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的解的预条件策略的研究。特别是，研究人员将在椭圆算子不是自伴的情况下使用预条件，例如在外部区域中的某些非自伴Helmholtz问题中。在用数值方法求解椭圆型方程边值问题的过程中，需要求解由连续问题转化为离散问题所产生的大型线性方程组。研究人员将开发出求解此类线性系统的方法，这些方法既高效又稳健，使研究人员能够节省时间和金钱。

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.