A Parallel Aggregation Algorithm for Inter-Grid Transfer Operators in Algebraic Multigrid

As finite element discretizations ever grow in size to address real-world problems, there is an increasing need for fast algorithms. Nowadays there are many GPU/CPU parallel approaches to solve such problems. Multigrid methods can be used to solve large-scale problems, or even better they can be used to precondition the conjugate gradient method, yielding better results in general. Capabilities of multigrid algorithms rely on the effectiveness of the inter-grid transfer operators. In this thesis we focus on the aggregation approach, discussing how different aggregation strategies affect the convergence rate. Based on these discussions, we propose an alternative parallel aggregation algorithm to improve convergence. We also provide numerous experimental results that compare different aggregation approaches, multigrid methods, and conjugate gradient iteration counts, showing that our proposed algorithm performs better in serial and parallel.

Name thesis:degree_name

M.S.

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2019

Author dc:creator

• Garcia Hilares, Nilton Alan

Chair dc:contributor.committeechair

• Embree, Mark P.

Committee members dc:contributor.committeemember

• de Sturler, Eric
• Warburton, Timothy

• Algebraic multigrid
• Aggregation
• Maximal independent set
• Poisson's equation

Statement dc:rights

• Creative Commons Attribution-ShareAlike 3.0 United States

Licence dc:rights.uri

• http://creativecommons.org/licenses/by-sa/3.0/us/

Language dc:language.iso

en_US

Handle dc:identifier.uri

http://hdl.handle.net/10919/94618

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/94618