KTH Toolbox: math

Files
file	math_tools.f
	Set of math related tools for KTH modules.

Functions/Subroutines
real function	mth_stepf (x)
	Step function. More...
real function	mth_rand (ix, iy, iz, ieg, xl, fcoeff)
	Give random distribution depending on position. More...

Detailed Description

Function/Subroutine Documentation

mth_rand()

real function mth_rand	(	integer	ix,
		integer	iy,
		integer	iz,
		integer	ieg,
		real, dimension(ldim)	xl,
		real, dimension(3)	fcoeff
	)

Give random distribution depending on position.

The original Nek5000 rundom number generator is implementted in ran1. This totally ad-hoc random number generator below could be preferable to the origina one for the simple reason that it gives the same initial cindition independent of the number of processors, which is important for code verification.

Parameters

[in]	ix,iy,iz	GLL point index
[in]	ieg	global element number
[in]	xl	physical point coordinates
[in]	fcoeff	function coefficients

Returns

random distribution

mth_stepf()

real function mth_stepf

(

real

x

)

Step function.

Continuous step function:

\begin{eqnarray*} stepf(x) = \left\{ \begin{array}{ll} 0 &\mbox{ if $x \leq x_{min}$} \\ \left(1+e^{\left((x-1)^{-1} + x^{-1}\right)}\right)^{-1} &\mbox{ if $x \leq x_{max}$} \\ 1 &\mbox{ if $x > x_{max}$} \end{array} \right. \end{eqnarray*}

with \( x_{min} = 0.02\) and \( x_{max}=0.98\)

Parameters

[in]

x

function argument

Returns

mth_stepf