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Dear all,<br>
<br>
I read on the web page the following:<br>
<br>
<a name="TSSSP">
<h1>TSSSP</h1>
</a>
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).
<p>
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
</p>
<p>
1. There are no explicit methods with c_eff > 1.
</p>
<p>
2. There are no explicit methods beyond order 4 (for nonlinear
problems) and c_eff > 0.
</p>
<p>
3. There are no implicit methods with order greater than 1 and
c_eff > 2.
</p>
<p>
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.
</p>
<p>
Methods can be chosen with -ts_ssp_type {rks2,rks3,rk104}
</p>
<p>
rks2: Second order methods with any number s>1 of stages. c_eff
= (s-1)/s
</p>
<p>
rks3: Third order methods with s=n^2 stages, n>1. c_eff =
(s-n)/s
</p>
<p>
rk104: A 10-stage fourth order method. c_eff = 0.6
</p>
However, when I write<br>
<br>
-ts_ssp_type rk53 <br>
<br>
<br>
I get<br>
<br>
PETSC ERROR: Unknown TS_SSP type rk253 given!<br>
<br>
Any suggestions?<br>
<br>
Costas<br>
<br>
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