◆ set_hierarchy_info_boundary()

procedure set_hierarchy_info_boundary

private

Definition at line 47 of file sll_m_sparse_grid_2d.F90.

◆ spfft()

procedure spfft

private

Definition at line 37 of file sll_m_sparse_grid_2d.F90.

◆ todehi()

procedure todehi

private

Definition at line 49 of file sll_m_sparse_grid_2d.F90.

◆ todehi1d()

procedure todehi1d

privateinherited

Definition at line 122 of file sll_m_sparse_grid_interpolator.F90.

◆ tohierarchical()

procedure tohierarchical

private

Definition at line 50 of file sll_m_sparse_grid_2d.F90.

◆ tohierarchical1d()

procedure tohierarchical1d

privateinherited

Definition at line 124 of file sll_m_sparse_grid_interpolator.F90.

◆ tohierarchical1d_comp()

procedure tohierarchical1d_comp

privateinherited

Definition at line 125 of file sll_m_sparse_grid_interpolator.F90.

◆ tohira()

procedure tohira

private

Definition at line 48 of file sll_m_sparse_grid_2d.F90.

◆ tohira1d()

procedure tohira1d

privateinherited

Definition at line 123 of file sll_m_sparse_grid_interpolator.F90.

◆ tonodal()

procedure tonodal

private

Definition at line 51 of file sll_m_sparse_grid_2d.F90.

◆ tonodal1d()

procedure tonodal1d

privateinherited

Definition at line 120 of file sll_m_sparse_grid_interpolator.F90.

◆ tonodal1d_comp()

procedure tonodal1d_comp

privateinherited

Definition at line 121 of file sll_m_sparse_grid_interpolator.F90.

Member Data Documentation

◆ boundary

integer(kind=i32) boundary

privateinherited

boundary specifies if the boundary is periodic (0) or usual sparse grid (1)

Definition at line 80 of file sll_m_sparse_grid_interpolator.F90.

◆ dim

integer(kind=i32) dim

privateinherited

dim defines the dimension of the sparse grid

Definition at line 68 of file sll_m_sparse_grid_interpolator.F90.

◆ eta_max

real(kind=f64), dimension(:), pointer eta_max

privateinherited

eta_max defines the upper bound of the computational domain

Definition at line 70 of file sll_m_sparse_grid_interpolator.F90.

◆ eta_min

real(kind=f64), dimension(:), pointer eta_min

privateinherited

eta_min defines the lower bound of the computational domain

Definition at line 69 of file sll_m_sparse_grid_interpolator.F90.

◆ fft_object

class(fft_hierarchical), dimension(:), pointer fft_object

privateinherited

fft_object is the object for hierarchical fft

Definition at line 84 of file sll_m_sparse_grid_interpolator.F90.

◆ hierarchy

class(sparsegrid_node), dimension(:), pointer hierarchy

privateinherited

hierarchy is an array containing the nodes

Definition at line 82 of file sll_m_sparse_grid_interpolator.F90.

◆ hs_weights

real(kind=f64), dimension(:), pointer hs_weights

privateinherited

hs_weights contains the weights for the computation of the hierarchical surplus

Definition at line 88 of file sll_m_sparse_grid_interpolator.F90.

◆ hs_weights_index

integer(kind=i32), dimension(:), pointer hs_weights_index

privateinherited

hs_weights_index is the index vector for hs_weights

Definition at line 89 of file sll_m_sparse_grid_interpolator.F90.

◆ index

integer(kind=i32), dimension(:, :), pointer index

private

2d mapping: for each 2d index l on the sparse grid, index gives the index of the first node belonging to this level

Definition at line 28 of file sll_m_sparse_grid_2d.F90.

◆ interp

type(interpolator_base_ptr), dimension(:, :), pointer interp

privateinherited

interp is the interpolator object for the 1d interpolations along the stripes

Definition at line 95 of file sll_m_sparse_grid_interpolator.F90.

◆ interp_per

type(sll_t_periodic_interpolator_1d), dimension(:, :), pointer interp_per

privateinherited

interp_per is the periodic interpolator object along the stripes

Definition at line 90 of file sll_m_sparse_grid_interpolator.F90.

◆ interpolation

integer(kind=i32) interpolation

privateinherited

specifies type of interpolation

Definition at line 76 of file sll_m_sparse_grid_interpolator.F90.

◆ length

real(kind=f64), dimension(:), pointer length

privateinherited

length defines the length of the computational domain

Definition at line 71 of file sll_m_sparse_grid_interpolator.F90.

◆ level_mapping

integer(kind=i32), dimension(:), pointer level_mapping

privateinherited

level_mapping is an index pointing the the start of each level

Definition at line 97 of file sll_m_sparse_grid_interpolator.F90.

◆ levels

integer(kind=i32), dimension(:), pointer levels

privateinherited

levels is the upper bound on the level in each direction

Definition at line 74 of file sll_m_sparse_grid_interpolator.F90.

◆ max_level

integer(kind=i32) max_level

privateinherited

max_level is the upper bound of the l_infinity norm of the level vector

Definition at line 73 of file sll_m_sparse_grid_interpolator.F90.

◆ modified

integer(kind=i32) modified

privateinherited

modified specifies the number of boundary points in sparse grid (0 for usual sparse grid, 1 for as many boundary as middle points)

Definition at line 79 of file sll_m_sparse_grid_interpolator.F90.

◆ no_basis_functions

integer(kind=i32) no_basis_functions

privateinherited

no_basis_functions is the number of different basis functions

Definition at line 77 of file sll_m_sparse_grid_interpolator.F90.

◆ order

integer(kind=i32) order

privateinherited

order it the (maximal) order of basis functions

Definition at line 75 of file sll_m_sparse_grid_interpolator.F90.

◆ size_basis

integer(kind=i32) size_basis

privateinherited

size_basis is the number of grid points

Definition at line 78 of file sll_m_sparse_grid_interpolator.F90.

◆ stripe

real(kind=f64), dimension(:), pointer stripe

privateinherited

Definition at line 87 of file sll_m_sparse_grid_interpolator.F90.

◆ stripe_out

real(kind=f64), dimension(:), pointer stripe_out

privateinherited

stripe and stripe are internal arrays to handle the 1d interpolations

Definition at line 87 of file sll_m_sparse_grid_interpolator.F90.

◆ volume

real(kind=f64) volume

privateinherited

volumne defines the volume of the computational domain

Definition at line 72 of file sll_m_sparse_grid_interpolator.F90.

Private Member Functions

Private Attributes

Detailed Description

Member Function/Subroutine Documentation

◆ basis_function()

◆ basis_function_derivative()

◆ compute_dehierarchical()

◆ compute_hierarchical_surplus()

◆ compute_linear_hierarchical_surplus()

◆ dehierarchical()

◆ dehierarchical_order()

◆ dehierarchical_part()

◆ dehierarchical_part_order()

◆ dehierarchical_stripe()

◆ displace()

◆ displace1d()

◆ extract_periodic()

◆ fg_to_sg()

◆ filter()

◆ filter_highest()

◆ free()

◆ hierarchical_part()

◆ hierarchical_part_order()

◆ hierarchical_stripe()

◆ init()

◆ initialize_sg()

◆ insert_periodic()

◆ integrate_trapezoidal()

◆ integrate_trapezoidal2()

◆ interpolate_array_disp_sgfft()

◆ interpolate_const_disp()

◆ interpolate_disp()

◆ interpolate_disp_1d_periodic()

◆ interpolate_disp_1d_periodic_for_neighbor()

◆ interpolate_disp_1d_periodic_self()

◆ interpolate_disp_linnconst_in_1d()

◆ interpolate_disp_nconst_in_1d()

◆ interpolate_from_interpolant_value()

◆ ispfft()

◆ linear_filter()

◆ set_hierarchy_info()

◆ set_hierarchy_info_boundary()

◆ spfft()

◆ todehi()

◆ todehi1d()

◆ tohierarchical()

◆ tohierarchical1d()

◆ tohierarchical1d_comp()

◆ tohira()

◆ tohira1d()

◆ tonodal()

◆ tonodal1d()

◆ tonodal1d_comp()

Member Data Documentation

◆ boundary

◆ dim

◆ eta_max

◆ eta_min

◆ fft_object

◆ hierarchy

◆ hs_weights

◆ hs_weights_index

◆ index

◆ interp

◆ interp_per

◆ interpolation

◆ length

◆ level_mapping

◆ levels

◆ max_level

◆ modified

◆ no_basis_functions

◆ order

◆ size_basis

◆ stripe

◆ stripe_out

◆ volume