type_int_fast_scheme Module Reference

The fast Interpolation/Reconstruction scheme type definition. The efficiency is based on: More...

Functions/Subroutines
subroutine	t_int_fast_scheme_init (self)
	Initialize a 1D point interpolant. More...
subroutine	t_int_fast_compute_stencil_generic_dummy (self, step, steps, derivative)
	Dummy function as it's not available for fast schemes.
subroutine	t_int_fast_compute_stencil_generic (self, preweight, step, steps, derivative)
	Compute the stencil with a generic fast interpolation procedure. More...
double precision function	t_int_fast_interpolate_dummy (self, step, steps, values, derivative)
	Dummy function as it's not available for fast schemes.
double precision function	t_int_fast_interpolate (self, preweight, step, steps, values, derivative)
	Interpolate. More...
pure double precision function	t_int_fast_scheme_apply_dummy (self, values)
	Dummy function (existing for architecture needs). More...
double precision function	t_int_fast_scheme_apply_fast (self, values, preweights)
	Apply the corresponding scheme. Could be overriden by a specific function, but should be fast enough. More...
subroutine	t_int_fast_scheme_precompute (self)
	Init the corresponding scheme. Should do the job for all fast schemes. More...

Detailed Description

• the fixed position of the interpolation: at the face between index 0 and index 1' cells ;
• the precomputation of finite differences stencils (that are used to recover interpolants and smoothness_indicator). Those are stored in the t_int_grid_preweights structure.

This definition of the interpolation scheme.

Important\n There are 2 functions that has to be specified when deriving a new scheme:

• 'compute_preweights': what is the formula for (pre)computing the stencil's weights.
• '' Optionaly, one can also specify the 'apply_fast' function.

Note

The scheme also works (efficiently) with non uniform grids.

Todo:

MCO: gfortran is making the code crash when using the inner compute_weights() method, while ifort is fine with it. For now, use a supplied procedure given to precompte(). When the problem is solved, switch back to overloaded compute_weights call, much more elegant.

Function/Subroutine Documentation

t_int_fast_compute_stencil_generic()

subroutine type_int_fast_scheme::t_int_fast_compute_stencil_generic	(	class(t_int_fast_scheme), intent(inout)	self,
		class(t_int_grid_preweights), intent(in)	preweight,
		double precision, intent(in)	step,
		double precision, dimension(:), intent(in)	steps,
		integer, intent(in), optional	derivative
	)

Note

This can be overloaded by a deriving scheme with an optimized version

Parameters

[in,out]	self	the element
[in]	preweight	the associated t_int_grid_preweights object
[in]	step	the step where to interpolate relatively to the reference node 0
[in]	steps	the steps between the node values (of size N-1)
[in]	derivative	*(optional)* the derivative number: 0 (default) for value interpolation, 1 for first derivative, etc.

dds is indexed over [points,derivative]

t_int_fast_interpolate()

double precision function type_int_fast_scheme::t_int_fast_interpolate	(	class(t_int_fast_scheme), intent(inout)	self,
		class(t_int_grid_preweights), intent(in)	preweight,
		double precision, intent(in)	step,
		double precision, dimension(:), intent(in)	steps,
		double precision, dimension(:), intent(in)	values,
		integer, intent(in), optional	derivative
	)

Warning

the parameters 'step', 'steps' and 'derivative' are useless as we are simply fast applying the pre computed scheme.

t_int_fast_scheme_apply_dummy()

pure double precision function type_int_fast_scheme::t_int_fast_scheme_apply_dummy	(	class(t_int_fast_scheme), intent(in)	self,
		double precision, dimension(:), intent(in)	values
	)

Parameters

[in,out]	self	The element
[in]	step	ignored for fixed position
[in]	steps	The spatial disc. steps of the intervals \( I_i \) where the mean values are defined
[in]	values	The discrete (mean) values of the function

Precondition

The scheme has already been initialized

Todo:

Throw exception

t_int_fast_scheme_apply_fast()

double precision function type_int_fast_scheme::t_int_fast_scheme_apply_fast	(	class(t_int_fast_scheme), intent(in)	self,
		double precision, dimension(:), intent(in)	values,
		class(t_int_grid_preweights), intent(in)	preweights
	)

Parameters

[in]

values

The discrete (mean) values of the function

Precondition

The scheme has already been initialized

t_int_fast_scheme_init()

subroutine type_int_fast_scheme::t_int_fast_scheme_init

(

class(t_int_fast_scheme), intent(inout)

self

)

See also

t_int_scheme_init

t_int_fast_scheme_precompute()

subroutine type_int_fast_scheme::t_int_fast_scheme_precompute

(

class(t_int_fast_scheme), intent(inout)

self

)

Parameters

[in]

self

The scheme.