Description

Interpolator for 2D tensor-product splines of arbitrary degree, on uniform and non-uniform grids (directions are independent)

Author: Yaman Güçlü - IPP Garching; Edoardo Zoni - IPP Garching

Derived types and interfaces
type	sll_t_spline_2d_boundary_data
	Container for 2D boundary condition data: . x1-derivatives at x1_min and x1_max, for all values of x2; . x2-derivatives at x2_min and x2_max, for all values of x1; . mixed derivatives at the four corners a,b,c,d. More...

type	sll_t_spline_interpolator_2d
	2D tensor-product spline interpolator More...

Functions/Subroutines
subroutine, public	sll_s_spline_2d_compute_num_cells (degree, bc_xmin, bc_xmax, nipts, ncells)
	Calculate number of cells from number of interpolation points. More...

subroutine	s_spline_interpolator_2d__init (self, bspl1, bspl2, bc_xmin, bc_xmax)
	Initialize a 2D tensor-product spline interpolator object. More...

subroutine	s_spline_interpolator_2d__free (self)
	Destroy local objects and free allocated memory. More...

subroutine	s_spline_interpolator_2d__get_interp_points (self, tau1, tau2)
	Get coordinates of interpolation points (2D tensor grid) More...

subroutine	s_spline_interpolator_2d__compute_interpolant (self, spline, gtau, boundary_data)
	Compute interpolating 2D spline. More...

Variables
integer, parameter	wp = f64
	Working precision. More...

Function/Subroutine Documentation

◆ s_spline_interpolator_2d__compute_interpolant()

subroutine sll_m_spline_interpolator_2d::s_spline_interpolator_2d__compute_interpolant	(	class(sll_t_spline_interpolator_2d), intent(inout)	self,
		type(sll_t_spline_2d), intent(inout)	spline,
		real(wp), dimension(:, :), intent(in)	gtau,
		type(sll_t_spline_2d_boundary_data), intent(in), optional	boundary_data
	)

private

Compute interpolating 2D spline.

Compute coefficients of 2D tensor-product spline that interpolates function values on grid. If Hermite BCs are used, function derivatives at appropriate boundaries are also needed.

Parameters

[in,out]	self	2D tensor-product spline interpolator
[in,out]	spline	2D tensor-product spline
[in]	gtau	function values of interpolation points
[in]	boundary_data	(optional) structure with boundary conditions

Definition at line 241 of file sll_m_spline_interpolator_2d.F90.

◆ s_spline_interpolator_2d__free()

subroutine sll_m_spline_interpolator_2d::s_spline_interpolator_2d__free ( class(sll_t_spline_interpolator_2d), intent(inout) self )

private

Destroy local objects and free allocated memory.

Parameters

[in,out] self 2D tensor-product spline interpolator

Definition at line 194 of file sll_m_spline_interpolator_2d.F90.

◆ s_spline_interpolator_2d__get_interp_points()

subroutine sll_m_spline_interpolator_2d::s_spline_interpolator_2d__get_interp_points	(	class(sll_t_spline_interpolator_2d), intent(in)	self,
		real(wp), dimension(:), intent(out), allocatable	tau1,
		real(wp), dimension(:), intent(out), allocatable	tau2
	)

private

Get coordinates of interpolation points (2D tensor grid)

Parameters

[in]	self	2D tensor-product spline interpolator
[out]	tau1	x1 coordinates of interpolation points
[out]	tau2	x2 coordinates of interpolation points

Definition at line 219 of file sll_m_spline_interpolator_2d.F90.

◆ s_spline_interpolator_2d__init()

subroutine sll_m_spline_interpolator_2d::s_spline_interpolator_2d__init	(	class(sll_t_spline_interpolator_2d), intent(out)	self,
		class(sll_c_bsplines), intent(in), target	bspl1,
		class(sll_c_bsplines), intent(in), target	bspl2,
		integer, dimension(2), intent(in)	bc_xmin,
		integer, dimension(2), intent(in)	bc_xmax
	)

private

Initialize a 2D tensor-product spline interpolator object.

Parameters

[out]	self	2D tensor-product spline interpolator
[in]	bspl1	B-splines (basis) along x1 direction
[in]	bspl2	B-splines (basis) along x2 direction
[in]	bc_xmin	boundary conditions at x1_min and x2_min
[in]	bc_xmax	boundary conditions at x1_max and x2_max

Definition at line 141 of file sll_m_spline_interpolator_2d.F90.

◆ sll_s_spline_2d_compute_num_cells()

subroutine, public sll_m_spline_interpolator_2d::sll_s_spline_2d_compute_num_cells	(	integer, dimension(2), intent(in)	degree,
		integer, dimension(2), intent(in)	bc_xmin,
		integer, dimension(2), intent(in)	bc_xmax,
		integer, dimension(2), intent(in)	nipts,
		integer, dimension(2), intent(out)	ncells
	)

Calculate number of cells from number of interpolation points.

Important for parallelization: for given spline degree and BCs, calculate the numbers of grid cells along x1 and x2 that yield the desired number of interpolation points along x1 and x2

Parameters

[in]	degree	spline degrees along x1 and x2
[in]	bc_xmin	boundary conditions at x1_min and x2_min
[in]	bc_xmax	boundary conditions at x1_max and x2_max
[in]	nipts	desired number of interpolation points along x1 and x2
[out]	ncells	calculated number of grid cells along x1 and x2