Performance and accuracy benchmarks for a next generation geodynamo simulation

Abstract:

A number of numerical dynamo models have successfully represented basic characteristics of the geomagnetic field in the last twenty years. However, parameters in the current dynamo model are far from realistic for the Earth's core. To approach a realistic parameters for the Earth's core in geodynmo simulations, extremely large spatial resolutions are required to resolve convective turbulence and small-scale magnetic fields. To assess the next generation dynamo models on a massively parallel computer, we performed performance and accuracy benchmarks from 15 dynamo codes which employ a diverse range of discretization (spectral, finite difference, finite element, and hybrid methods) and parallelization methods. In the performance benchmark, we compare elapsed time and parallelization capability on the TACC Stampede platform, using up to 16384 processor cores. In the accuracy benchmark, we compare required resolutions to obtain less than 1% error from the suggested solutions.

The results of the performance benchmark show that codes using 2-D or 3-D parallelization models have a capability to run with 16384 processor cores. The elapsed time for Calypso and Rayleigh, two parallelized codes that use the spectral method, scales with a smaller exponent than the ideal scaling. The elapsed time of SFEMaNS, which uses finite element and Fourier transform, has the smallest growth of the elapsed time with the resolution and parallelization. However, the accuracy benchmark results show that SFEMaNS require three times more degrees of freedoms in each direction compared with a spherical harmonics expansion. Consequently, SFEMaNS needs more than 200 times of elapsed time for the Calypso and Rayleigh with 10000 cores to obtain the same accuracy. These benchmark results indicate that the spectral method with 2-D or 3-D domain decomposition is the most promising methodology for advancing numerical dynamo simulations in the immediate future.