Implicit Finite Element Contact With a Multigrid Solver on Parallel Computers

Finite element contact is an important analysis tool that has received a significant amount of research attention. The fact that contact problems are geometrically non-smooth as well as algebraically non-linear makes them difficult to solve. Since the bulk of the work in a contact algorithm is associated with solving systems of linear equations, efficient linear solvers are attractive. The geometric multigrid method is an iterative linear equation solving method able to arrive at a solution after O(n) work. Enabling a multigrid method to work for a contact problem requires special treatment of the contact stiffness matrix on coarse meshes. This dissertation describes the mathematical formulation of finite element contact, the multigrid method, and how to couple finite element contact and the multigrid method. The dissertation also demonstrates the scalability of the resulting scheme on several parallel computers and gives results for non-trivial test problems.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Civil Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Hales, Jason Dean

Contributors dc:contributor

• Dennis Parsons

• Engineering, Civil

Language dc:language

eng

Identifier

(MiAaPQ)AAI3023069

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/83162