Newton.f90 - Revision history

Apwillis at 10:43, 12 March 2018

2018-03-12T10:43:22Z

← Older revision		Revision as of 03:43, 12 March 2018
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	The outputs from each continuation step are moved to directories		The outputs from each continuation step are moved to directories
	<tt>0001</tt>, <tt>0002</tt>, <tt>0003</tt>... and a brief summary		<tt>0001</tt>, <tt>0002</tt>, <tt>0003</tt>... and a brief summary
	of the data in each is written to <tt>newton.dat_ct</tt>. It columns are		of the data in each is written to <tt>newton.dat_ct</tt>. Its columns are
	number of continuation step (= directory number),		number of continuation step (= directory number),
	number of newton iterations required,		number of newton iterations required,

Apwillis at 10:42, 12 March 2018

2018-03-12T10:42:15Z

← Older revision		Revision as of 03:42, 12 March 2018
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	If the descending eigenvalues are e.g.		If the descending eigenvalues are e.g.
	real, complex, real, real, complex, real,...		real, complex, real, real, complex, real,...
	then the respective state numbers are		then the respective state numbers for the eigenvectors are
	1001, 1002+3, 1004, 1005, 1006+7, 1008,...		1001, 1002+3, 1004, 1005, 1006+7, 1008,...
	where 1002+3 are real and imaginary components respectively.		where 1002+3 are real and imaginary components respectively.

Apwillis: /* Outputs */

2018-03-12T10:39:38Z

Outputs

← Older revision		Revision as of 03:39, 12 March 2018
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	Along the top: ndts, max GMRES iterations, degrees of freedom.		Along the top: ndts, max GMRES iterations, degrees of freedom.

	~~Columns~~: Newton iteration, GMRES iterations taken,		Then columns: Newton iteration, GMRES iterations taken,
	$\|\|g(x(T))-x(0)\|\|$, $\delta$,		$\|\|g(x(T))-x(0)\|\|$, $\delta$,
	$\|\|g(x(T))-x(0)\|\|\,/\,\|\|x(0)\|\|$ and $\|\|x(0)\|\|$, where $g(x)$ denotes the spatial shift of $x$ (backwards by <tt>sz</tt>).		$\|\|g(x(T))-x(0)\|\|\,/\,\|\|x(0)\|\|$ and $\|\|x(0)\|\|$, where $g(x)$ denotes the spatial shift of $x$ (backwards by <tt>sz</tt>).

Apwillis at 10:36, 12 March 2018

2018-03-12T10:36:37Z

← Older revision		Revision as of 03:36, 12 March 2018
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	Continuation restarting from two previous steps is possible.		Continuation restarting from two previous steps is possible.
	If <tt>state10.cdf.in</tt> is present, then for example <tt>params_ct.in</tt>		If <tt>state10.cdf.in</tt> is present, then for example, <tt>params_ct.in</tt>
	2 3 1		2 3 1
	1.5		1.5

Apwillis at 10:32, 12 March 2018

2018-03-12T10:32:41Z

← Older revision		Revision as of 03:32, 12 March 2018
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	Continuation restarting from two previous steps is possible.		Continuation restarting from two previous steps is possible.
	If <tt>~~state0010~~.cdf.in</tt> is present, then for example <tt>params_ct.in</tt>		If <tt>state10.cdf.in</tt> is present, then for example <tt>params_ct.in</tt>
	2 3 1		2 3 1
	1.5		1.5

Apwillis at 10:23, 12 March 2018

2018-03-12T10:23:34Z

← Older revision		Revision as of 03:23, 12 March 2018
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	1001, 1002+3, 1004, 1005, 1006+7, 1008,...		1001, 1002+3, 1004, 1005, 1006+7, 1008,...
	where 1002+3 are real and imaginary components respectively.		where 1002+3 are real and imaginary components respectively.

			==== Continuation of solutions ====

			If the file <tt>params_ct.in</tt> is present, the code will attempt
			continuation from the input <tt>state.cdf.in</tt>. A typical <tt>params_ct.in</tt> is:
			2 3 1
			-50.
			On the first line, 2 and 3 are the minimum and maximum number of
			newton iterations per continuation step, and 1 indicates the
			parameter to be continued, 1==$Re$, 2==$\alpha$.
			On the second line -50 is the size of the first step in the
			chosen parameter from the (assumed to be converged) input
			<tt>state.cdf.in</tt>.

			The outputs from each continuation step are moved to directories
			<tt>0001</tt>, <tt>0002</tt>, <tt>0003</tt>... and a brief summary
			of the data in each is written to <tt>newton.dat_ct</tt>. It columns are
			number of continuation step (= directory number),
			number of newton iterations required,
			$Re$, $\alpha$, wavespeed $c$.

			Continuation restarting from two previous steps is possible.
			If <tt>state0010.cdf.in</tt> is present, then for example <tt>params_ct.in</tt>
			2 3 1
			1.5
			asks the code to start from a linear extrapolation: if
			<tt>state.cdf.in</tt>=$u_0$ and <tt>state10.cdf.in</tt>=$u_1$, then
			it would restart with initial guess $u=u_1+ 1.5*(u_1-u_0)$.
			The corresponding extrapolation for the initial shifts should be supplied
			in <tt>shifts.in</tt>.

			Note: actual shifts should be given for the starting point. Do not use the <tt>-1.</tt> flag in <tt>shifts.in</tt>.

Apwillis at 11:27, 10 November 2017

2017-11-10T11:27:57Z

← Older revision		Revision as of 04:27, 10 November 2017
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	{{latexPreamble}}		{{latexPreamble}}

			This page describes usage of the Newton solver for pipe flow. See also the generic routine [[File:NewtonHook.f90]].

	==== Inputs ====		==== Inputs ====

Apwillis at 15:14, 1 September 2017

2017-09-01T15:14:51Z

← Older revision		Revision as of 08:14, 1 September 2017
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	$\delta$ is the step size being taken (trust-region approach).		$\delta$ is the step size being taken (trust-region approach).

	Other outputs:		'''Other outputs''':

	<tt>shift.dat</tt> records the shift at each iteration. Each line		* <tt>shift.dat</tt> records the shift at each iteration. Each line is like <tt>shifts.in</tt> preceded by the iteration number.
	is like <tt>shifts.in</tt> preceded by the iteration number.

	<tt>state0???.cdf.dat</tt> is the state at each iteration.		* <tt>state0???.cdf.dat</tt> is the state at each iteration.

	<tt>state1000.cdf.dat</tt> is the converged state.		* <tt>state1000.cdf.dat</tt> is the converged state.

	<tt>state1001.cdf.dat, state1002.cdf.dat...</tt> are eigenvectors.		* <tt>state1001.cdf.dat, state1002.cdf.dat...</tt> are eigenvectors.

	Eigenvalues are found in <tt>arnoldi.dat</tt>.		Eigenvalues are found in <tt>arnoldi.dat</tt>.

Apwillis at 13:53, 13 December 2016

2016-12-13T13:53:48Z

← Older revision		Revision as of 06:53, 13 December 2016
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	<tt>state1001.cdf.dat, state1002.cdf.dat...</tt> are eigenvectors.		<tt>state1001.cdf.dat, state1002.cdf.dat...</tt> are eigenvectors.

			Eigenvalues are found in <tt>arnoldi.dat</tt>.
	If the descending eigenvalues are e.g.		If the descending eigenvalues are e.g.
	real, complex, real, real, complex, real,...		real, complex, real, real, complex, real,...

Apwillis: Created page with "{{latexPreamble}} ==== Inputs ==== This is the contents of a typical `params.in` file: 0 150 100 1 5 3d-6 -1d0 1d-7 1d+7 1d-3 1d-6 You are unlikely to need ..."

2016-12-13T13:52:25Z

Created page with "{{latexPreamble}} ==== Inputs ==== This is the contents of a typical <tt>params.in</tt> file: 0 150 100 1 5 3d-6 -1d0 1d-7 1d+7 1d-3 1d-6 You are unlikely to need ..."

New page

{{latexPreamble}}

==== Inputs ====

This is the contents of a typical <tt>params.in</tt> file:
0
150 100 1 5
3d-6
-1d0 1d-7 1d+7
1d-3 1d-6
You are unlikely to need to change these settings, except perhaps
the value 5, which is the number of leading eigenvalues that
are calculated if newton converges.
150 is the max number of GMRES iterations. If it is taking this
many iterations (per Newton iteration), convergence is unlikely.
100 is the max number of Newton iterations.

A typical <tt>shifts.in</tt> file:
10000
0. -1. 100.
Respectively:
* ndts - Number of timesteps to take in period T,
* sth - shift in $\theta$,
* sz - shift in $z$,
* T - period.
A value <tt>-1.</tt> for <tt>sz</tt> informs the code to search for a
suitable initial guess for the shift.

The timestep size follows from the inputs, T/ndts (=0.01 in the example) which is stretched slightly if
T changes. The shifts are shifts ''backwards'', i.e. if a travelling wave
has phase speed c (>0), then after time T we expect sz=c*T (>0).

The value T is arbitrary for a travelling wave, but T=10 usually works
well. If the number of GMRES iterations is observed to be large
(more than 50), try doubling T. If it is small (less than 10), halve
T.

The initial guess should be in <tt>state.cdf.in</tt>.

==== Outputs ====

The output file of most interest is <tt>newton.dat</tt>:
14679 150 279939
0 0 0.21542E-02 0.21542E-03 0.25636E-01 0.84033E-01
1 18 0.46324E-03 0.21542E-03 0.55202E-02 0.83918E-01
2 19 0.12734E-03 0.83324E-04 0.15176E-02 0.83905E-01
3 23 0.20499E-04 0.83324E-04 0.24427E-03 0.83920E-01
Along the top: ndts, max GMRES iterations, degrees of freedom.

Columns: Newton iteration, GMRES iterations taken,
$||g(x(T))-x(0)||$, $\delta$,
$||g(x(T))-x(0)||\,/\,||x(0)||$ and $||x(0)||$, where $g(x)$ denotes the spatial shift of $x$ (backwards by <tt>sz</tt>).

The penultimate column, relative error, is the most important one.
If it drops below 3d-6, this is usually considered sufficient.
$\delta$ is the step size being taken (trust-region approach).

Other outputs:

<tt>shift.dat</tt> records the shift at each iteration. Each line
is like <tt>shifts.in</tt> preceded by the iteration number.

<tt>state0???.cdf.dat</tt> is the state at each iteration.

<tt>state1000.cdf.dat</tt> is the converged state.

<tt>state1001.cdf.dat, state1002.cdf.dat...</tt> are eigenvectors.

If the descending eigenvalues are e.g.
real, complex, real, real, complex, real,...
then the respective state numbers are
1001, 1002+3, 1004, 1005, 1006+7, 1008,...
where 1002+3 are real and imaginary components respectively.