Acta Univ. Sapientiae, Informatica, 5, 2 (2013) 184–211 Yang-Mills lattice on CUDA Rich´ ard FORSTER E¨ otv¨osUniversity email: forceuse@inf.elte.hu ´ Agnes F ¨ UL ¨ OP E¨ otv¨osUniversity email: fulop@caesar.elte.hu Abstract. The Yang-Mills fields have an important role in the non- Abelian gauge field theory which describes the properties of the quark- gluon plasma. The real time evolution of the classical fields is given by the equations of motion which are derived from the Hamiltonians to contain the term of the SU(2) gauge field tensor. The dynamics of the classi- cal lattice Yang-Mills equations are studied on a 3 dimensional regular lattice. During the solution of this system we keep the total energy on constant values and it satisfies the Gauss law. The physical quantities are desired to be calculated in the thermodynamic limit. The broadly available computers can handle only a small amount of values, while the GPUs provide enough performance to reach out for higher volumes of lattice vertices which approximates the aforementioned limit. 1 Introduction In particle physics there are many fundamental questions which demand the GPU, from both theoretical and experimental point of view. In the CERN NA61 collaboration one of the most important research field is the quark- gluon plasma’s critical point examination. The topics of theoretical physics includes the lattice field theory which is a crossover phase transition in the quark gluon plasma and SU(N) gauge theory with topological lattice action in the QCD. We present an algorithm which determines the real time dynamics of Yang- Mills fields which uses the parallel capabilities of the CUDA platform. We Computing Classification System 1998: I.1.4 Mathematics Subject Classification 2010: 81T25 Key words and phrases: lattice gauge field, parallel computing, GPU, CUDA 184