[petsc-dev] Another SSP method

Jed Brown jed at jedbrown.org
Thu May 12 11:40:38 CDT 2022

You'll want to use the low-storage form. It's discussed in Ketcheson's paper; the method was originally discovered by Kraaijevanger 1991 and rediscovered by Spiter and Ruuth 2002. Note that the effective SSP coefficient is 0.302 while Ketcheson's rk104 has effective coefficient 0.6. As a result, you can take time steps 4x larger with rk104 using 10 stages per step. For most purposes, you'll prefer this over the 5-stage method. Feel free to add it.

Emil Constantinescu via petsc-dev <petsc-dev at mcs.anl.gov> writes:

> Matt, they seem to be provided in Butcher tableau form in the paper. One 
> can register an RK method and use it.
> An example (for ARKIMEX) is here: 
> https://petsc.org/release/src/ts/tutorials/ex19.c.html
> Emil
> *From: *petsc-dev <petsc-dev-bounces at mcs.anl.gov> on behalf of Matthew 
> Knepley <knepley at gmail.com>
> *Date: *Wednesday, May 11, 2022 at 6:01 AM
> *To: *PETSc <petsc-dev at mcs.anl.gov>
> *Subject: *[petsc-dev] Another SSP method
> Someone from my class requested
>    R. J. Spiteri, S. J. Ruuth, A new class of optimal high-order 
> strong-stability-
> preserving time discretization methods, SIAM J. Numer. Anal. 40 (2002) 
> 469-491.
> which is a fourth order, five stage method that we do not appear to 
> have. How hard is this to add?
>    Thanks,
>       Matt
> -- 
> 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
> https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>

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