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I describe a method that places the fermion fields and the gauge fields ondifferent lattice spacings during the Hybrid Monte Carlo generation ofGinsparg-Wilson dynamical ensembles. The idea is motivated by Wilson'sformulation of the renormalisation group. After outlining the underlyingtheory, I describe a method to perform most of the work of the HMC on a coarselattice, only requiring to convert to and from the fine lattice once for eachindependent configuration. Because the bulk of the work takes place on thecoarse lattice, including the calculation of most observables, this methodsaves over an order of magnitude in computer time over previous methods.

Multi-grid HMC for Ginsparg-Wilson fermions