On Mon, Dec 12, 2016 at 2:29 AM, Praveen C <[email protected]> wrote:
> Hello Matt > > I have attached the detailed output. > > Fenics automatically computes Jacobian, so I think Jacobian should be > correct. I am not able to run the Fenics code without giving the Jacobian. > I am currently writing a C code where I can test this. > > This equation is bit weird. Its like this > > u_t = ( K u_x)_x > > K = u / sqrt(u_x^2 + eps^2) > I do not understand how to show parabolicity in this case. However, I have a more fundamental misunderstanding. In your code, I see R0 = idt*(u-uold)*v*dx + K0*ux*vx*dx for the residual, which looks like R0 = u_t + K u_x to me. Where is the extra derivative you show above? Thanks, Matt > If u > 0, then this is a nonlinear parabolic eqn. Problem is that eps = h > (mesh size), so at extrema, it is like > > u_t = (u/eps)*u_xx > > and (1/eps) is approximating a delta function. > > Best > praveen > > On Mon, Dec 12, 2016 at 12:41 PM, Matthew Knepley <[email protected]> > wrote: > >> On Mon, Dec 12, 2016 at 1:04 AM, Matthew Knepley <[email protected]> >> wrote: >> >>> On Mon, Dec 12, 2016 at 12:56 AM, Praveen C <[email protected]> wrote: >>> >>>> Increasing number of snes iterations, I get convergence. >>>> >>>> So it is a problem of initial guess being too far from the solution of >>>> the nonlinear equation. >>>> >>>> Solution can be seen here >>>> >>>> https://github.com/cpraveen/fenics/blob/master/1d/cosmic_ray >>>> /cosmic_ray.ipynb >>>> >>> >> Also, how is this a parabolic equation? It looks like u/|u'| to me, which >> does not look parabolic at all. >> >> Matt >> >> >>> Green curve is solution after two time steps. >>>> >>>> It took about 100 snes iterations in first time step and about 50 in >>>> second time step. >>>> >>>> I use exact Jacobian and direct LU solve. >>>> >>> >>> I do not believe its the correct Jacobian. Did you test it as I asked? >>> Also run with >>> >>> -snes_monitor -ksp_monitor_true_residual -snes_view >>> -snes_converged_reason >>> >>> and then >>> >>> -snes_fd >>> >>> and send all the output >>> >>> Matt >>> >>> >>>> Thanks >>>> praveen >>>> >>> >>> >>> >>> -- >>> 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 >> > > -- 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
