Constructing of constraint preserving scheme for Einstein equations

Takuya Tsuchiya; Gen Yoneda

doi:10.14495/jsiaml.9.57

Constructing of constraint preserving scheme for Einstein equations

General Relativity and Quantum Cosmology 2017-10-24 v3 Dynamical Systems Numerical Analysis

Authors: Takuya Tsuchiya , Gen Yoneda

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Abstract

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.

Keywords

gas-kinetic scheme nonlinear evolution equations proper orthogonal decomposition

Cite

@article{arxiv.1610.04543,
  title  = {Constructing of constraint preserving scheme for Einstein equations},
  author = {Takuya Tsuchiya and Gen Yoneda},
  journal= {arXiv preprint arXiv:1610.04543},
  year   = {2017}
}