type_fd_scheme Module Reference

The Finite Difference Scheme type definition. More...

Data Types
interface	fd_scheme_init
	Fill the weights. This has to be overriden by each scheme. More...
type	t_fd_scheme
	The Finite Difference type. More...

Functions/Subroutines
subroutine	scheme_construct (self)
	Construct a FD Scheme (will use the polymorph "init" procedure) More...
subroutine	scheme_declare_stencil (self, index_start, index_end)
	Declare a fd_scheme istarting and ending at the specified indices. More...
double precision function	scheme_apply (self, values)
	Simply apply the scheme to the given values. More...
subroutine	scheme_init_fill (self, steps)
	Simply call init() and fill() procedures. More...

Detailed Description

A finite difference scheme is defined as an array of weights associated to a serie of discrete values of a function \( \phi \). The reference element \( \phi_i \) is numbered \( 0 \). The finite difference scheme is relative to this element. Thus, relative indices are used as the array indices.

Example

weight(-2) is the weight associated to \( \phi_{i-2} \)

Note

The maximum size of any fd_scheme is defined by \( max\_index*2+1 \)

The value of fd_scheme%index_start (resp. index_end) is set to the index of the first (resp. last) usable value in fd_scheme%weight, when the scheme is built (see the various scheme constructors).

We advise the developer who develops his own scheme to read the Schemes documentation page.

Function/Subroutine Documentation

scheme_apply()

double precision function type_fd_scheme::scheme_apply	(	class(t_fd_scheme), intent(in)	self,
		double precision, dimension(:), intent(in)	values
	)

Parameters

[in,out]	self	the element
[in]	values	the input \( \phi_i \) values, where the array is of of size thisindex_end:thisindex_start.

Returns

the resulting scheme applied to the input values

scheme_construct()

subroutine type_fd_scheme::scheme_construct

(

class(t_fd_scheme), intent(inout)

self

)

Parameters

[in,out]

self

the element

scheme_declare_stencil()

subroutine type_fd_scheme::scheme_declare_stencil	(	class(t_fd_scheme), intent(inout)	self,
		integer, intent(in)	index_start,
		integer, intent(in)	index_end
	)

Parameters

[in,out]	self	the element
[in]	index_start	the istarting index, between -max_index and +max_index-1
[in]	index_end	the ending index, between -max_index+1 and +max_index

scheme_init_fill()

subroutine type_fd_scheme::scheme_init_fill	(	class(t_fd_scheme), intent(inout)	self,
		double precision, dimension(:), intent(in)	steps
	)

Parameters

[in,out]	self	the element
[in]	steps	the disc. steps