  At the heart of the Met Office climate and weather forecasting capabilities
lies a sophisticated numerical model which solves the equations of large-scale
atmospheric flow. Since this model uses semi-implicit time-stepping, it
requires the repeated solution of a large sparse system of linear equations
with hundreds of millions of unknowns. This is one of the computational
bottlenecks of operational forecasts and efficient numerical algorithms are
crucial to ensure optimal performance. We developed and implemented a bespoke
multigrid solver to address this challenge. Our solver reduces the time for
solving the linear system by a factor two, compared to the previously used
BiCGStab method. This leads to significant improvements of overall model
performance: global forecasts can be produced 10%-15% faster. Multigrid also
avoids stagnating convergence of the iterative scheme in single precision. By
allowing better utilisation of computational resources, our work has led to
estimated annual cost savings of GBP 300k for the Met Office.
