Abstract
In lattice QCD simulations the formulation of the theory in lattice should be chiral in order that symmetry breaking happens dynamically from interactions. In order to guarantee this symmetry on the lattice one uses overlap and domain wall fermions. On the other hand high computational cost of lattice QCD simulations with overlap or domain wall fermions remains a major obstacle of research in the field of elementary particles. We have developed the preconditioned GMRESR algorithm as fast inverting algorithm for chiral fermions in U(1) lattice gauge theory. In this algorithm we used the geometric multigrid idea along the extra dimension.The main result of this work is that the preconditioned GMRESR is capable to accelerate the convergence 2 to 12 times faster than the other optimal algorithms (SHUMR) for different coupling constant and lattice 32x32. Also, in this paper we tested it for larger lattice size 64x64. From the results of simulations we can see that our algorithm is faster than SHUMR. This is a very promising result that this algorithm can be adapted also in 4 dimension.
Highlights
Lattice QCD is a lattice gauge theory formulated on a lattice of points in space and time
In this work we develop prototypes of algorithms that are using high-end computing as our contribution to QCDLAB package [2],[3] for simulating chiral fermions
In order to develop fast algorithms, we use the truncated overlap variant of domain wall fermions in 2 + 1 dimensions with the extra finite dimension N3. Using this idea we have developed an algorithm called the preconditioned GMRESR in [15] which converges faster than optimal algorithms used in simulations with chiral fermions.In essence the preconditioned GMRESR follows two levels;
Summary
Lattice QCD is a lattice gauge theory formulated on a lattice of points in space and time. It is important to build in lattice a theory with chiral fermions as chiral symmetry is characteristic of strong interactions. It should be made inversion of the chiral Dirac operator in the lattice which has high complexity [14]. In this work we develop prototypes of algorithms that are using high-end computing as our contribution to QCDLAB package [2],[3] for simulating chiral fermions. This package, a MATLAB/OCTAVE based environment, allows fast prototyping of linear algebraic computations and accelerates the process of finding the most efficient fermion algorithm
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