PSU Mathematics Department - Meeting Details

For more information about this meeting, contact Xiantao Li, Yuxi Zheng, Kris Jenssen, Jinchao Xu, Hope Shaffer.

Abstract:
Title:	Leveraging Flexibility in Energy Minimization Algebraic Multigrid
Seminar:	Computational and Applied Mathematics Colloquium
Speaker:	Ray Tuminaro, Sandia Lab
A general interpolation strategy for algebraic multigrid that uses an energy-minimization principle is presented based on minimization ideas for Krylov solvers. The proposed strategy is applicable to symmetric and nonsymmetric problems in both a classical and smoothed-aggregation-based algebraic multigrid framework. Each column of the interpolation operator is minimized in an energy-based norm, while enforcing two constraints. A sparsity pattern is enforced on the interpolation matrix and important user-defined modes, such as the constant, are preserved in the span of the prolongator. A key advantage of energy-minimization approaches is that they are quite flexible. In particular, it is relatively straight-forward to use an energy-minimization approach with a variety of coarsening schemes, to specify the basis function support in a fairly arbitrary way for grid transfers, to accurately interpolate user-defined important modes, and to have some choice of norm for minimization and search space. In this talk, we consider a few application areas where this flexibility is advantageous. These include extended finite elements and fracture propagation, traditional finite elements and anisotropic elasticity, reservoir simulation, and some fluid flow problems.