IFEG   20353
INSTITUTO DE FISICA ENRIQUE GAVIOLA
Unidad Ejecutora - UE
congresos y reuniones científicas
Título:
Multigrid Numerical Simulation of the Ricci Flow equation in S3
Autor/es:
FLORENCIA PARISI; OSCAR REULA
Lugar:
Mexico DF
Reunión:
Conferencia; 19th International Conference on General Relativity and Gravitation; 2010
Resumen:
In this work we develop a numerical
method to evolve the Ricci Flow equation in 3-dimensions in a spherical
background geometry, which uses a multigrid formulation where the computational
domain (S3) is covered by 8 identical grids or patches. This allows both to
study non trivial topologies, as well as parallelize the computations, where
each patch is evolved separately by a processor. This brings the problem of
ensuring the proper trans-mission of data between grids, by means of imposing
suitable conditions at the interfaces without loosing precision in the results.
In order to achieve this, we obtained the SAT (standing for Simultaneous
Approximation Term) or penalty operators that adequate to the formalism, and
successfully implemented them in a numerical code based on MPI. This work is an
ongoing project, where the mentioned numerical code is in a test and optimization
stage. We do, however, have some preliminary results that seem to point out its
correct and stable operation, faithfully reproducing the expected behavior of
some known solutions.