We present in detail the Einstein equations in the
Baumgarte-Shapiro-Shibata-Nakamura formulation for the case of D dimensional
spacetimes with SO(D−d) isometry based on a method originally introduced in
Ref.1. Regularized expressions are given for a numerical implementation of this
method on a vertex centered grid including the origin of the quasi-radial
coordinate that covers the extra dimensions with rotational symmetry.
Axisymmetry, corresponding to the value d=D−2, represents a special case with
fewer constraints on the vanishing of tensor components and is conveniently
implemented in a variation of the general method. The robustness of the scheme
is demonstrated for the case of a black-hole head-on collision in D=7
spacetime dimensions with SO(4) symmetry.U.S. is supported by the H2020 ERC Consolidator Grant “Matter and strong-field gravity: New frontiers in Einstein’s theory” grant agreement No. MaGRaTh–646597, the H2020-MSCA-RISE-2015 Grant No. StronGrHEP-690904, the STFC Consolidator Grant No. ST/L000636/1, the SDSC Comet and TACC Stampede clusters through NSF-XSEDE Award Nos. PHY-090003, the Cambridge High Performance Computing Service Supercomputer Darwin using Strategic Research Infrastructure Funding from the HEFCE and the STFC, and DiRAC’s Cosmos Shared Memory system through BIS Grant No. ST/J005673/1 and STFC Grant Nos. ST/H008586/1, ST/K00333X/1. P.F. and S.T. are supported by the H2020 ERC Starting Grant “New frontiers in numerical general relativity” grant agreement No. NewNGR- 639022. P.F. is also supported by a Royal Society University Research Fellowship. W.G.C. and M.K. are supported by STFC studentships.This is the final version of the article. It first appeared from the World Scientific Publishing Company via http://dx.doi.org/10.1142/S021827181641013