FiPy still does not support remeshing. As Dario said, choice of solver can make a big difference. I've not used PyAMG much, but PySparse is dramatically faster than SciPy. PyTrilinos is slower than PySparse, but enables you to solve in parallel.
I've also found that 2D problems solve much better than the 1D performance would lead you to believe. There's just a lot of overhead in setting up the problem and the Python communication with the lower-level libraries. > On Jul 23, 2018, at 6:44 PM, Carsten Langrock <[email protected]> wrote: > > Hi, > > Thanks for the help with getting FiPy running under Linux! I am trying to > re-create a 1D nonlinear diffusion problem for which we have C++ code that > uses the implicit Thomas algorithm based on > > J. Weickert, B. Romerny, M. Viergever, "Efficient and Reliable Schemes > for Nonlinear Diffusion Filtering”, IEEE transactions on Image Processing, > vol.7, N03, page 398, March 1998 > > I have been able to get results in FiPy that match this code very closely > which was a great start. Our C++ code uses a fixed number of spatial points > and a fixed time step, but re-meshes space to most efficiently use the size > of the array; it increases the spatial step size by 2 whenever the > concentration at a particular point reaches a set threshold. I tried > implementing this in FiPy as well, but haven’t had much luck so far. I saw an > old mailing-list entry from 2011 where a user was told that FiPy wasn’t meant > to do remeshing. Is that still the case? > > I’d imagine one would somehow need to update the Grid1D object with the new > ‘dx’, but since the CellVariable that holds the solution was initialized with > that mesh object, I am not sure that such a change would propagate in a > sensible fashion. I think I know how to map the value of the CellVariable to > account for the change in ‘dx’ by > > array_size = 2000 > phi.value = numpy.concatenate((phi.value[1:array_size/2:2], > numpy.zeros(1500))) > > for the case when the initial variable holds 2000 spatial points. Maybe > there’s a more elegant way, but I think this works in principle. > > Another question would be execution speed. Right now, even when not plotting > the intermediate solutions, it takes many seconds on a very powerful computer > to run a simple diffusion problem. I am probably doing something really > wrong. I wasn’t expecting the code to perform as well as the C++ code, but I > had hoped to come within an order of magnitude. Are there ways to optimize > the performance? Maybe select a particularly clever solver? If someone could > point me into the right direction that’d be great. In the end, I would like > to expand the code into 2D, but given the poor 1D performance, I don’t think > that this would be feasible at this point. > > Thanks, > Carsten > > _____________________________________ > Dipl.-Phys. Carsten Langrock, Ph.D. > > Senior Research Scientist > Edward L. Ginzton Laboratory, Rm. 202 > Stanford University > > 348 Via Pueblo Mall > 94305 Stanford, CA > > Tel. (650) 723-0464 > Fax (650) 723-2666 > > Ginzton Lab Shipping Address: > James and Anna Marie Spilker Engineering and Applied Sciences Building > 04-040 > 348 Via Pueblo Mall > 94305 Stanford, CA > _____________________________________ > _______________________________________________ > fipy mailing list > [email protected] > http://www.ctcms.nist.gov/fipy > [ NIST internal ONLY: https://email.nist.gov/mailman/listinfo/fipy ] _______________________________________________ fipy mailing list [email protected] http://www.ctcms.nist.gov/fipy [ NIST internal ONLY: https://email.nist.gov/mailman/listinfo/fipy ]
