GPU-based Arnoldi factorisation for accelerating finite element eigenanalysis

We present a GPU-accelerated implementation of the k-step Arnoldi factorisation [1] 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 [2] 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 [3] routines for the CUDA API from NVIDIA (cublas) [4]. 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 in [5] further improving performance.

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