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We have developed a numerical framework for a full solution of therelativistic Boltzmann equations for the quark-gluon matter using the multipleGraphics Processing Units (GPUs) on distributed clusters. Including all the $2\to 2$ scattering processes of 3-flavor quarks and gluons, we compute the timeevolution of distribution functions in both coordinate and momentum spaces forthe cases of pure gluons, quarks and the mixture of quarks and gluons. Byintroducing a symmetrical sampling method on GPUs which ensures the particlenumber conservation, our framework is able to perform the space-time evolutionof quark-gluon system towards thermal equilibrium with high performance. Wealso observe that the gluons naturally accumulate in the soft region at theearly time, which may indicate the gluon condensation.

Towards a full solution of relativistic Boltzmann equation for quark-gluon matter on GPUs