Loading...
Please wait, while we are loading the content...
Similar Documents
Ordering for Factored Approximate Inverse Preconditioners
| Content Provider | Semantic Scholar |
|---|---|
| Author | Bridson, Robert Tang, Wei-Pai |
| Copyright Year | 2007 |
| Abstract | 1. Summary. We highlight how ordering can play an important role in the performance of factored approximate inverse preconditioners, concentrating on the AINV scheme of Benzi and Tůma ([1],[2]). After discussing some theory and heuristics for structure-based ordering schemes, we demonstrate that several practical algorithms can dramatically speed up the calculation of the preconditioner. Furthermore, these orderings generally improve convergence of Krylov subspace methods, especially Minimum Inverse Priority, a new algorithm we propose here. Recalling the problems anisotropy can pose for ILU (e.g. [6], [7], [8]) and noticing some discrepancies in testing data with highly anisotropic matrices, we are lead to consider the benefit of weighted orderings. These are algorithms that take into account the magnitude of entries in the original matrix as well as its structure. A simple demonstration problem shows the potential of weighted orderings, significantly improving both the speed of preconditioner calculation and the convergence to solutions. We finish by proposing a weighted version of Nested Dissection which shows promise for a robust high-performance ordering. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://phase.etl.go.jp/mgnet/mgnet/Conferences/CMCIM98/robinson.ps.gz |
| Alternate Webpage(s) | http://people.cs.ubc.ca/~rbridson/docs/orderainvabs.pdf |
| Alternate Webpage(s) | http://www.cs.ubc.ca/~rbridson/docs/orderainvabs.pdf |
| Alternate Webpage(s) | http://www.stanford.edu/~rbridson/download/orderainvabs.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
