预条件在谐波平衡仿真算法中的应用

A Preconditioner for the Simulation Using Harmonic Balance

在运用谐波平衡算法对射频集成电路进行仿真时,针对Krylov子空间迭代算法在计算速度和内存存储量等方面存在的限制问题,提出了一种运用稀疏-分段矩阵作为预条件的方法.该方法采用稀疏化、分段压缩以及对称连续超松弛处理,得到的预条件矩阵是原Jacobian矩阵的良好近似.实例表明运用这种稀疏-分段矩阵作为预条件,不仅保证了迭代算法的准确性和优良的收敛性,解决了用块对角矩阵作为预条件时引起收敛速度变慢甚至无法收敛的问题,而且与块对角矩阵做为预条件相比计算速度提高了近50%,所需内存存储量减少了近60%.

To overcome the limitation of Krylov subspace techniques using standard preconditioners on speed and memory requirement in harmonic balance simulations of the steady-state response under multitones drive, a new sparse-subsecional matrix as the preconditioner is developed in this paper. This preconditioner, different form the ordinary block-diagonal matrix, not only is a sufficient approximation of Jacobian matrix, but also exploits the techniques of sparseness and subsecional condensation. With this preconditioner, it could be faster by 50% and ucenwry requirement is reduced by 60% than that of block-diagonal matrix. Some numeric experiments illustrating it are presented.