The K method

The loop is solved by means of the implicit function theorem.

\begin{displaymath}
g(\mbox{\boldmath${\xi}$},\Delta p)=f\left( \mbox{\boldmath${K}$} \Delta p+ \mbox{\boldmath${\xi}$} \right) -\Delta p =0
\end{displaymath}

If $g$ satisfies the hypotheses of the theorem, then
$
\Delta p=f \left( \mbox{\boldmath${K}$}\Delta p+\mbox{\boldmath${\xi}$} \righ...
...gmapsto
\hspace{.5 cm}\Delta p=\bar{f}\left( \mbox{\boldmath${\xi}$} \right)
$


At each step

Function $\bar{f}$ can be stored as a precomputed table. No iterative solvers are needed.

2000-09-12