Tera-Scalable Algorithms for Variable-Density Elliptic Hydrodynamics with Spectral Accuracy

Authors:
Andrew W. Cook;William H. Cabot;Peter L. Williams;Brian J. Miller;Bronis R. de Supinski;Robert K. Yates;Michael L. Welcome
Affiliations:
Lawrence Livermore National Laboratory;Lawrence Livermore National Laboratory;Lawrence Livermore National Laboratory;Lawrence Livermore National Laboratory;Lawrence Livermore National Laboratory;Lawrence Livermore National Laboratory;Lawrence Berkeley National Laboratory
Venue:
SC '05 Proceedings of the 2005 ACM/IEEE conference on Supercomputing
Year:
2005

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Abstract

We describe Miranda, a massively parallel spectral/compact solver for variabledensity incompressible flow, including viscosity and species diffusivity effects. Miranda utilizes FFTs and band-diagonal matrix solvers to compute spatial derivatives to at least 10th-order accuracy. We have successfully ported this communicationintensive application to BlueGene/L and have explored both direct block parallel and transpose-based parallelization strategies for its implicit solvers. We have discovered a mapping strategy which results in virtually perfect scaling of the transpose method up to 65,536 processors of the BlueGene/L machine. Sustained global communication rates in Miranda typically run at 85% of the theoretical peak speed of the BlueGene/L torus network, while sustained communication plus computation speeds reach 2.76 TeraFLOPS. This effort represents the first time that a high-order variable-density incompressible flow solver with species diffusion has demonstrated sustained performance in the TeraFLOPS range.