Exploiting GPU capability in the fully spectral magnetohydrodynamics code QuICC

QuiCC is a code designed to solve the equations of magnetohydrodynamics in a full sphere and other geometries. The aim is to provide understanding of the dynamo process
that sustains planetary magnetic fields for billions of years by thermally-driven convective motion of an electrically-conducting fluid. It also aims to provide the first
clues as to how and why the magnetic fields can undergo reversals. The code must solve the coupled equations of conservation of momentum (the Navier Stokes equation), Maxwell's equations of electrodynamics and the equation of heat transfer. For accuracy and to facilitate imposition of boundary conditions,
a fully spectral method is used in which angular variables in a spherical polar coordinate system are expanded in spherical harmonics, and radial variables are expanded in a
special polynomial expansion in Jones-Worland polynomials. As a result the coordinate singularities at the north and south poles and at the origin disappear.
The code is designed to run on upward of 10^4 processors using MPI and shows excellent scaling.
At the heart of the method is the ability to move between physical and spectral space by a variety of exact transforms: these involve the well-known Fast Fourier Transform (FFT) and also the Legendre transform and Jones-Worland transform.
In this talk we will focus on the latest advancements in the field of fast GPU algorithms for these types of discrete transforms. We present an extension to the publicly-released VkFFT library - GPU Fast Fourier Transform library for Vulkan, CUDA, HIP and OpenCL, that allows the calculation of the Discrete Cosine Transforms of types I-IV. This is a very exciting addition to what VkFFT can do as DCTs are often used in image processing, data compression and numerous other scientific tasks.
So far, this is the first publicly available optimized GPU implementation of DCTs. We also present our progress in creating efficient Spherical Harmonic transforms (SHTs) and radial transforms using  GPU implementations.  This talk will present Jones-Worland and Associated Legendre Polynomial Transforms for modern GPU architectures, implemented based on the VkFFT runtime kernel optimization model. Combined, they can be used to create a new era of full-sphere models for planetary simulations in geophysics.