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

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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.