Algorithms for calculating quark propagators on large lattices (Q1088375)

We describe methods for solving large sparse systems of linear equations on computers with limited fast memory, or high ratios of processor speed to bandwidth between main and fast memory. Our algorithms are designed for calculating quark propagators, columns of the inverse of the fermion matrix in lattice quantum chromodynamics, but are more generally applicable. We compare their rates of convergence and the balance between CPU time and I/O overhead. We present a block-iterative algorithm which when implemented on the DAP is 5 times as efficient as the conjugate gradient method for \(16^ 3\times 24\) lattices (complex linear systems of size approximately \(3\times 10^ 5)\).