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docs:utils:findorbit [2009/02/03 08:29]
gibson
docs:utils:findorbit [2010/02/02 07:55] (current)
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   -Ng       ​--Ngmres ​           <​int> ​      ​default == 40          max number of GMRES iterations per restart   -Ng       ​--Ngmres ​           <​int> ​      ​default == 40          max number of GMRES iterations per restart
   -d        --delta ​            <​real> ​     default == 0.01        initial radius of trust region   -d        --delta ​            <​real> ​     default == 0.01        initial radius of trust region
-  -sx       --x-sign ​                                              ​change u,x sign +  -sigma    ​--sigma             <string                          file containing symmetry of relative eqb/orb 
-  -sy       ​--y-sign ​                                              ​change v,y sign +  -symms    ​--symmetries ​       ​<string                          constrain u(t) to invariant subspace generated ​by symmetries in listed file, arg is filename
-  -sz       ​--z-sign ​                                              ​change w,z sign +
-  -ax       ​--axshift ​          <real     ​default == 0           ​translate by ax*Lx +
-  -az       --azshift ​          <real     ​default == 0           ​translate ​by az*Lz+
   -R        --Reynolds ​         <​real> ​     default == 400         ​Reynolds number   -R        --Reynolds ​         <​real> ​     default == 400         ​Reynolds number
   -vdt      --variableDt ​                                          ​adjust dt to keep CFLmin<​=CFL<​CFLmax   -vdt      --variableDt ​                                          ​adjust dt to keep CFLmin<​=CFL<​CFLmax
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 [[docs:​utils:​findorbit:​alloptions|complete option list]] [[docs:​utils:​findorbit:​alloptions|complete option list]]
  
-==== example 1: equilibrium ​ ====+The most important options are -orb, -eqb, -rel, and -ax and -az. You use these to specify the 
 +kind of solution you are searching for.  
 + 
 +  * -orb and -eqb are mutually exclusive and you must pick one (search for periodic orbit or equilibrium) 
 +  * -eqb leaves the integration time fixed 
 +  * -orb adds the integration time T to the search space 
 +  * -rel modifies -orb / -eqb, makes the search for a relative periodic orbit or relative equilibrium (traveling wave), by adding finite-time phase shift variables ''​ax''​ and ''​az''​ to the search space 
 +  * -sigma <​filename>​ sets the initial guess (if -rel) or fixed value (if not -rel) of the symmetry \sigma  
 +  * -symms <​filename>​ constrains the search to an invariant subspace. The file is a list of generators for the isotropy group. ​  
 + 
 +In all cases we search for a solution of  
 + 
 +<​latex>​ 
 + ​\sigma f^T(u) - u = 0 
 +</​latex>​ 
 + 
 +where  
 + 
 +<​latex>​ 
 +  \sigma [u,​v,​w](x,​y,​z) \rightarrow s [s_x u, \, s_y v, \, s_z w](s_x x + a_x/L_x, \, s_y y, \, s_z z + a_z/L_z) 
 +</​latex>​ 
 + 
 +(will continue later today.... /2009-06-08 jfg) 
 + 
 +====== Usage examples ====== 
 + 
 +===== equilibrium ​=====
 Find an equilibrium from initial guess ''​guess.ff''​ Find an equilibrium from initial guess ''​guess.ff''​
 <​code>​ <​code>​
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 </​code>​ </​code>​
  
-==== example 2: traveling wave ====+====traveling wave =====
 Find a traveling wave (relative equilibrium) from initial guess ''​guess.ff'',​ with initial guess for wavespeed Find a traveling wave (relative equilibrium) from initial guess ''​guess.ff'',​ with initial guess for wavespeed
-specified in terms of finite shifts (ax/Lx, az/Lz) in finite time T (giving wavespeeds are ax/(Lx T), az/(Lz T)+specified in terms of finite shifts (ax/Lx, az/Lz) in finite time T. Equivalent to wavespeed ​(cx, cz) =  1/(ax/Lx, az/Lz).
 <​code>​ <​code>​
   findorbit -eqb -rel -ax 0.3  -az 0.4 -T 10 guess.ff   findorbit -eqb -rel -ax 0.3  -az 0.4 -T 10 guess.ff
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 the ''​--rel''​ option adds the finite shift variables (ax, az) to the search space. the ''​--rel''​ option adds the finite shift variables (ax, az) to the search space.
  
-=== example 3: periodic orbit ===+===== periodic orbit =====
 Find a periodic orbit with initial guess for period T=83 Find a periodic orbit with initial guess for period T=83
 <​code>​ <​code>​
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 </​code>​ </​code>​
  
-=== example 4: relative periodic orbit===+===== relative periodic orbit ====
 Find a relative periodic orbit with initial guess of a shift by Lz/4 every period T=83 Find a relative periodic orbit with initial guess of a shift by Lz/4 every period T=83
 <​code>​ <​code>​
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 </​code>​ </​code>​
  
 +It takes half a minute'​s thinking to determine the right -orb, -eqb, -rel, -ax, and -az options based on the type of search you want.
  
 ====== Mathematics ====== ====== Mathematics ======
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 Beyonce, "​Single Ladies",​ http://​www.youtube.com/​watch?​v=8mVEGfH4s5g Beyonce, "​Single Ladies",​ http://​www.youtube.com/​watch?​v=8mVEGfH4s5g
- 
docs/utils/findorbit.1233678543.txt.gz · Last modified: 2009/02/03 08:29 by gibson