Introduction to algorithms
Matrix computations (3rd ed.)
Highly Scalable Parallel Algorithms for Sparse Matrix Factorization
IEEE Transactions on Parallel and Distributed Systems
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
Algorithm 837: AMD, an approximate minimum degree ordering algorithm
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
Computational Optimization and Applications
SIAM Journal on Matrix Analysis and Applications
Hybrid, Multiresolution Wires with Massless Frictional Contacts
IEEE Transactions on Visualization and Computer Graphics
IEEE Transactions on Visualization and Computer Graphics
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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 a priori 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.