Semi-Lagrangian Library: sll_m_spline_interpolator_1d Module Reference

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Semi-Lagrangian Library

Modular library for kinetic and gyrokinetic simulations of plasmas in fusion energy devices.

Description

Interpolator for 1D splines of arbitrary degree, on uniform and non-uniform grids.

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

Derived types and interfaces
type	sll_t_spline_interpolator_1d
	1D spline interpolator More...

Functions/Subroutines
subroutine, public	sll_s_spline_1d_compute_num_cells (degree, bc_xmin, bc_xmax, nipts, ncells)
	Calculate number of cells from number of interpolation points. More...

subroutine	s_spline_interpolator_1d__init (self, bspl, bc_xmin, bc_xmax)
	Initialize a 1D spline interpolator object. More...

subroutine	s_spline_interpolator_1d__free (self)
	Destroy local objects and free allocated memory. More...

subroutine	s_spline_interpolator_1d__get_interp_points (self, tau)
	Get coordinates of interpolation points (1D grid) More...

subroutine	s_spline_interpolator_1d__compute_interpolant (self, spline, gtau, derivs_xmin, derivs_xmax)
	Compute interpolating 1D spline. More...

subroutine	s_build_system (self, matrix)
	Private subroutine for assembling and factorizing linear system for any kind of boundary conditions at xmin and xmax. More...

subroutine	s_compute_interpolation_points_uniform (self, tau)

subroutine	s_compute_num_diags_uniform (self, kl, ku)

subroutine	s_compute_interpolation_points_non_uniform (self, tau)

subroutine	s_compute_num_diags_non_uniform (self, kl, ku)

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

integer, dimension(1:3), parameter	allowed_bcs = [sll_p_periodic, sll_p_hermite, sll_p_greville]
	Allowed boundary conditions. More...

Function/Subroutine Documentation

◆ s_build_system()

subroutine sll_m_spline_interpolator_1d::s_build_system	(	class(sll_t_spline_interpolator_1d), intent(in)	self,
		class(sll_c_spline_matrix), intent(inout)	matrix
	)

private

Private subroutine for assembling and factorizing linear system for any kind of boundary conditions at xmin and xmax.

Parameters

[in]	self	1D spline interpolator object
[in,out]	matrix	generic 'spline' matrix (dense/banded/periodic-banded)

Definition at line 330 of file sll_m_spline_interpolator_1d.F90.

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◆ s_compute_interpolation_points_non_uniform()

subroutine sll_m_spline_interpolator_1d::s_compute_interpolation_points_non_uniform	(	class(sll_t_spline_interpolator_1d), intent(in)	self,
		real(wp), dimension(:), intent(out), allocatable	tau
	)

private

Definition at line 546 of file sll_m_spline_interpolator_1d.F90.

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◆ s_compute_interpolation_points_uniform()

subroutine sll_m_spline_interpolator_1d::s_compute_interpolation_points_uniform	(	class(sll_t_spline_interpolator_1d), intent(in)	self,
		real(wp), dimension(:), intent(out), allocatable	tau
	)

private

Definition at line 427 of file sll_m_spline_interpolator_1d.F90.

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◆ s_compute_num_diags_non_uniform()

subroutine sll_m_spline_interpolator_1d::s_compute_num_diags_non_uniform	(	class(sll_t_spline_interpolator_1d), intent(in)	self,
		integer, intent(out)	kl,
		integer, intent(out)	ku
	)

private

Definition at line 627 of file sll_m_spline_interpolator_1d.F90.

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◆ s_compute_num_diags_uniform()

subroutine sll_m_spline_interpolator_1d::s_compute_num_diags_uniform	(	class(sll_t_spline_interpolator_1d), intent(in)	self,
		integer, intent(out)	kl,
		integer, intent(out)	ku
	)

private

Definition at line 513 of file sll_m_spline_interpolator_1d.F90.

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◆ s_spline_interpolator_1d__compute_interpolant()

subroutine sll_m_spline_interpolator_1d::s_spline_interpolator_1d__compute_interpolant	(	class(sll_t_spline_interpolator_1d), intent(in)	self,
		type(sll_t_spline_1d), intent(inout)	spline,
		real(wp), dimension(:), intent(in)	gtau,
		real(wp), dimension(:), intent(in), optional	derivs_xmin,
		real(wp), dimension(:), intent(in), optional	derivs_xmax
	)

private

Compute interpolating 1D spline.

Compute coefficients of 1D spline that interpolates function values on grid. If Hermite BCs are used, function derivatives at appropriate boundary are also needed.

Parameters

[in]	self	1D spline interpolator
[in,out]	spline	1D spline
[in]	gtau	function values of interpolation points
[in]	derivs_xmin	(optional) array with boundary conditions at xmin
[in]	derivs_xmax	(optional) array with boundary conditions at xmax

Definition at line 243 of file sll_m_spline_interpolator_1d.F90.

◆ s_spline_interpolator_1d__free()

subroutine sll_m_spline_interpolator_1d::s_spline_interpolator_1d__free ( class(sll_t_spline_interpolator_1d), intent(inout) self )

private

Destroy local objects and free allocated memory.

Parameters

[in,out] self 1D spline interpolator

Definition at line 202 of file sll_m_spline_interpolator_1d.F90.

◆ s_spline_interpolator_1d__get_interp_points()

subroutine sll_m_spline_interpolator_1d::s_spline_interpolator_1d__get_interp_points	(	class(sll_t_spline_interpolator_1d), intent(in)	self,
		real(wp), dimension(:), intent(out), allocatable	tau
	)

private

Get coordinates of interpolation points (1D grid)

Parameters

[in]	self	1D spline interpolator
[out]	tau	x coordinates of interpolation points

Definition at line 221 of file sll_m_spline_interpolator_1d.F90.

◆ s_spline_interpolator_1d__init()

subroutine sll_m_spline_interpolator_1d::s_spline_interpolator_1d__init	(	class(sll_t_spline_interpolator_1d), intent(out)	self,
		class(sll_c_bsplines), intent(in), target	bspl,
		integer, intent(in)	bc_xmin,
		integer, intent(in)	bc_xmax
	)

private

Initialize a 1D spline interpolator object.

Parameters

[out]	self	1D spline interpolator
[in]	bspl	B-splines (basis)
[in]	bc_xmin	boundary condition at xmin
[in]	bc_xmax	boundary condition at xmax

Definition at line 124 of file sll_m_spline_interpolator_1d.F90.

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◆ sll_s_spline_1d_compute_num_cells()

subroutine, public sll_m_spline_interpolator_1d::sll_s_spline_1d_compute_num_cells	(	integer, intent(in)	degree,
		integer, intent(in)	bc_xmin,
		integer, intent(in)	bc_xmax,
		integer, intent(in)	nipts,
		integer, intent(out)	ncells
	)

Calculate number of cells from number of interpolation points.

Important for parallelization: for given spline degree and BCs, calculate the number of grid cells that yields the desired number of interpolation points

Parameters

[in]	degree	spline degree
[in]	bc_xmin	boundary condition type at left boundary (x=xmin)
[in]	bc_xmax	boundary condition type at right boundary (x=xmax)
[in]	nipts	desired number of interpolation points
[out]	ncells	calculated number of cells in domain

Definition at line 84 of file sll_m_spline_interpolator_1d.F90.

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Variable Documentation

◆ allowed_bcs

integer, dimension(1:3), parameter allowed_bcs = [sll_p_periodic, sll_p_hermite, sll_p_greville]

private

Allowed boundary conditions.

Definition at line 39 of file sll_m_spline_interpolator_1d.F90.

◆ wp

integer, parameter wp = f64

private

Working precision.

Definition at line 36 of file sll_m_spline_interpolator_1d.F90.

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