GPU-based Arnoldi factorisation for accelerating finite element eigenanalysis

We present a GPU-accelerated implementation of the k-step Arnoldi factorisation that forms the basis of a number of iterative eigenvalue system solvers. These solvers are important for the finite element analysis of the cutoff and dispersion characteristics of waveguide structures as well as cavity resonances and since they contribute significantly to the runtime in computing a solution, their acceleration is of interest. The initial GPU-based implementation makes use of accelerated BLAS routines for the CUDA API from NVIDIA (cublas). This allows us to utilise the computational power of the GPU at a functional level as a proof of concept with minimal coding effort. The implementation is then refined to make use of enhancements to the matrix-vector multiplication routines proposed by Fujimoto further improving performance.