neumann_spline_quadrature.hpp File Reference

File providing quadrature coefficients via a spline quadrature. More...

#include <cassert>
#include <ddc/ddc.hpp>
#include <ddc/kernels/splines.hpp>
#include <sll/matrix.hpp>
#include "ddc_aliases.hpp"

Go to the source code of this file.

Functions
template<class ExecSpace , class Grid1D , class SplineBuilder >
DFieldMem< IdxRange< Grid1D >, typename ExecSpace::memory_space >	neumann_spline_quadrature_coefficients_1d (IdxRange< Grid1D > const &idx_range, SplineBuilder const &builder)
	Get the spline quadrature coefficients in 1D.
template<class ExecSpace , class... DDims, class... SplineBuilders>
DFieldMem< IdxRange< DDims... >, typename ExecSpace::memory_space >	neumann_spline_quadrature_coefficients (IdxRange< DDims... > const &idx_range, SplineBuilders const &... builders)
	Get the spline quadrature coefficients in ND from N 1D quadrature coefficient.

Detailed Description

File providing quadrature coefficients via a spline quadrature.

Function Documentation

neumann_spline_quadrature_coefficients_1d()

template<class ExecSpace , class Grid1D , class SplineBuilder >

DFieldMem< IdxRange< Grid1D >, typename ExecSpace::memory_space > neumann_spline_quadrature_coefficients_1d	(	IdxRange< Grid1D > const &	idx_range,
		SplineBuilder const &	builder
	)

Get the spline quadrature coefficients in 1D.

This function calculates the quadrature coefficients which define a quadrature equivalent to calculating and integrating a spline approximation of a function. The spline approximation would be calculated with homogeneous Neumann boundary conditions. This method of defining quadrature coefficients is described in section Emily Bourne's thesis[1].

[1] Non-Uniform Numerical Schemes for the Modelling of Turbulence in the 5D GYSELA Code Emily Bourne, December 2022-

Parameters

[in]	idx_range	The index range on which the splines quadrature will be carried out.
[in]	builder	The spline builder used for the quadrature coefficients.

Returns

The quadrature coefficients for the method defined on the provided index range.

neumann_spline_quadrature_coefficients()

template<class ExecSpace , class... DDims, class... SplineBuilders>

DFieldMem< IdxRange< DDims... >, typename ExecSpace::memory_space > neumann_spline_quadrature_coefficients	(	IdxRange< DDims... > const &	idx_range,
		SplineBuilders const &...	builders
	)

Get the spline quadrature coefficients in ND from N 1D quadrature coefficient.

This function calculates the quadrature coefficients which define a quadrature equivalent to calculating and integrating a spline approximation of a function. The spline approximation would be calculated with homogeneous Neumann boundary conditions.

Parameters

[in]	idx_range	The index range on which the coefficients will be defined.
[in]	builders	The spline builder used for the quadrature coefficients in the different dimensions.

Returns

The coefficients which define the spline quadrature method in ND.