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Next: 4. Non-incremental form for Up: Main page Previous: 2. Non-incremental (classical) form

3. Incremental form for predictor-step

The equations are written for the "increment" variable:


Y* = X*F - X0F

Note that the computation of Y* from X0, X* does not require any interpolation. Hence (1) writes:


\begin{displaymath}\frac{Y^* + X^0_F - X^0_O}{\Delta t} = \frac{(1 + \epsilon)... ...n) {\bf M}(X^0_O)}{2} + {\bf L}^*\frac{(1+ \epsilon) Y^*}{2} \end{displaymath}

$\Longrightarrow$


 \begin{displaymath}\left[{\bf I} - (1 + \epsilon) \frac{\Delta t}{2} {\bf L}^*\r... ...psilon) {\bf M}(X^0_F) + (1 - \epsilon) {\bf M}(X^0_O) \right] \end{displaymath} (3)

We see that with this formulation, there is no linear explicit term to be computed, thus obtaining a gain in efficiency.


Pierre BENARD
2002-06-17
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