PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

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Title:10/17 2:00pm (special time) Efficient algebraic preconditioners for large-scale electromagnetic problems
Seminar:CCMA PDEs and Numerical Methods Seminar Series
Speaker:Tzanio V. Kolev, LLNL
Abstract:
ABSTRACT: Numerical simulation of electromagnetic phenomena is of critical importance in a number of practical applications. In many simulation codes, Maxwell's equations are reduced to a second-order PDE system involving one of the vector fields or a new vector potential. The definite Maxwell equations, for example, arise after discretization in time, while magnetostatics with a vector potential leads to the semidefinite Maxwell problem. In this talk, I will present some recent work on algebraic preconditioners for unstructured finite element discretizations of the above problems. Such discretizations result in large sparse linear systems that could not be solved efficiently by the previously existing algebraic multigrid (AMG) solvers. The first preconditioning scheme that I will discuss uses an auxiliary problem posed on a related mesh, which is more amenable for constructing optimal order multigrid methods. In combination with a domain embedding technique, this method can precondition a problem defined on a very complicated mesh by a standard geometric multigrid on a box. The main tool in the theory and the implementation of the above approach is the interpolation operator, which maps auxiliary functions into the (edge) finite element space. Recently, Hiptmair and Xu showed that one could use an auxiliary space that is conforming and is defined on the same mesh. I will present a number of numerical experiments with a parallel version of their method, which utilizes two internal AMG V-cycles: one for a scalar and one for a vector Poisson-like matrix. The results demonstrate very good scalability on unstructured 3D grids, including on problems with variable coefficients and zero conductivity.

Room Reservation Information

Room Number:MB216
Date:10 / 15 / 2007
Time:03:35pm - 04:25pm