Efficient spherical harmonic transforms on GPU and its use in planetary core dynamics simulations

Most of the new supercomputers now use acceleration technology such as GPUs. They promise much higher performance than traditional CPU-only servers, both in terms of floating point operation throughput and memory bandwidth. Furthermore, the electric consumption is significantly reduced, resulting in lower carbon emissions.
However, such high computation speeds can only be achieved if a set of more or less stringent rules are followed with respect to memory access and program flow. As a consequence some algorithms more easily approach peak performance.

Here, we present the results of an effort to achieve high performance on recent nvidia GPU accelerators for the spherical harmonic transform. The spherical harmonic transform can be split into a Legendre transform (which is compute bound) and a Fourier transform (which is memory bound).
By taking advantage of recent algorithmic improvements as well as by tuning the Fourier transform, the can now compute a full forward or backward spherical harmonic transform up to degree 8191 on a single 16GB Volta GPU in less than 0.35 seconds.
For lower resolution (up to degree 1023), a single Volta GPU performs a full transform more than 3 times faster than a 48-cores dual socket Skylake Xeon Platinum server.

We also present results of an ongoing effort to port the (simulation of planetary core fluid and magnetic field dynamics) to GPU-accelerated computers.