标题： 二维和三维非自伴算子谱的数值方法 显示英文标题

标题： Numerical approaches to compute spectra of non-self adjoint operators in dimensions two and three

摘要： 在本文中，我们关注非自伴二次算子谱的数值计算，在二维和三维空间维度中。确实，在多维情况下，关于特征值位置的结果非常有限。这导致需要解决非线性特征值问题。在引言中，我们首先回顾一维情况下的理论结果和数值结果。然后，我们介绍为计算二维和三维情况下的谱而开发的数值方法（有限差分离散化）。给出了获得的数值结果并进行了分析。这里的一个困难是我们必须计算强非自伴算子的特征值，这些算子是不稳定的。这项工作延续了之前在一维空间维度上的工作。 显示英文摘要

摘要： In this article we are interested for the numerical computation of spectra of non-self adjoint quadratic operators, in two and three spatial dimensions. Indeed, in the multidimensional case very few results are known on the location of the eignevalues. This leads to solve nonlinear eigenvalue problems. In introduction we begin with a review of theoretical results and numerical results obtained for the one dimensional case. Then we present the numerical methods developed to compute the spectra (finite difference discretization) for the two and three dimensional cases. The numerical results obtained are presented and analyzed. One difficulty here is that we have to compute eigenvalues of strongly non-self-adjoint operators which are unstable. This work is in continuity of a previous work in one spatial dimension.