【摘要】 实现ADI-FDTD并行计算的关键是三对角线性方程组的求解。提出了一种新的分解方法实现三对角线性方程组的并行求解,使得修正值计算方程组仍为三对角线性方程组,且具有对角占优特性。修正值方程组采用循环归约算法求解,根据三对角系统的对角占优的强弱和预期的计算精度选择适当的归约次数,近似处理可加速方程组的求解。利用FDTD的重复计算特性,保存适当的中间量可降低算法的计算复杂性和通信复杂性,但对存储空间的要求更高。算例验证了算法的正确性。更多还原

【Abstract】 The key for parallel implementation of ADI-FDTD is the solution of tri-diagonal linear system.A new decomposition method is proposed to realize the parallel solution of tri-diagonal linear equations,which remains the correction equations in tri-diagonal linear equations and diagonally dominant.The correction equations are solved in the cyclic reduction algorithm.Based on the precondition precision and the diagonally dominant of tri-diagonal system,the appropriate reduction times are determined to speed up the solution.The repeating calculation characteristics of FDTD are considered,the appropriate intermediate quantity can reduce both computational complexity and communication complexity,but more storage space is highly required.Numerical examples verify the correctness of the algorithm.更多还原