J. Hollander (2016) Cache-aware multilevel Schur-complement-based preconditioning. Bachelor's Thesis, Mathematics.
|
Text
thesis.pdf - Published Version Download (6MB) | Preview |
|
![[img]](https://fse.studenttheses.ub.rug.nl/style/images/fileicons/text.png) |
Text
Toestemming.pdf - Other Restricted to Backend only Download (494kB) |
Abstract
Sparse matrices arising from the numerical solution of partial differential equations often exhibit a fine-grained block structure, meaning that the sparsity pattern may contain many dense, or nearly dense, small submatrices. Algorithms recognizing such dense structures can take advantage of the improved data-locality on modern cache-based computer architectures. In this thesis we overview blocking techniques for sparse matrices and we discuss how to exploit them, improving the performance of modern multilevel Schur-complement-based iterative solvers. We propose novel compression strategies for the Schur-complement that may lead to better numerical stability, and we test their implementation in the Variable Block Algebraic Recursive Multilevel Solver (VBARMS) [Carpentieri et al., 2014], which is a Schur-complement based multilevel incomplete LU factorization preconditioner. The performed numerical experiments support our theoretical findings.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 15 Feb 2018 08:13 |
| Last Modified: | 15 Feb 2018 08:13 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/14005 |
Actions (login required)
 |
View Item |