一种高效的宽带简正波本征值计算方法

An efficient method for broadband eigenvalue computation

为提高宽带简正波本征值的计算效率,汉密尔顿方法通过公式变换抵消频率项,将宽带简正波本征值的计算由频率、本征值实部和虚部的三维寻根降低至本征值实部和虚部的二维寻根,可以一次性求解单号简正波所有频率对应的简正波本征值。在已有工作的基础上优化和完善了汉密尔顿宽带简正波本征值算法,并加入并行计算方法进一步提高计算效率。以简正波模型KRAKENC作为对比,通过若干数值算例验证了该算法对于宽带简正波本征值的计算精度和计算效率。数值仿真结果显示,在保证宽带简正波本征值计算精度的前提下,该方法的计算效率相对KRAKENC有着明显的优势;加入并行算法后,该方法的计算效率得到大幅提高。

Based on existing Hamiltonian method for eigenvalue calculation of normal mode, an efficient method for broadband eigenvalue calculation is developed. Hamiltonian method gets rid of the frequency term by formula transformation to change the root finding problem from a three-dimensional problem with respect to frequency as well as real and imaginary parts of eigenvalue into a two-dimensional one. As a result, the eigenvalues of singular normal mode corresponding to all frequencies could be solved at one time. A MATLAB parallel computing method and other optimizations are included to improve the computational efficiency of Hamiltonian method. The significant advantage of Hamiltonian method in efficiency is indicated by several numerical simulation comparisons with KRAKENC, while retaining the same accuracy.