Adaptive methods for nonlinear eigenvalue problems with parameters

本计画主要研究非线性特征值问题的自适应方法，这些问题的特征值参数是非线性的。许多这类问题都是由微分和积分方程的离散化引起的。此外，它们通常取决于附加参数。本研究的目的在于填补离散化过程中的差距，并设计一种稳健的数值方法来有效地解决离散化问题。为了解决这些研究目标，该项目将结合专业知识，从频谱和扰动理论，变分表征，预处理迭代方法，连续方法和后验误差分析。

This project is concerned with adaptive methods for nonlinear eigenvalue problems that are nonlinear in the eigenvalue parameter. Many problems of this type arise from the discretization of differential and integral equations. Furthermore, very often they depend on additional parameters. The proposed research aims to fill the gap in understanding and improving discretization processes and design a robust numerical methods to solve the resulting discretized problems efficiently. To address these research objectives the project will incorporate expertise from the spectral and perturbation theory, variational characterizations, preconditioned iterative methods, continuation methods and a posteriori error analysis.