标题： 任意精度的流体动力学稳定性特征值计算 显示英文标题

标题： Arbitrary precision computation of hydrodynamic stability eigenvalues

摘要： 我们证明，通过使用高阶精度算术，即使用比标准双精度数字具有更多有效位数的浮点类型，可以准确计算出流体动力稳定性问题中出现的非正规矩阵的特征值。 这一基本原理通过两个著名的$7\times 7$矩阵的经典例子来说明，众所周知，当使用标准双精度算术时，特征值计算会失败。 然后我们提出了Chebyshev tau-QZ方法的一个实现，该实现允许结合大量的切比雪夫多项式和任意精度算术的使用。 这被用来计算在高雷诺数下库特流和泊肃叶流的谱的行为。 最后的实验收敛性分析清楚地表明，需要高阶精度才能获得准确的结果。 显示英文摘要

摘要： We show that by using higher order precision arithmetic, i.e., using floating point types with more significant bits than standard double precision numbers, one may accurately compute eigenvalues for non-normal matrices arising in hydrodynamic stability problems. The basic principle is illustrated by a classical example of two $7\times 7$ matrices for which it is well known that eigenvalue computations fail when using standard double precision arithmetic. We then present an implementation of the Chebyshev tau-QZ method allowing the use of a large number of Chebyshev polynomials together with arbitrary precision arithmetic. This is used to compute the behavior of the spectra for Couette and Poiseuille flow at high Reynolds number. An experimental convergence analysis finally makes it evident that high order precision is required to obtain accurate results.