Hi Daniel, Thank you for your reply. I had seen all the tutorials you mentioned.
Let me further clarify some of the things in my PDE that are somewhat different from the tutorials. 1. Unlike Step-7, I have Neumann-only BCs. In my prior experience with the FD and FV methods, this is a difficult problem. Is there any specific advice that can help me with this? 2. Step-15 solves a static non-linear problem and step-26 solves a linear time-dependent problem. I somehow need to combine these ideas to solve my non-linear time-dependent problem. Does this mean, I first make the problem a static one by time discretisation (Rothe method), and apply Newton iterations at every time step. Also, it scares me to derive the Newton update equation symbolically and was thinking of automatic differentiation. Can this be done in an easier way than the sacado package interface? Also, the amount of boiler-plate code and text (step-33) for this auto diff is overwhelming for me. Regards, Krishna On Fri, 13 Mar, 2020, 3:01 AM Daniel Arndt, <d.arndt.m...@gmail.com> wrote: > Krishna, > > Have a look at step-7 for Neumann boundary conditions, step-15 for > nonlinear problems and step-26 for time-dependent problems to get started. > Let us know if you have more specific questions. > > Best, > Daniel > > Am Do., 12. März 2020 um 17:38 Uhr schrieb Krishnakumar Gopalakrishnan < > krish...@vt.edu>: > >> I need to solve the following non-linear diffusion equation on a unit 1D >> domain: >> >> du/dt = \nabla \dot ( D(u) \grad u) >> >> subject to Neumann bcs at both ends. D(u)*grad(u) = f(t) at x=0, and >> D(u)*grad(u) = 0 at x=1, with a constant initial condition u(x,0) = u0 >> >> The difficulty with this problem is two fold >> >> - The diffusion coefficient D is a function of the field variable u, >> - Diffusion coefficient D(u) varies by 4 orders of magnitute between >> 10^-12 and 10^-16 >> >> Being 1D, the problem size is very small and I am thnking of just using >> direct solvers. However, I don't quite know how to start approaching this >> problem and how to begin the coding this in deal.ii. >> >> I'd appreciate any thoughts/help/suggestions/guidance from the deal.II >> community. >> >> Regards, >> Krishna >> >> >> >> -- >> The deal.II project is located at http://www.dealii.org/ >> For mailing list/forum options, see >> https://groups.google.com/d/forum/dealii?hl=en >> --- >> You received this message because you are subscribed to the Google Groups >> "deal.II User Group" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to dealii+unsubscr...@googlegroups.com. >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/dealii/3c0a13b9-1d59-443d-97bf-5a95440281d3%40googlegroups.com >> <https://groups.google.com/d/msgid/dealii/3c0a13b9-1d59-443d-97bf-5a95440281d3%40googlegroups.com?utm_medium=email&utm_source=footer> >> . >> > -- > The deal.II project is located at http://www.dealii.org/ > For mailing list/forum options, see > https://groups.google.com/d/forum/dealii?hl=en > --- > You received this message because you are subscribed to a topic in the > Google Groups "deal.II User Group" group. > To unsubscribe from this topic, visit > https://groups.google.com/d/topic/dealii/xX4IMnVymCw/unsubscribe. > To unsubscribe from this group and all its topics, send an email to > dealii+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/dealii/CAOYDWbK8fuCwiTQPjKO%2BaNhtLeAvCtXonskzS5%2BBha8CEkjw3w%40mail.gmail.com > <https://groups.google.com/d/msgid/dealii/CAOYDWbK8fuCwiTQPjKO%2BaNhtLeAvCtXonskzS5%2BBha8CEkjw3w%40mail.gmail.com?utm_medium=email&utm_source=footer> > . > -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to dealii+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/CABvf3kY4WUPvLnCtac6wA%2BhXtLVE4TUeQnqBQ6D2Bvg0u7ez2w%40mail.gmail.com.
