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:
Leicester
Reunión:
Conferencia; ENUMATH 2011: European Numerical Mathematics and Advanced Applications; 2011
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 ($S^3$) 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 transmission 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.