Multigrid methods for solving Einstein field equations and general-relativistic hydrodynamics simulations

The formation and behaviour of compact objects are highly complex and relativistic phenomena that require numerical simulation to model accurately.
Most of the existing numerical relativity codes solve the metric with the hyperbolic evolution schemes.
Although the constrained formulation is accurate and stable, they are not widely used because solving elliptic PDEs require more computational time than hyperbolic evolution schemes.
Multigrid methods solve differential equations with a hierarchy of discretizations and its computational cost is generally lower than other methods such as direct methods, relaxation methods, SOR etc.
With multigrid acceleration, we are able to solve the metric with the comparable time scale as solving hydro equations.
This makes the constrained formulations more affordable in numerical relativity simulations.
We present the methodology and implementation of a new multidimensional cell-centred multigrid metric solver and its properties and performance in the relativistic problems.