Multigrid methods are ideal for solving the increasingly large-scale problems that arise in numerical simulations of physical phenomena because their computational costs and memory requirements scale linearly with the degrees of freedom. Unfortunately, they have been historically limited by their applicability to elliptic-type problems and the need for special handling in their implementation. In this talk, we give an overview of several recent theoretical and algorithmic advances that have led to extended applicability of multigrid methods. Specific applications that will be discussed include electromagnetics, radiation transport, and quantum chromodynamics.
CASC LLNL, J. Xu and L. Zikatanov at PSU, and S. MacLachlan at Univ. of Minnesota. This work is an ongoing collaboration with M. Brezina, T. Manteuffel, S. McCormick, and John Ruge at CU Boulder, R. Falgout and P. Vassilevski at CASC LLNL, D. Keyes at Columbia, J. Xu and L. Zikatanov at PSU, and S. MacLachlan at Univ. of Minnesota.