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5.5.3 Parallel IUL factorization

To reduce the communication in Alg. 5.15 we use an incomplete factorization $ {\ensuremath{\color{red}\mathfrak{U}}}{\ensuremath{\color{red}\mathfrak{L}}}$-factorization.

Here, the unknowns will be passed in the reverse order. Thus the redundant stored matrices $ {\ensuremath{\color{red}\mathfrak{K}}}_V$, $ {\ensuremath{\color{red}\mathfrak{K}}}_E$, $ {\ensuremath{\color{red}\mathfrak{K}}}_E$, $ {\ensuremath{\color{red}\mathfrak{K}}}_{EV}$ and  $ {\ensuremath{\color{red}\mathfrak{K}}}_{VE}$ will updated locally during the factorization so that their accumulation is only allowed previously to their factorization !
\begin{algorithmus} % latex2html id marker 20281 [H]\caption{Parallel IUL factor... ..._{V} $\ & mesh $\rightarrow$\ diagonal matrix \end{tabular} \end{algorithmus}
The elimination step is a simple application of (4.12a).
\begin{algorithmus} % latex2html id marker 20413 [H]\caption{Parallel eliminatio... ...\ensuremath{\color{red}\mathfrak{w}}}}_V)$\ \\ \end{tabular} \end{algorithmus}

Gundolf Haase 2000-03-20