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<div id="version" align=right><b>petsc-3.7.5 2017-01-01</b></div>
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<A NAME="TSPSEUDO"><H1>TSPSEUDO</H1></A>
Solve steady state ODE and DAE problems with pseudo time stepping This method solves equations of the form
<P>
<pre>
F(X,Xdot) = 0
</pre>
<P>
for steady state using the iteration
<P>
<pre>
[G'] S = -F(X,0)
</pre>
<pre>
X += S
</pre>
<P>
where
<P>
<pre>
G(Y) = F(Y,(Y-X)/dt)
</pre>
<P>
This is linearly-implicit Euler with the residual always evaluated "at steady
state". See note below.
<P>
<H3><FONT COLOR="#CC3333">Options database keys</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-ts_pseudo_increment <real> </B></TD><TD>- ratio of increase dt
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-ts_pseudo_increment_dt_from_initial_dt <truth> </B></TD><TD>- Increase dt as a ratio from original dt
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-ts_pseudo_fatol <atol> </B></TD><TD>- stop iterating when the function norm is less than atol
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-ts_pseudo_frtol <rtol> </B></TD><TD>- stop iterating when the function norm divided by the initial function norm is less than rtol
</TD></TR></TABLE>
<P>
<P>
<H3><FONT COLOR="#CC3333">References</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>1. </B></TD><TD>- Todd S. Coffey and C. T. Kelley and David E. Keyes, Pseudotransient Continuation and Differential Algebraic Equations, 2003.
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>2. </B></TD><TD>- C. T. Kelley and David E. Keyes, Convergence analysis of Pseudotransient Continuation, 1998.
</TD></TR></TABLE>
<P>
<H3><FONT COLOR="#CC3333">Notes</FONT></H3>
The residual computed by this method includes the transient term (Xdot is computed instead of
always being zero), but since the prediction from the last step is always the solution from the
last step, on the first Newton iteration we have
<P>
<pre>
Xdot = (Xpredicted - Xold)/dt = (Xold-Xold)/dt = 0
</pre>
<P>
Therefore, the linear system solved by the first Newton iteration is equivalent to the one
described above and in the papers. If the user chooses to perform multiple Newton iterations, the
algorithm is no longer the one described in the referenced papers.
<P>
<H3><FONT COLOR="#CC3333">See Also</FONT></H3>
<A HREF="../TS/TSCreate.html#TSCreate">TSCreate</A>(), <A HREF="../TS/TS.html#TS">TS</A>, <A HREF="../TS/TSSetType.html#TSSetType">TSSetType</A>()
<BR>
<P>
<P><B><P><B><FONT COLOR="#CC3333">Level:</FONT></B>beginner
<BR><FONT COLOR="#CC3333">Location:</FONT></B><A HREF="../../../src/ts/impls/pseudo/posindep.c.html#TSPSEUDO">src/ts/impls/pseudo/posindep.c</A>
<BR><A HREF="./index.html">Index of all TS routines</A>
<BR><A HREF="../../index.html">Table of Contents for all manual pages</A>
<BR><A HREF="../singleindex.html">Index of all manual pages</A>
<P><H3><FONT COLOR="#CC3333">Examples</FONT></H3>
<A HREF="../../../src/ts/examples/tutorials/ex1.c.html">src/ts/examples/tutorials/ex1.c.html</A><BR>
<A HREF="../../../src/ts/examples/tutorials/ex24.c.html">src/ts/examples/tutorials/ex24.c.html</A><BR>
<A HREF="../../../src/ts/examples/tutorials/ex42.c.html">src/ts/examples/tutorials/ex42.c.html</A><BR>
<A HREF="../../../src/ts/examples/tutorials/ex1f.F.html">src/ts/examples/tutorials/ex1f.F.html</A><BR>
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