A Fast Parallel Algorithm Based on GPU for Harmonic Balance Method

Computational electromagnetics methods for analysing nonlinear systems are computationally complex, such as harmonic balance (HB) method, especially when dealing with a large number of frequency points. In this paper, we propose a fast parallel algorithm for HB method to accelerate electromagnetic simulation. The new algorithm parallelizes the construction of nonlinear Jacobian matrix, utilizing graphical processing unit (GPU) to realize improvements for electromagnetic simulation. We present the formulations of the parallel HB method, and subsequently provide its implementation details based on the mixed platform with GPU and CPU. Experimental results from several industrial cases illustrate that the new parallel algorithm leads to $3 \times$ speedup compared to the conventional HB method while still maintaining the similar accuracy, where the GPU-accelerated part is about 10 times faster than its CPU counterpart.