GPU-accelerated Eigenmode Solver for Coaxial Half-Wave Resonator Cavities

We present a GPU-accelerated finite-difference frequency-domain (FDFD) eigenmode solver for coaxial half-wave resonator (HWR) cavities in cylindrical coordinates. The solver applies a matrix-free curl–curl operator on a staggered Yee grid, treats curved beam-pipe boundaries with the Dey–Mittra conformal subcell method, and incorporates wall losses through a Leontovich impedance boundary condition (IBC) that yields a complex eigenvalue from which the resonant frequency and unloaded quality factor are obtained directly. The resulting complex, non-Hermitian eigenvalue problem is solved by Rayleigh Quotient Iteration with an inner restarted GMRES solver, implemented entirely in CUDA C. We describe the GPU implementation in detail: the structure-of-arrays data layout, the cylindrical curl kernels, the conformal subcell kernels and their additional memory traffic, the complex IBC arithmetic, and the warp-level reductions for the volume-weighted inner products. A roofline characterization shows the curl–curl operator is memory-bandwidth-bound (arithmetic intensity  ≈ 0.72 floating-point operations (FLOPs) per byte); the GPU sustains up to 35% of peak bandwidth and achieves a matrix–vector product (matvec) speedup of up to 26 ×  over a single CPU thread and 8 ×  over a 16-thread CPU, consistent with the architectural bandwidth ratio. A grid convergence study confirms second-order accuracy, and validation against CST Microwave Studio® and COMSOL Multiphysics® shows agreement within 0.01% in frequency. A three-step solution strategy isolates the perturbative effects of radial and endcap pipes on a fixed grid. Finally, a single-pass beam dynamics demonstration confirms that the structured cylindrical field maps are used directly by a GPU particle tracker without interpolation, with the computed energy gain matching the expected radial gap voltage.