5.5.4 Comparison of ILU- and IUL-factorization

The two algorithms introduced in the previous two sections differ mainly in the communication behavior sampled in table 5.1.

Table 5.1: Communication in ILU and IUL

			ILU : ${\ensuremath{\color{red}\mathfrak{L}}}\cdot{\ensuremath{\color{red}\mathfrak{U}}}$			IUL : ${\ensuremath{\color{red}\mathfrak{U}}}\cdot{\ensuremath{\color{red}\mathfrak{L}}}$
start up			matrix accumulation			--
factorization			--			matrix accumulation
elimination			$2 \times$ vector accumulation			$1 \times$ vector accumulation

The accumulation of the matrix is split into separate calls for accumulation of cross points and interface nodes. Therefore, the communication load in algorithms 5.16 and 5.14 is the same. According to the FE-discretization, the stiffness matrix $K$ is distributed stored (Sec. 4.3.1) so that we cannot save that one communication at all.

With respect to the communication we recommend to use the IUL factorization in parallel implementations.