Impact of Reordering on the LU Factorization Performance of Bordered Block-Diagonal Sparse Matrix

Power engineers rely on computer-based simulation tools to assess grid performance and ensure security. At the core of these tools are solvers for sparse linear equations. When transformed into a bordered block-diagonal (BBD) structure, part of the sparse linear equation solving can be parallelized. This work focuses on using the Schur-complement-based method for LU factorization on BBD matrices, specifically, Jacobian matrices from large-scale systems. Our findings show that the natural ordering method outperforms the default ordering method in computational performance for each block of the BBD matrix. This observation is validated using synthetic 25k-bus and 70k-bus cases, showing a speedup of up to 38% when using natural ordering without permutation. Additionally, the impact of the number of partitions is studied, and the result shows that computational performance improves with more, smaller partitions in the BBD matrices.