A robust and efficient harmonic balance (HB) using direct solution of HB Jacobian

In this paper we introduce a new method of performing direct solution of the harmonic balance Jacobian. For examples with moderate number of harmonics and moderate to strong nonlinearities, we demonstrate that the direct solver has far superior performance with a moderate increase in memory compared to the best preconditioned iterative solvers. This solver is especially suited for Fourier envelope analysis where the number of harmonics is small, circuits are nonlinear and Jacobian bypass can be used for additional speed. For examples with large number of harmonics and moderate to strong nonlinearities, the performance advantage is maintained but the memory requirements increase. We propose efficient preconditioners based on direct solution of harmonic balance matrices which provide the user with a memory-speed trade-off.