From: Vijay S. Mahadevan <vijay.m@gm...>  20100126 19:23:28

Jed, I know that Implicit Midpoint (IM2) is not Lstable either but it is my understanding that it has a lower truncation error because the coefficient in front of the error is smaller compared to that of CN. So I usually prefer IM2 to CN. I'm curious about the TSGL methods and will try out those integrators soon. It might be a stretch to do that in the current problem implementation but I have other coupled problems that could use adaptive, higher order temporal integration. If there are references explaining the properties of these methods, their butcher tableau and such, please do let me know. Also, are these implemented only in petscdev currently since I do not see it in the latest release of petsc. Vijay On Tue, Jan 26, 2010 at 1:08 PM, Jed Brown <jed@...> wrote: > On Tue, 26 Jan 2010 12:42:58 0600, "Vijay S. Mahadevan" <vijay.m@...> wrote: >> I'm solving a pure diffusion problem and there is no convection here. >> But I do understand that time integration makes a big difference and >> even making delt=1e10 does not seem to help. The negativity occurs on >> the first step, the first call to nonlinear residual. When you say >> trapezoidal rule, are you talking about Implicit midpoint here because >> CN is based on the trapezoidal rule and is not Lstable (spurious >> oscillations are not damped). > > Implicit midpoint is also not Lstable, it actually has exactly the same > stability function as trapezoid: > > (1 + z/2) / (1  z/2) > > Implicit Euler, BDF2, and various implicit RungeKutta schemes are > Lstable. Also, if you're feeling adventurous, I'd love to hear how > your system works with TSGL (in PETScdev). These are A and Lstable > methods of order and stage order 1 through 5, with adaptive controllers > (though the adaptive controllers may not robust, they haven't had much > tuning). > > For oscillations, as in hyperbolic systems and I think not the issue > here, you may need a strong stability preserving integrator. There do > not exist SSP integrators without a CFL constraint and order greater > than 1 (implicit Euler is the only SSP method without a CFL constraint). > > Jed > 