A GPU-Accelerated Parallel Shooting Algorithm for Analysis of Radio Frequency and Microwave Integrated Circuits

This paper presents a new parallel shooting-Newton method based on a graphic processing unit (GPU)-accelerated periodic Arnoldi shooting solver (GAPAS) for fast periodic steady-state analysis of radio frequency/millimeter-wave integrated circuits. The new algorithm first explores a periodic structure of the state matrix by using a periodic Arnoldi algorithm for computing the resulting structured Krylov subspace in the generalized minimal residual (GMRES) solver. The resulting periodic Arnoldi shooting method is very amenable for massive parallel computing, such as GPUs. Second, the periodic Arnoldi-based GMRES solver in the shooting-Newton method is parallelized on the recent NVIDIA Tesla GPU platforms. We further explore CUDA GPUs features, such as coalesced memory access and overlapping transfers with computation to boost the efficiency of the resulting parallel GAPAS method. Experimental results from several industrial examples show that when compared with the state-of-the-art implicit GMRES method under the same accuracy, the new parallel shooting-Newton method can lead up to $8\times$ speedup.