[petsc-users] Question about ts_ssp

[Kostas Kontzialis]

Dear all,

  I read on the web page the following:


  TSSSP

Explicit strong stability preserving ODE solver Most hyperbolic 
conservation laws have exact solutions that are total variation 
diminishing (TVD) or total variation bounded (TVB) although these 
solutions often contain discontinuities. Spatial discretizations such as 
Godunov's scheme and high-resolution finite volume methods (TVD 
limiters, ENO/WENO) are designed to preserve these properties, but they 
are usually formulated using a forward Euler time discretization or by 
coupling the space and time discretization as in the classical 
Lax-Wendroff scheme. When the space and time discretization is coupled, 
it is very difficult to produce schemes with high temporal accuracy 
while preserving TVD properties. An alternative is the semidiscrete 
formulation where we choose a spatial discretization that is TVD with 
forward Euler and then choose a time discretization that preserves the 
TVD property. Such integrators are called strong stability preserving 
(SSP).

Let c_eff be the minimum number of function evaluations required to step 
as far as one step of forward Euler while still being SSP. Some 
theoretical bounds

1. There are no explicit methods with c_eff > 1.

2. There are no explicit methods beyond order 4 (for nonlinear problems) 
and c_eff > 0.

3. There are no implicit methods with order greater than 1 and c_eff > 2.

This integrator provides Runge-Kutta methods of order 2, 3, and 4 with 
maximal values of c_eff. More stages allows for larger values of c_eff 
which improves efficiency. These implementations are low-memory and only 
use 2 or 3 work vectors regardless of the total number of stages, so 
e.g. 25-stage 3rd order methods may be an excellent choice.

Methods can be chosen with -ts_ssp_type {rks2,rks3,rk104}

rks2: Second order methods with any number s>1 of stages. c_eff = (s-1)/s

rks3: Third order methods with s=n^2 stages, n>1. c_eff = (s-n)/s

rk104: A 10-stage fourth order method. c_eff = 0.6

However, when I write

  -ts_ssp_type rk53


I get

PETSC ERROR: Unknown TS_SSP type rk253 given!

Any suggestions?

Costas

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