  For conventional smoothed particle hydrodynamics (SPH), obtaining the static
solution of a problem is time-consuming. To address this drawback, we propose
an efficient dynamic relaxation method by adding large
artificial-viscosity-based damping into the momentum conservation equation.
Then, operator splitting methods are introduced to discretize the added viscous
term for relaxing the time-step limit. To further improve the convergence rate,
a random-choice strategy is adopted, in which the viscous term is imposed
randomly rather than at every time step. In addition, to avoid the
thread-conflict induced by applying shared-memory parallelization to accelerate
implicit method, a splitting cell-linked list scheme is devised. A number of
benchmark tests suggest that the present method helps systems achieve
equilibrium state efficiently.
