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 _____________________________________
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