Note: Different Date and Location
Abstract:
In this talk, we present our recent progress in both the theoretical
analysis as well as the design of robust algebraic multigrid (AMG)
methods. In addition, we introduce a practical AMG solver that
maintains multigrid-like optimality, without the need for parameter
tuning, for some problems where current algorithms exhibit degraded
performance.
Our approach falls into the class of adaptive algebraic multigrid (aAMG) solvers, in which the MG hierarchy is generated adaptively using the evolving error of the current solver. The coarse degrees of freedom are selected using a compatible relaxation (CR) based coarsening process, which generally leads to a well-conditioned splitting of the matrix. Then, the nonzero supports of the basis spanning the coarse space are determined using an approximation of the so-called two-level ``ideal'' interpolation operator. The nonzero coefficients of the basis are computed in a way that minimizes the trace of the coarse-level operator. Numerical experiments are presented that demonstrate the efficacy of the approach. In addition, it is demonstrated that this method can be extended in a straightforward manner to handle more complicated situations, for example higher-order scalar partial differential equations or even systems of partial differential equations. Some other adaptive methods are also considered.
This seminar is easily accessible to persons with disabilities. For more information or for assistance, please contact the Mathematics Department at 743-3500.