docs:utils:findorbit
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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 | ||
| Line 33: | Line 30: | ||
| [[docs:utils:findorbit:alloptions|complete option list]] | [[docs:utils:findorbit:alloptions|complete option list]] | ||
| - | ===== Usage examples ===== | + | 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. | ||
| - | ==== equilibrium ==== | + | * -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> | ||
| Line 41: | Line 62: | ||
| </code> | </code> | ||
| - | ==== 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/T (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 | ||
| Line 49: | Line 70: | ||
| 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. | ||
| - | ==== 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> | ||
| Line 55: | Line 76: | ||
| </code> | </code> | ||
| - | ==== 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> | ||
| Line 61: | Line 82: | ||
| </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 ====== | ||
| Line 214: | Line 235: | ||
| Beyonce, "Single Ladies", http://www.youtube.com/watch?v=8mVEGfH4s5g | Beyonce, "Single Ladies", http://www.youtube.com/watch?v=8mVEGfH4s5g | ||
| - | |||
docs/utils/findorbit.1233678691.txt.gz · Last modified: 2009/02/03 08:31 by gibson
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