Strategies For Recycling Krylov Subspace Methods and Bilinear Form Estimation

The main theme of this work is effectiveness and efficiency of Krylov subspace methods and Krylov subspace recycling. While solving long, slowly changing sequences of large linear systems, such as the ones that arise in engineering, there are many issues we need to consider if we want to make the process reliable (converging to a correct solution) and as fast as possible. This thesis is built on three main components. At first, we target bilinear and quadratic form estimation. Bilinear form c^TA^-1b is often associated with long sequences of linear systems, especially in optimization problems. Thus, we devise algorithms that adapt cheap bilinear and quadratic form estimates for Krylov subspace recycling. In the second part, we develop a hybrid recycling method that is inspired by a complex CFD application. We aim to make the method robust and cheap at the same time. In the third part of the thesis, we optimize the implementation of Krylov subspace methods on Graphic Processing Units (GPUs). Since preconditioners based on incomplete matrix factorization (ILU, Cholesky) are very slow on the GPUs, we develop a preconditioner that is effective but well suited for GPU implementation.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2017

Author dc:creator

• Swirydowicz, Katarzyna

Chair dc:contributor.committeechair

• de Sturler, Eric

Committee members dc:contributor.committeemember

• Roy, Christopher J.
• Zietsman, Lizette
• Embree, Mark P.

• Bilinear form estimation
• quadratic form estimation
• sparse approximate inverse preconditioning
• high performance computing
• Krylov subspace recycling
• diffuse optical tomography
• topology optimization
• computational fluid dynamics

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

vt_gsexam:12508

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/78695