We present a parallel algorithm for the direct factorization of sparse saddle-point matrices of moderate size coming from real-time multibody dynamics simulations. We used the specific structure of these problems both for
construction of supernodes and to avoid all dynamic permutations during factorization. For the latter, we present a technique we call “leaf swapping” which performs permutations of the supernodes in the elimination tree without any reference to numerical values. The results compare favorably with currently available high performance codes on our problem sets because of the high overhead necessary to process very large problems on increasingly complex supercomputers.