I do not see why 1,2, and 3 are incompatiable with an "algebra based" TS level. It just requires a smart design.
Barry On Tue, 18 Sep 2007, Matthew Knepley wrote: > On 9/17/07, Matthew Knepley <knepley at gmail.com> wrote: > > I think this example demonstrates my major problem with the current TS > > implementation. I have had this problem since I was in grad school. We > > would like to abstract different "methods" like CN for timestepping. This > > is really abstracting the process of temporal discretization, and so far we > > choose finite difference type discretizations. When these are combined > > with FEM in space, this becomes difficult since we have no prescription for > > constructing the operators we might need (like the identity in the FEM > > space). Moreover, even when I added methods allowing the user to specify > > these, the computation is not optimal since the parts are distended. > > Okay "algebra only" crowd, I agree this would be great. However, please > address > the two problems I identify in the above paragraph, namely: > > 1) How can you handle user-discretized operators, like the identity, which > are > necessary for any of these schemes? > > 2) Even if you get these from the user, how can you efficiently implement > the > scheme, since what we really want is assembly of the entire F() at each > timestep (in method of lines)? > > 3) Moreover, how can this scheme ever do spacetime formulations, which are > much better for many problems? > > Matt > > > Matt > > > > On 9/17/07, Lisandro Dalcin <dalcinl at gmail.com> wrote: > > > Current TS implementations never fited my needs. Why? My target > > > application is solving incompressible NS equations with FEM and fully > > > implicit schemes (trapezoidal rule with theta in [0.5, 1.0] ) and > > > residual-based stabilization (SUPG/PSPG). Then I need to solve at each > > > time step a nonlinear problem like F(t, u, t0, u0), where F is > > > nonlinear in u. I'm surelly naive, and I could not accomodate my > > > function and Jacobian code for the beuler/cn TS implementations. > > > > > > Futhermore, I've recently convinced some coworkers to take advance of > > > SNES/TS features and my Python wrappers (petsc4py) to manage the the > > > time evolution of some problems related to fluid-structure interaction > > > and mesh movement (formulated as an optimization problem, only nodal > > > positions change, not remeshing needed for many timesteps). > > > > > > In order to support those applications setups, I've wrote a new TS > > > implemetation, which enables users to (almost) completely define the > > > temporal evolution of their problems, with pre/post solve/step > > > methods and support for accept/reject steps and implementing timestep > > > size control. Some of these features are available in some TS types, > > > but not all-in-one. > > > > > > This code is available for review in petsc4py SVN repo (link below), > > > an python example of this in action (very simple, just for testing all > > > is working) is attached. Currently it only support implicit schemes > > > and nonlinear problems, but I believe it can be extended to support > > > explicit schemes and linear problems. > > > > > > http://petsc4py.googlecode.com/svn/trunk/petsc/lib/ext/src/ts/impls/implicit/user/ > > > > > > I want to know the opinion of PETSc core developers and potential > > > users ot this, and I hope anyone can provide suggestions for > > > improvements. After that, I can push this to petsc-dev for general > > > availability (in fact, the code is almost ready to be integrated in > > > petsc). > > > > > > Perhaps in the long term, all this can be integrated in the generic TS > > > interface if that is appropriate. Of course, this would require some > > > (I hope minor) changes in TS interface, some additions, and a > > > reimplementation of some default TS types > > > > > > Regards, and I'm waiting for your comments. > > > > > > > > > -- > > > Lisandro Dalc?n > > > --------------- > > > Centro Internacional de M?todos Computacionales en Ingenier?a (CIMEC) > > > Instituto de Desarrollo Tecnol?gico para la Industria Qu?mica (INTEC) > > > Consejo Nacional de Investigaciones Cient?ficas y T?cnicas (CONICET) > > > PTLC - G?emes 3450, (3000) Santa Fe, Argentina > > > Tel/Fax: +54-(0)342-451.1594 > > > > > > > > > > > > -- > > 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 > > > > >
