Preordering saddle‐point systems for sparse L D L T factorization without pivoting

This paper focuses on efficiently solving large sparse symmetric indefinite systems of linear equations in saddle‐point form using a fill‐reducing ordering technique with a direct solver. Row and column permutations partition the saddle‐point matrix into a block structure constituting a priori pivots of order 1 and 2. The partitioned matrix is compressed by treating each nonzero block as a single entry, and a fill‐reducing ordering is applied to the corresponding compressed graph. It is shown that, provided the saddle‐point matrix satisfies certain criteria, a block L D L T factorization can be computed using the resulting pivot sequence without modification. Numerical results for a range of problems from practical applications using a modern sparse direct solver are presented to illustrate the effectiveness of the approach.