稀疏化递归Cholesky分解预条件技术加速PO-MoM迭代求解

提出了一种新的稀疏化递归Cholesky分解预条件技术,并应用于加速物理光学和矩量法(PO-MoM)混合方法分析大型复杂载体上线天线的辐射问题.基于积分方程积分核的物理意义,忽略MoM区与PO区的耦合,构造出一个PO-MoM混合方法系数矩阵的稀疏近似阵.然后采用Cholesky分解方法将该稀疏阵的逆阵进行递归分解,得到一个矩阵连乘形式的预条件阵.将该预条件阵用于预条件广义最小留数(GM RES)法迭代求解线性方程组,应用该技术对卫星和舰船两个电大尺寸复杂载体模型上天线辐射问题进行了求解.结果表明,采用这种新的预条件技术可以大大加快方程组迭代求解的收敛速度,明显提高计算效率.

Sparse Recursive Cholesky Factorization Preconditioning Technique for Acceleration of Iterative Solution to PO-MoM Problems

A novel sparse recursive Cholesky factorization preconditioning technique is proposed for accelerating analyses of radiation problems of wire antennas mounted on large complex platforms with a hybrid method of physical optics and moments(PO-MoM).Based on the physical meanings of the electric field integral equation(EFIE) kernel and neglecting coupling between MoM and PO regions,an approximate sparse matrix of the coefficient matrix derived from the PO-MoM hybrid method is obtained.Inverse of the sparse matrix is then factorized recursively with Cholesky factorization.Thereafter,a preconditioner in a form of successive multiplication is constructed.It is used in a preconditioned generalized minimal residual(GMRES) method to iteratively solve the systems of linear equations.The proposed preconditioning technique is applied to solve radiation problems of antennas mounted on a satellite model and a ship model in electrically large size.Numerical results demonstrate that the new preconditioning technique is efficient in reducing the number of iterations in solving the linear systems derived from PO-MoM.