Constructing of constraint preserving scheme for Einstein equations
For researchers in numerical relativity, this provides a constraint-preserving scheme that improves stability over standard methods.
The paper proposes a new numerical scheme for evolving Einstein equations that preserves constraints at the discrete level, showing better stability than the Crank-Nicolson scheme in simulations.
We propose a new numerical scheme of evolution for the Einstein equations using the discrete variational derivative method (DVDM). We derive the discrete evolution equation of the constraint using this scheme and show the constraint preserves in the discrete level. In addition, to confirm the numerical stability using this scheme, we perform some numerical simulations by discretized equations with the Crank-Nicolson scheme and with the new scheme, and we find that the new discretized equations have better stability than that of the Crank-Nicolson scheme.