An efficient multigrid solver for finite element methods on multi-GPU systems

We present a matrix-free p-multigrid method for solving the Poisson problem using the finite element method on GPU-based supercomputers. The solver uses optimised matrix-free kernels to compute the action of arbitrary-degree finite element operators, matrix-free interpolation between finite element spaces of different polynomial degrees, and parallel vector updates, all operating on the GPU. On the coarsest level, we use an algebraic multigrid solver. We examine performance and scalability for the Poisson problem on a number of different meshes. Numerical experiments on the LUMI supercomputer show good parallel performance.