三维局部多层快速多极子算法

Three-dimensional local multilevel fast multipole algorithm

为了进一步加速多层快速多极子算法求解电大尺寸目标电磁散射,提出了一种基于局部耦合技术计算矩阵矢量相乘的多层快速多极子方法。通过在迭代过程中设置与迭代误差相关的最初层,每次迭代仅仅需要考虑局部的耦合区域。该方法在保证合理计算精度的同时大大降低了迭代过程中矩阵矢量相乘的计算复杂度,提高了多层快速多极子方法计算效率。数值结果说明了所提方法的有效性。

To further speed up the solution of scattering from three dimensional electrically large object by multilevel fast multipole algorithm（MLFMA）, a local multilevel fast multipole algorithm （LMLFMA） based on local interactions is proposed to evaluate matrix vector multiplication. Only local interaction regions need to be considered by setting the coarsest level related to iteration error in the iteration process. It reduces greatly the computational complexity of matrix-vector multiplication in conjugate gradient iteration, improves the efficiency of MLFMA while the reasonable accuracy is maintained. Numerical results demonstrate the validity of the presented method.