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.