Large scale numerical computation for quantum field theory is entering a new phase. For the first time cost effective dedicated Terascale hardware provides the capability to simulate the full non-linearities of the fundamental theory of nuclear forces and to confront experimental data with ab initio theoretical predictions. Indeed there is a range of high precision experimental results coming from the major nuclear and particle physics laboratories that can no longer be fully understood by conventional models. They require accurate full Quantum Chromodynamics (QCD) simulations to interpret the data. However the full potential of the international lattice gauge theory initiative will be missed if new or substantially improved algorithms are not developed and optimized on the multi-Terascale architectures for the next decade. The main problem in getting accurate answers for lattice QCD is an efficient algorithm for determining the effects of quark loops on physical quantities. This effect was ignored in earlier quenched approximations which just treated the effects of the gluons of QCD. To solve this problem one needs to evaluate the eigenvalues of the (Dirac) quark propagator in the presence of external gluon fields. In this proposal we will make a concerted and sustained r effort to find new algorithms for the Dirac inverter for QCD in the context of the evolving scientific objective of the National Lattice Gauge theory initiative and the actual architectures being brought into production. Our design focus is on using the best physical and empirical knowledge of the QCD vacuum to guide the design of appropriate multi-scale Krylov space inverters which are known to dominate the compute intensive kernel of all QCD simulation codes.
