Ok, thanks for the information. I am looking at a Hamiltonian system, and I wanted to try out different schemes for preserving the energy. I was curious about textbook projected RK, so I think I’ll try Barry’s suggestion about TSSetPostStep.
-gideon > On Feb 4, 2017, at 10:26 PM, Emil Constantinescu <[email protected]> wrote: > > > > On 2/4/17 11:00 AM, Matthew Knepley wrote: >> On Sat, Feb 4, 2017 at 9:47 AM, Gideon Simpson <[email protected] >> <mailto:[email protected]>> wrote: >> >> Would setting it up as a DAE in petsc be algorithmically euivalent >> to a projected method (i.e., step of standard RK followed by >> nonlinear projection)? > > Not quite, if you set it as a DAE, then both the time stepping part and the > algebraic constraint are solved at the same time (you are going to use an > implicit time stepping method. > > So for backward Euler and DAE, PETSc solves something like: > > y_{n+1} - y{n} - dt* f(y_{n+1}) = 0 > g(y_{n+1}) = 0 > > By projection (assuming index 1 or 2): you are solving > > y* - y{n} - dt* f(y*) = 0 > > then initialize SNES to y* and solve: > > g(y_{n+1}) = 0 > > In some cases g(y_{n+1}) may not have a value (you may not land on the > manifold that is defined by the conservation property). Whereas, if you > define it as a DAE in almost all cases (there are crazy exceptions) you will. > > > Emil > >> >> I am not sure, as I do not understand those solvers. However, I wrote my >> own solver that does exactly that MIMEX. >> >> Matt >> >> >> -gideon >> >>> On Feb 3, 2017, at 11:47 PM, Matthew Knepley <[email protected] >>> <mailto:[email protected]>> wrote: >>> >>> That is one answer. Another one is that this particular system is >>> a DAE and we have methods for that. >>> >>> Matt >>> >>> On Fri, Feb 3, 2017 at 8:40 PM, Barry Smith <[email protected] >>> <mailto:[email protected]>> wrote: >>> >>> >>> TSSetPostStep(); in your function use TSGetSolution() to get >>> the current solution. >>> >>> Please let us know how it works out >>> >>> Barry >>> >>> >>> >>> > On Feb 3, 2017, at 7:14 PM, Gideon Simpson >>> <[email protected] <mailto:[email protected]>> >>> wrote: >>> > >>> > I’m interested in implementing a projection method for an >>> ODE of the form: >>> > >>> > y’ = f(y), >>> > >>> > such that g(y) = 0 for all time (i.e., g is conserved). >>> Note that in a projection method, a standard time step is made >>> to produce y* from y_{n}, and then this is corrected to obtain >>> y_{n+1} satisfying g(y) = 0. >>> > >>> > There were two ways I was thinking of doing this, and I was >>> hoping to get some input: >>> > >>> > Idea 1: Manually loop through using taking a time step and >>> then implementing the projection routine. I see that there is >>> a TSStep command, but this doesn’t seem to be much >>> documentation on how to use it in this scenario. Does anyone >>> have any guidance? >>> > >>> > Idea 2: Is there some analog to TSMonitor that allows me to >>> modify the solution after each time step, instead of just >>> allowing for some computation of a statistic? >>> > >>> > >>> >>> >>> >>> >>> -- >>> What most experimenters take for granted before they begin their >>> experiments is infinitely more interesting than any results to >>> which their experiments lead. >>> -- Norbert Wiener >> >> >> >> >> -- >> What most experimenters take for granted before they begin their >> experiments is infinitely more interesting than any results to which >> their experiments lead. >> -- Norbert Wiener
