A performance benchmark test for geodynamo simulations

In the last ten years, a number of numerical dynamo models have successfully represented basic characteristics of the geomagnetic field. As new models and numerical methods continue to be developed, it is important to update and extend benchmarks for testing these models. The first dynamo benchmark of Christensen et al. (2001) was applied to models based on spherical harmonic expansion methods. However, only a few groups have reported results of the dynamo benchmark using local methods (Harder and Hansen, 2005; Matsui and Okuda, 2005; Chan et al., 2007) because of the difficulty treating magnetic boundary conditions based on the local methods. On the other hand, spherical harmonics expansion methods perform poorly on massively parallel computers because global data communications are required for the spherical harmonics expansions to evaluate nonlinear terms. We perform benchmark tests to asses various numerical methods for the next generation of geodynamo simulations. The purpose of this benchmark test is to assess numerical geodynamo models on a massively parallel computational platform. To compare among many numerical methods as possible, we consider the model with the insulated magnetic boundary by Christensen et al. (2001) and with the pseudo vacuum magnetic boundary, because the pseudo vacuum boundaries are implemented easier by using the local method than the magnetic insulated boundaries. In the present study, we consider two kinds of benchmarks, so-called accuracy benchmark and performance benchmark. In the accuracy benchmark, we compare the dynamo models by using modest Ekman and Rayleigh numbers proposed by Christensen et. al. (2001). We investigate a required spatial resolution for each dynamo code to obtain less than 1% difference from the suggested solution of the benchmark test using the two magnetic boundary conditions. In the performance benchmark, we investigate computational performance under the same computational environment. We perform these dynamo models on XSEDE TACC Stampede, and investigate computational performance. To simplify the problem, we choose the same model and parameter regime as the accuracy benchmark test, but perform the simulations with much finer spatial resolutions to investigate computational capability under the closer condition to the Earth's outer core. We compare the results of the accuracy benchmark and performance benchmark tests by various codes and discuss characteristics of the simulation methods for geodynamo problems.