Matrix-free GPU implementation of a preconditioned conjugate gradient solver for anisotropic elliptic PDEs

Many problems in geophysical and atmospheric modelling require the fast solution of elliptic partial differential equations (PDEs) in "flat" three dimensional geometries. In particular, an anisotropic elliptic PDE for the pressure correction has to be solved at every time step in the dynamical core of many numerical weather prediction models, and equations of a very similar structure arise in global ocean models, subsurface flow simulations and gas and oil reservoir modelling. The elliptic solve is often the bottleneck of the forecast, and an algorithmically optimal method has to be used and implemented efficiently. Graphics Processing Units have been shown to be highly efficient for a wide range of applications in scientific computing, and recently iterative solvers have been parallelised on these architectures. We describe the GPU implementation and optimisation of a Preconditioned Conjugate Gradient (PCG) algorithm for the solution of a three dimensional anisotropic elliptic PDE for the pressure correction in NWP. Our implementation exploits the strong vertical anisotropy of the elliptic operator in the construction of a suitable preconditioner. As the algorithm is memory bound, performance can be improved significantly by reducing the amount of global memory access. We achieve this by using a matrix-free implementation which does not require explicit storage of the matrix and instead recalculates the local stencil. Global memory access can also be reduced by rewriting the algorithm using loop fusion and we show that this further reduces the runtime on the GPU. We demonstrate the performance of our matrix-free GPU code by comparing it to a sequential CPU implementation and to a matrix-explicit GPU code which uses existing libraries. The absolute performance of the algorithm for different problem sizes is quantified in terms of floating point throughput and global memory bandwidth.Comment: 18 pages, 7 figure

Random Linear Network Coding for 5G Mobile Video Delivery

An exponential increase in mobile video delivery will continue with the demand for higher resolution, multi-view and large-scale multicast video services. Novel fifth generation (5G) 3GPP New Radio (NR) standard will bring a number of new opportunities for optimizing video delivery across both 5G core and radio access networks. One of the promising approaches for video quality adaptation, throughput enhancement and erasure protection is the use of packet-level random linear network coding (RLNC). In this review paper, we discuss the integration of RLNC into the 5G NR standard, building upon the ideas and opportunities identified in 4G LTE. We explicitly identify and discuss in detail novel 5G NR features that provide support for RLNC-based video delivery in 5G, thus pointing out to the promising avenues for future research.Comment: Invited paper for Special Issue "Network and Rateless Coding for Video Streaming" - MDPI Informatio