Parallel Sparse Direct Solver for Integrated Circuit Simulation by Xiaoming Chen Yu Wang & Huazhong Yang

Author:Xiaoming Chen, Yu Wang & Huazhong Yang
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

3.3.2 Numerical Update

The purpose of numerical update is to calculate the numerical values for a given column based on the symbolic pattern obtained in the symbolic prediction . Algorithm 7 shows the algorithm flow of the numerical update for a given column. This is typically the most time-consuming step in numerical LU factorization.

When updating a given column, say column k, numerical update uses dependent columns on the left side to update column k. The dependence is determined by the symbolic pattern of . Namely, column k depends on column j (), if and only if is a nonzero element. The numerical update is actually a set of multiplication-and-add (MAD) operations. Figure 3.6 illustrates the MAD operation in a clearer way. In this example, we are doing numerical update for column k and has two nonzero elements. The numerical update for column k involves three MAD operations, as marked by different colors in Fig. 3.6.

Fig. 3.6Illustration of the numerical update

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