Mathematical Sciences: Numerical Solution of Elliptic Equations

该奖项涉及对椭圆边值问题离散化中出现的大型线性系统解的预处理策略的研究。特别地，研究者将在椭圆算子不自伴随的情况下使用预处理，如在某些非自伴随的外域亥姆霍兹问题中。在求解椭圆方程边值问题的数值过程中，当用离散问题代替连续问题时，需要求解非常大的线性方程组。研究者将开发方法来解决这样的线性系统，既有效又稳健，使研究人员节省时间和金钱。

This award involves the study of preconditioning strategies for the solution of the large linear systems that arise in the discretization of elliptic boundary value problems. In particular, the investigator will use preconditioning in cases when the elliptic operator is not self-adjoint, as in certain non-self-adjoint Helmholtz problems in exterior domains. In the course of solving boundary value problems for elliptic equations numerically it is necessary to solve very large systems of linear equations that arise when the continuous problem is replaced with a discrete one. The investigator will develop methods for solving such linear systems that are both efficient and robust, enabling researchers to save time and money.