I and collaborators have developed a new high-order algorithm for solving the characteristic initial boundary value problem of the Einstein equations.
In the characteristic initial boundary value problem of general relativity, the Einstein equations are recast using a particular coordinate system along outgoing nullrays (along the light (or null) cone).
The characteristic Einstein evolution system is useful for modeling the far-field region of the gravitational-wave zone, and allows one to include future null infinity on the computational grid via radial compactification.
Future null infinity is the region where gravitational waves are unambiguously defined, and is also the place where a gravitational-wave detector would be located.
Previous characteristic evolution schemes were limited to second-order accuracy. The system is peculiar to discretize since there is a hierarchy of equations that must be solved via an outward radial march.
We have devised a new high-order scheme which solves the radial and time direction via a fourth-order Runge-Kutta scheme. The angular differential operators are approximated via a pseudo-spectral collocation method.
The resulting code requires only a fraction of the computational costs of previous algorithms while offering significantly higher accuracy.
More details can be found here.