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docs:utils:continuesoln [2010/02/02 07:55]
docs:utils:continuesoln [2010/02/02 07:55] (current)
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 +====== continuesoln ======
 +
 +''​continuesoln''​ continues an equilibrium,​ traveling wave, or periodic orbit in a parameter μ. The parameter μ is one of Reynolds number, //Lx, Lz, Lx/Lz, sqrt(Lx^2 + Lz^2)//, or //dPdx//. Continuation is done by a predictor-corrector method, using quadratic extrapolation in pseudo-arclength //s// along curves in the //(μ,D)// plane for prediction, and Newton-Krylov-hookstep search for correction. ​
 +
 +====== main options =====
 +
 +<​code>​
 +main options : 
 +  -r         ​--restart ​                                            start from three previously computed solutions
 +  -eqb       ​--equilibrium ​                                        ​search for equilibrium or relative equilibrium (trav wave)
 +  -orb       ​--periodicorbit ​                                      ​search for periodic orbit or relative periodic orbit
 +  -poinc ​    ​--poincare ​                                           (relative) periodic orbit search constrained to I-D=0 Poincare section
 +  -xrel      --xrelative ​                                          ​search over x phase shift for relative orbit or eqb
 +  -zrel      --zrelative ​                                          ​search over z phase shift for relative orbit or eqb
 +  -contRe ​   --continueRe ​                                         continue solution in Reynolds number
 +  -contdPdx ​ --continuedPdx ​                                       continue solution in imposed pressure gradient
 +  -contLx ​   --continueLx ​                                         continue solution in streamwise width Lx
 +  -contLz ​   --continueLz ​                                         continue solution in spanwise width Lz
 +  -contAsp ​  ​--continueAspect ​                                     continue solution in aspect ratio Lx/Lz
 +  -contDiag ​ --continueDiagonal ​                                   continue solution along diagonal with const aspect ratio Lx/Lz
 +  -contLtarg --continueLtarget ​                                    ​continue solution towards a target Lx,Lz
 +  -up        --upwards ​                                            for non-restart searches, search in dir of increasing free parameter
 +  -Lxtarg ​   --LxTarget ​         <​real> ​     default == 6.28319 ​   aim for this value of Lx in target Lx,Lz continuation
 +  -Lztarg ​   --LzTarget ​         <​real> ​     default == 3.14159 ​   aim for this value of Lz in target Lx,Lz continuation
 +  -T         ​--maptime ​          <​real> ​     default == 15         ​initial guess for orbit period or time of eqb/reqb map f^T(u)
 +  -R         ​--Reynolds ​         <​real> ​     default == 400        Reynolds number
 +  -dPdx      --dPdx ​             <​real> ​     default == 0          imposed mean pressure gradient
 +  -s0        --s0                <​real> ​     default == 0          start value for arclength (arbitrary)
 +  -ds        --ds                <​real> ​     default == 0.001      initial arclength increment for quadratic extrapolation
 +  -dsmin ​    ​--dsmin ​            <​real> ​     default == 0.0001 ​    ​minimum arclength increment (in normalized D,Re space)
 +  -dsmax ​    ​--dsmax ​            <​real> ​     default == 0.05       ​maximum arclength increment (in normalized D,Re space)
 +  -errmin ​   --errmin ​           <​real> ​     default == 1e-05      minimum error for extrapolated guesses
 +  -errmax ​   --errmax ​           <​real> ​     default == 0.001      maximum error for extrapolated guesses
 +  -sigma ​    ​--sigma ​            <​string> ​                         file containing sigma of sigma f^T(u) - u = 0 (default == identity)
 +  -symms ​    ​--symmetries ​       <​string> ​                         file containing generators of isotropy group for symmetry-constrained search
 +
 +</​code>​
 +
 +===== output =====
 +
 +''​continuesoln''​ produces a lot of output data. For each step in the continuation it produces a new subdirectory of the working directory and populates it with data files and log files. The output directories are named ''​startup-2'',​ ''​startup-1'',​ ''​startup-0'',​ and ''​search-0'',​ ''​search-1'',​ ''​search-1'',​ .... The three ''​startup''​ directories contain solutions computed either for very small perturbations of a single initial solutions, or solutions from previous computation (see the ''​--restart''​ option below). The ''​search''​ directories are indefinite in number, they just keep going as the continuation proceeds. Each of these directories contains data files for the solution'​s velocity field, phase shift σ, etc., as well as a logfile ''​findsoln.log''​ with detailed information about the Newton-Krylov search. The ''​convergence.asc''​ file shows the convergence of the residual with each Newton-Krylov step.
 +
 +===== initial data and the --restart option ​ =====
 +
 +The quadratic extrapolation method requires three consecutive data points. These can either be generated by very making small perturbations in the continuation parameter from a single existing solution, or by reading in three consecutive solutions from a previous continuation calculation. ​
 +
 +This example starts a continuation of a periodic orbit in Reynolds number, by specifying an initial solution //​(u,​T,​σ)//​ on the command-line. ​
 +
 +<​code>​
 +   ​continuesoln -orb -contRe -T 87.25853994 -sigma sigma.asc P87p25.h5
 +</​code>​
 +
 +This example starts from three consecutive solutions from a previous computation. The three arguments following the ''​--restart''​ option are directories containing solutions generated by a previous continuation. Those directories ​
 +contain values of //​(u,​T,​σ)//​ at different values of μ.
 +
 +<​code>​
 +   ​continuesoln -orb -contRe --restart ../​previous/​search-22 ../​previous/​search-23 ../​previous/​search-24
 +</​code>​
 +
 +
 +===== solution type options =====
 +
 +Choose one of ''​-eqb''​ or ''​-orb''​ to specify whether the solution type is (relative) equilibrium or
 +(relative) periodic orbit. ​
 +
 +For periodic orbit searches, ''​-poinc''​ specifies that the orbit starting and end points are confined to the //​I-D=0//​Poincare section. If you use this, make sure your initial data lie on the section (use ''​fieldprops -e''​).
 +
 +To specify a search for a relative eqb or orbit, use the ''​-xrel''​ and/or ''​-zrel''​ options. ​
  
docs/utils/continuesoln.txt · Last modified: 2010/02/02 07:55 (external edit)