On Tue, 26 Jan 2010 12:42:58 -0600, "Vijay S. Mahadevan" <[email protected]> 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=1e-10 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 L-stable (spurious > oscillations are not damped).
Implicit midpoint is also not L-stable, it actually has exactly the same stability function as trapezoid: (1 + z/2) / (1 - z/2) Implicit Euler, BDF2, and various implicit Runge-Kutta schemes are L-stable. Also, if you're feeling adventurous, I'd love to hear how your system works with TSGL (in PETSc-dev). These are A- and L-stable 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 ------------------------------------------------------------------------------ The Planet: dedicated and managed hosting, cloud storage, colocation Stay online with enterprise data centers and the best network in the business Choose flexible plans and management services without long-term contracts Personal 24x7 support from experience hosting pros just a phone call away. http://p.sf.net/sfu/theplanet-com _______________________________________________ Libmesh-users mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/libmesh-users
