pb3d_utilities Module Reference

Numerical utilities related to PB3D operations. More...

Interfaces and Types
interface	conv_1d2nd
	Converts 1-D to n-D variables. More...

Functions/Subroutines
integer function, dimension(3), public	setup_par_id (grid, rich_lvl_max, rich_lvl_loc, tot_rich, par_lim, par_id_mem)
	Setup parallel id. More...
integer function, dimension(2), public	setup_rich_id (rich_lvl_max, tot_rich)
	Returns richardson id. More...

Detailed Description

Numerical utilities related to PB3D operations.

Function/Subroutine Documentation

setup_par_id()

integer function, dimension(3), public pb3d_utilities::setup_par_id	(	type(grid_type), intent(in)	grid,
		integer, intent(in)	rich_lvl_max,
		integer, intent(in)	rich_lvl_loc,
		logical, intent(in), optional	tot_rich,
		integer, dimension(2), intent(in), optional	par_lim,
		integer, dimension(2), intent(inout), optional	par_id_mem
	)

Setup parallel id.

The parallel id consists of:

• par_id(1): start index
• par_id(2): end index
• par_id(3): stride

These are set up by considering the transformation between a point \(r \in (1\ldots n)\) in the local variable, with corresponding indices \((a\ldots b)\) indicated by par_lim in the HDF5 variable in memory, so that \(n = b-a+1\):

\[p + k s = a + r - 1,\]

where \(k\) is an integer, \(s\) is the stride for Richardson level \(i\) (with max. level \(I\)):

\[\begin{aligned} s &= 2^{I-1} \ \text{for} \ i = 1 \\ &= 2^{I-i+1} \ \text{for} \ i > 1 \end{aligned}\]

and where \(p\) is the starting point in the HDF5 variables:

\[\begin{aligned} p &= 1 \ \text{for} \ i = 1 \\ &= 1 + s/2 \ \text{for} \ i > 1 \end{aligned}\]

Therefore, the minimum possible \(r\) lies in \((0..s-1)\):

\[\mod(r-1,s) = r_\text{min}-1, \]

which leads to

\[r_\text{min} = 1 + \mod(p-a,s). \]

The maximum possible \(r\), then, lies in \((n-s+1..n)\), which leads to:

\[ r_\text{max} = n - s + 1 + \mod(p-b-1,s). \]

These limits and the strides are saved in par_id = \(\vec{r} = \begin{pmatrix}r_\text{min}\\ r_\text{max}\end{pmatrix}\).

If the optional indices \(a\) and \(b\) are not given they are assumed to be 1 and \(n\), with \(n = 1+ks\), which simplifies the equations to:

\[\begin{aligned} r_\text{min} &= p \\ r_\text{max} &= n-p+1 . \end{aligned}\]

Optionally, the indices in the HDF5 arrays can also be returned in par_id_mem = \(\begin{pmatrix}R_\text{min}\\ R_\text{max}\end{pmatrix}\). These are equal to \(k-1\), where \(k\) is the integer refered to above:

\[\vec{R} = 1 + \frac{a-1-p+\vec{r}}{s}, \]

where the addition between a vector and a scalar should be seen as the element-wise operation.

Parameters

[in]	rich_lvl_max	maximum Richardson level
[in]	rich_lvl_loc	local Richardson level
[in]	tot_rich	whether to combine with previous Richardson levels
[in]	par_lim	limits (a..b) of variable requested
[in,out]	par_id_mem	parallel id in memory

Returns

parallel id

Definition at line 181 of file PB3D_utilities.f90.

setup_rich_id()

integer function, dimension(2), public pb3d_utilities::setup_rich_id	(	integer, intent(in)	rich_lvl_max,
		logical, intent(in), optional	tot_rich
	)

Returns richardson id.

rich_id has the following structure:

• rich_id(1): start Richardson level
• rich_id(2): end Richardson level

  Parameters

  [in]	rich_lvl_max	maximum Richardson level
  [in]	tot_rich	whether to combine with previous Richardson levels

  Returns

  Richardson id

Definition at line 234 of file PB3D_utilities.f90.