Full-Chip Harmonic Balance Analysis in Parallel

Harmonic balance (HB) is an important method for computation of the steady-state response of circuits under periodic and quasi-periodic excitations. HB method uses a linear combination of sinusoids to build the solution, which gives it significant advantage in terms of accuracy and efficiency. However, HB method consumes much more memory than traditional transient analysis method, which prevents us from applying it to large-scale circuits. In this paper, we propose a parallel approach to resolve the memory issue and improve the speed drastically. We implement parallel HB on a Beowulf cluster with four Pentium III computers. The circuit is partitioned, the Jacobian matrix is spread over the cluster, and a parallel GMRES is implemented to solve the linear equation over the spread Jacobian. With four computer node, the experiment result shows our parallel approach can solve circuit of 4x times bigger size compared to non-parallel approach, and the speed up of our approach is around 300%.