Numerical studies of perturbed static solutions decay in the coupled system of Yang-Mills-dilaton equations with use of MPI technology

Numerical study results for nonlinear decay of perturbed static spherically symmetric regular solutions in the coupled system of Yang-Mills-dilaton equations are presented. The system under the consideration is a coupled system of nonlinear evolution equations of a hyperbolic type. To attack the problem numerically we used an adaptive mesh refinement algorithm which allows us to investigate the evolution of solutions on a very small and large spatial and time scales without loss of accuracy. The parallel computing technique with use of multiprocessor computing system was applied in order to reduce sufficiently a total simulation time. We used parallelization of counter Thomas algorithm, that is effective for solving on two processors as well as the partition method, that allows one to solve the problem in parallel on $p$ processors with the scope to solve tridiagonal systems of linear equations that arise from finite difference approximations to the original problem. Parallel computing with use of the message passing interface (MPI) was done on cluster with $p=1,2,3,\dots,7$ processors. As a result the total simulation time decreasing and acceleration of calculations is of order $p/2$.