Consider nonlinear eigenvalue problems to compute all eigenvalues in a given region on the complex plane. We propose a parallel multi-step spectral indicator method with the contour integrals being the main ingredient. Step 1 (screening) divides the given region into subregion and compute an indicator for each subregion. Then it decides candidate regions that contain eigenvalues. Step 2 (computation) computes eigenvalues in each candidate region. Step 3 (validation) double checks each eigenvalue by substituting it back to the system and computing the smallest eigenvalue. Each step is carried out in parallel. Two examples are presented for demonstration.

翻译：考虑在复平面给定区域内计算全部特征值的非线性特征值问题。本文提出一种以围道积分为核心的并行多步谱指示法。第一步（筛选）将给定区域划分为子区域并计算每个子区域的指示值，进而确定包含特征值的候选区域；第二步（计算）在每个候选区域中计算特征值；第三步（验证）将每个特征值回代至原系统并计算最小特征值以进行双重校验。各步骤均并行执行。文中通过两个算例进行方法演示。