Implicit finite element contact with a multigrid solver on parallel computers.

摘要

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.