Preprocessing of sparse unassembled linear systems for efficient solution using element-by-element preconditioners
We believe that these preliminary results indicate that the amalgamation methods considered here hold promise, especially for large, ill-conditioned problems for which direct methods are inappropriate and simple element-by-element pre-conditioners ineffective. However, we must be cautious as our proposals are merely heuristics, and believe that further experimentation is necessary to assess the full potential of the methods.
The technique can also be applied to other element-by-element preconditioners or to block methods. For example, the assembly of some super-elements would decrease the cost of the solution step for the GS EBE preconditioner (see Hughes et al., 1983, and Ortiz et al., 1983).
Unable to display preview. Download preview PDF.
- Amestoy, P. R., Daydé, M. J., Duff, I. S., L'Excellent, J.-Y., Gould, N. I. M., Reid, J. K. and Scott, J. A. (1994), MUSSELS — a multifrontal sparse symmetric element-input linear solver. Technical report, Rutherford Appleton Laboratory, Chilton, Oxfordshire, England. Working note.Google Scholar
- Daydé, M. J., L'Excellent, J.-Y. and Gould, N. I. M. (1994), On the use of elementby-element preconditioners to solve large scale partially separable optimization problems, Technical Report RT/APO/94/4, ENSEEIHT-IRIT, Toulouse, France. To appear in SIAM Journal on Scientific Computing.Google Scholar
- Daydé, M. J., L'Excellent, J.-Y. and Gould, N. I. M. (1995), User's guide to PAREBE: parallel element-by-element preconditioners for the conjugate gradient algorithm, Technical report, ENSEEIHT-IRIT, Toulouse, France. To appear.Google Scholar
- Harwell Subroutine Library (1993), A catalogue of subroutines (release 11), Advanced Computing Department, Harwell Laboratory, Harwell, UK.Google Scholar
- Karypis, G. and Kumar, V. (1995), METIS: Unstructured graph partitioning and sparse matrix ordering system, version 2.0, Technical report, University of Minnesota, Department of Computer Science, Minneapolis.Google Scholar
- L'Excellent, J.-Y. (1995), Utilisation de préconditionneurs élément-par-élément pour la résolution de problèmes d'optimisation de grande taille, PhD thesis, ENSEEIHT-INPT.Google Scholar