一种基于不连续伽辽金方法求解多区域目标散射问题的优化预处理器

在电磁散射问题中，由均匀介质和金属组合而成的多区域结构目标在天线仿真、雷达成像等工程问题中有着广泛应用. 针对多区域目标的散射问题，研究了不连续伽辽金（discontinuous Galerkin, GD）方法在多区域面积分（surface integral equation, SIE）矩量法中的使用，同时提出了一种优化的距离稀疏预处理（optimized distance sparse preconditioner, O-DSP）方法。该方法根据阻抗矩阵中不同积分算子随距离变化的特性来个性化选择预处理矩阵，进一步增加了预处理矩阵的稀疏性. 数值计算表明，相比之前的距离稀疏预处理方法，优化的预处理矩阵非零元素仅为以前的一半，而且具有相同加速迭代效果.

An optimal preconditioning scheme for the discontinuous Galerkin solution of multi-region target scattering problems

The electromagnetic scattering from multi-region targets with homogeneous dielectrics and metals are of significant importance in various microwave applications from antenna design to radar imaging. Aiming at the multi-region target scattering problems, the discontinuous Galerkin(GD) solution in the surface integral equation(SIE) method of moment(MoM) is studied, and an optimized distance sparse preconditioner(O-DSP) is proposed. Based on the different matrix characteristics associated with different integrodifferential operators, the proposed preconditioner is constructed by adopting customized sparse strategies, and the sparsity of the preconditioner is further improved. Numerical studies demonstrate that, compared with the conventional DSP, the number of nonzero elements in the proposed precondition matrix is nearly halved, while maintaining similar convergence rate.