Richard Brower
Physics Department
Boston University

Abstract. Quantum Chromodynamics (QCD) is the precise theory of nuclear forces, which like all fundamental quantum field theories requires solving the linear Dirac equation in an ensemble of fluctuating gauge potentials. In the next decade Petaflop/years of computational hardware will work on inverting this elliptic differential operator for the Dirac (quark) propagator for QCD. Even modest progress on this problem could profoundly impact QCD predictions and related Dirac simulations in electronic materials. This talk will define the problem from the perspective of multi-scale domain decomposition solvers. The crucial role of "gauge", "chiral" and "scaling" symmetries in QCD will be emphasized. Earlier experiments circa 1990 with (gauge invariant) multi-grid will be contrasted with on going developments using adaptive smooth aggregation methods.