  A new computationally efficient method has been introduced to treat
self-gravity in mesh based hydrodynamical simulations. It is applied simply by
slightly modifying the Poisson equation into an inhomogeneous wave equation.
This roughly corresponds to the weak field limit of the Einstein equations in
general relativity, and as long as the gravitation propagation speed is taken
to be larger than the hydrodynamical characteristic speed, the results agree
with solutions for the Poisson equation. The solutions almost perfectly agree
if the domain is taken large enough, or appropriate boundary conditions are
given. Our new method can not only significantly reduce the computational time
compared with existent methods, but is also fully compatible with massive
parallel computation, nested grids and adaptive mesh refinement techniques, all
of which can accelerate the progress in computational astrophysics and
cosmology.
