Space-filling curves for 2-simplicial meshes created with bisections and reflections

Numerical experiments in J. Maubach, Local bisection refinement and optimal order algebraic multilevel preconditioners, PRISM-97 conference Proceedings (eds. O. Axelsson et al), University of Nijmegen, the Netherlands, 1997, 121-136 indicated that the refinement with the use of local bisections presented in J. Maubach, Local bisection refinement for n-simplicial grids generated by reflections, SIAM Journal on Scientific Computing, 16(1995), 210-227 leads to highly locally refined computational 2-meshes which can be very efficiently load-balanced with the use of a space-filling curve. This paper introduces the construction of this curve, which can be produced at almost no costs, proofs that all its properties are invariant under the local bisection, and comments at the 3-dimensional case.