Direct Sparse Factorization of Blocked Saddle Point Matrices
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.
KeywordsBipartite Graph Multibody System Kinematic Constraint Data Layout Elimination Tree
Unable to display preview. Download preview PDF.
- 2.Amestoy, P.R., Enseeiht-Irit, Davis, T.A., Duff, I.S.: Algorithm 837: AMD, an approximate minimum degree ordering algorithm. ACM Trans. Math. Softw. 30(3), 381–388 (2004)Google Scholar
- 3.Bodin, K., Lacoursière, C., Servin, M.: Constraint fluids. IEEE Trans. on Visualization and Computer Graphics (2010) (to appear)Google Scholar
- 10.Lacoursière, C.: Regularized, stabilized, variational methods for multibodies. In: Bunus, D.F.P., Führer, C. (eds.) The 48th Scandinavian Conference on Simulation and Modeling (SIMS 2007). Linköping Electronic Conference Proceedings, pp. 40–48. Linköping University Electronic Press, Linköping (2007)Google Scholar
- 14.Servin, M., Lacoursière, C., Nordfelth, F., Bodin, K.: Hybrid, multiresolution wires with massless frictional contacts. IEEE Transactions on Visualization and Computer Graphics (2010) (in press)Google Scholar