Numerical methods for linear and nonlinear implicit PDE simulation ---- Domain Decomposition and Nonlinear Multigrid Methods

本课题将线性和非线性偏微分方程（PDEs）的数学分析和数值算法设计相结合。算法将被纳入在科学界广泛用于物理建模的科学软件库PETSc中。这些算法具有可扩展性和可并行性，因此对大规模多学科模拟非常有用。此外，PI的研究为算法提供了坚实的理论支持。PI的研究有望在几个领域产生重大影响：计算流体动力学、材料科学和声散射。PI和她的合作者计划发表关于新算法的档案文章，并在会议上展示结果。堪萨斯大学（University of Kansas）的研究生受到了PI计划的影响，该计划将研究成果纳入她的研究生水平的数值方法课程。本课程面向数学系和工程系的广大学生。

This project combines mathematical analysis and numerical algorithm design for the solution of linear and nonlinear partial differential equations (PDEs). Algorithms will be incorporated in the scientific software library PETSc which is widely used in the scientific community for physical modeling. These algorithms are bscalable, and easily parallelizable, and thus useful for large scale multidisciplinary simulations. Additionally the PI's research provides a solid theoretical support for the algorithms. The PI's research promises to have a major impact in several areas: computational fluid dynamics, material sciences, and acoustic scattering. The PI and her collaborators plan to publish archival articles on the new algorithms and also present results in conferences. Graduate students at the University of Kansas are impacted through the PI's plans to incorporate research results into her graduate level class on numerical methods. This course is available to a broad group of students from mathematical and engineering departments.