docs:utils:findorbit
====== Differences ====== This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision | ||
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docs:utils:findorbit [2009/02/11 08:38] 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 | ||
| Line 39: | Line 36: | ||
| * -eqb leaves the integration time fixed | * -eqb leaves the integration time fixed | ||
| * -orb adds the integration time T to the search space | * -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 the finite-time phase shift variables ''ax'' and ''az'' 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 |
| - | * -ax and -az specify a fixed or initial guess finite-time phase shifts for the solution (depending on whether -rel is specified) | + | * -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 | In all cases we search for a solution of | ||
| <latex> | <latex> | ||
| - | \tau_{a_x, a_z} f^T(u) - u = 0 | + | \sigma f^T(u) - u = 0 |
| </latex> | </latex> | ||
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| <latex> | <latex> | ||
| - | \tau_{a_x, a_z} [u,v,w](x,y,z) \rightarrow [u,v,w](x+a_x/L_x, \, y, \, z+a_z/L_z) | + | \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> | </latex> | ||
| - | Further symmetry operations are available but not yet documented. | + | (will continue later today.... /2009-06-08 jfg) |
| ====== Usage examples ====== | ====== Usage examples ====== | ||
| - | ==== equilibrium ==== | + | ===== equilibrium ===== |
| Find an equilibrium from initial guess ''guess.ff'' | Find an equilibrium from initial guess ''guess.ff'' | ||
| <code> | <code> | ||
| Line 63: | 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. Equivalent to wavespeed (cx, cz) = 1/T (ax/Lx, az/Lz). | 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). | ||
| Line 71: | 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 77: | 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 83: | Line 82: | ||
| </code> | </code> | ||
| - | It takes a small amount of thinking to determine the right -orb, -eqb, -rel, -ax, and -az options based on the type of | + | 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. |
| - | search you want and | + | |
| ====== Mathematics ====== | ====== Mathematics ====== | ||
docs/utils/findorbit.1234370286.txt.gz · Last modified: 2009/02/11 08:38 by gibson
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