%0 Generic %1 Barrett1994 %A Barrett, John W. %A Galassi, Mark %A Miller, Warner A. %A Sorkin, Rafael D. %A Tuckey, Philip A. %A Williams, Ruth M. %D 1994 %K gravitation reggecalculus %T A Parallelizable Implicit Evolution Scheme for Regge Calculus %U http://arxiv.org/abs/gr-qc/9411008 %X The role of Regge calculus as a tool for numerical relativity is discussed, and a parallelizable implicit evolution scheme described. Because of the structure of the Regge equations, it is possible to advance the vertices of a triangulated spacelike hypersurface in isolation, solving at each vertex a purely local system of implicit equations for the new edge-lengths involved. (In particular, equations of global ``elliptic-type'' do not arise.) Consequently, there exists a parallel evolution scheme which divides the vertices into families of non-adjacent elements and advances all the vertices of a family simultaneously. The relation between the structure of the equations of motion and the Bianchi identities is also considered. The method is illustrated by a preliminary application to a 600--cell Friedmann cosmology. The parallelizable evolution algorithm described in this paper should enable Regge calculus to be a viable discretization technique in numerical relativity.

@misc{Barrett1994, abstract = { The role of Regge calculus as a tool for numerical relativity is discussed, and a parallelizable implicit evolution scheme described. Because of the structure of the Regge equations, it is possible to advance the vertices of a triangulated spacelike hypersurface in isolation, solving at each vertex a purely local system of implicit equations for the new edge-lengths involved. (In particular, equations of global ``elliptic-type'' do not arise.) Consequently, there exists a parallel evolution scheme which divides the vertices into families of non-adjacent elements and advances all the vertices of a family simultaneously. The relation between the structure of the equations of motion and the Bianchi identities is also considered. The method is illustrated by a preliminary application to a 600--cell Friedmann cosmology. The parallelizable evolution algorithm described in this paper should enable Regge calculus to be a viable discretization technique in numerical relativity. }, added-at = {2009-08-11T22:33:09.000+0200}, author = {Barrett, John W. and Galassi, Mark and Miller, Warner A. and Sorkin, Rafael D. and Tuckey, Philip A. and Williams, Ruth M.}, biburl = {https://www.bibsonomy.org/bibtex/2b746d65bc4c7d85a0acb390b4c891cbe/random3f}, description = {A Parallelizable Implicit Evolution Scheme for Regge Calculus}, interhash = {53cce2458c7d7a52186e98606c1ccb9a}, intrahash = {b746d65bc4c7d85a0acb390b4c891cbe}, keywords = {gravitation reggecalculus}, note = {cite arxiv:gr-qc/9411008 Comment: 19 pages, Plain TeX, 10 figures}, timestamp = {2009-08-11T22:33:10.000+0200}, title = {A Parallelizable Implicit Evolution Scheme for Regge Calculus}, url = {http://arxiv.org/abs/gr-qc/9411008}, year = 1994 }