Optimization of Parallel Legendre Transform using Graphics Processing Unit (GPU) for a Geodynamo Code

Abstract:

Convection and magnetic field of the Earth's outer core are expected to have vast length scales. To resolve these flows, high performance computing is required for geodynamo simulations using spherical harmonics transform (SHT), a significant portion of the execution time is spent on the Legendre transform. Calypso is a geodynamo code designed to model magnetohydrodynamics of a Boussinesq fluid in a rotating spherical shell, such as the outer core of the Earth. The code has been shown to scale well on computer clusters capable of computing at the order of 10⁵ cores using Message Passing Interface (MPI) and Open Multi-Processing (OpenMP) parallelization for CPUs. To further optimize, we investigate three different algorithms of the SHT using GPUs. One is to preemptively compute the Legendre polynomials on the CPU before executing SHT on the GPU within the time integration loop. In the second approach, both the Legendre polynomials and the SHT are computed on the GPU simultaneously. In the third approach , we initially partition the radial grid for the forward transform and the harmonic order for the backward transform between the CPU and GPU. There after, the partitioned works are simultaneously computed in the time integration loop. We examine the trade-offs between space and time, memory bandwidth and GPU computations on Maverick, a Texas Advanced Computing Center (TACC) supercomputer. We have observed improved performance using a GPU enabled Legendre transform. Furthermore, we will compare and contrast the different algorithms in the context of GPUs.