基于COCG的组合迭代法求解电磁场FEM线性方程组

针对COCG算法在求解有限元法分析电磁场边值问题所得到的线性系统时存在的不稳定性问题,提出了一种基于COCG的组合迭代方法。该方法通过在低精度迭代阶段采用COCG,而在其易出现迭代崩溃问题的高精度迭代阶段采用其他相对更稳定的迭代法来进行联合求解。该方法不仅能有效避免COCG算法的不稳定性问题,同时也让其高效率的优点得到充分保留因而有利于整个迭代收敛过程。数值结果表明,提出的组合迭代法能将COCG的高效率和其他迭代法的稳定性进行优势互补,从而能获得比常规的单独迭代法更高的求解性能。

Combined Iterative Method Based on COCG Algorithm for Solving Electromagnetic FEM Linear Equations

A combined iterative method based on COCG algorithm is proposed for overcoming the instability problem of COCG during the process of solving the linear system which is arised from the finite element method for analyzing the electromagnetic boundary problems. The proposed method is constructed to solve the linear system in a combined mode by applying COCG in low-precision stage and another more stable iterative method in high-precision stage in which COCG is easy to suffer from iteration break. Through this method, the instability problem of COCG can be avoided effectively, and in the meanwhile the high efficiency can be kept so as to benefit the overall iterative process. Numerical results show that, both the high efficiency of COCG and the stability of other iterative method can be combined properly by the proposed method, thus much better iterative performance can be achieved when compared with conventional single iterative methods.