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.

翻译：本文研究二维与三维空间中非自伴二次算子谱的数值计算问题。事实上，在多维情形下，关于特征值分布的理论结果极为有限，这导致需要求解非线性特征值问题。引言部分首先回顾一维情形下已获得的理论与数值结果，随后重点阐述针对二维与三维情形所开发的谱计算方法（基于有限差分离散化）。文中系统展示并分析了所获得的数值结果。本研究的核心难点在于需要计算强非自伴算子的不稳定特征值。此项工作是先前一维空间研究的延续与发展。