Assistant Professor Sara Pollock, Ph.D., in the Department of Mathematics and Statistics, is the Principle Investigator on a recently approved National Science Foundation grant. Her grant will fund the development of numerical tools to approximate solutions of nonlinear problems found in realistic physical models. Pollock's grant is titled: Regularized adaptive methods for classes of nonlinear partial differential equations.
The goal of the grant project is to develop efficient and robust simulation technology for classes of nonlinear diffusion equations. These equations appear often in physically realistic and environmentally relevant modeling problems, such as heat conduction and groundwater flow. Many systems in nature are inherently nonlinear, and standard methods of successive approximation may fail to produce solutions to these models.
The focus of this work is on the mathematically rigorous development of stable and convergent iterative numerical algorithms for the target class of problems. Usually only linear systems can be solved directly, so here the linear approximations to the nonlinear model are adaptively updated until a good approximation is found. The solution methods will be developed based on finite element and related discretizations. The anticipated technical advances of this project will progress the realization of efficient and accurate numerical simulation tools, addressing a substantial problem in scientific computing for realistic physical modeling.
As an Assistant Professor at Wright State, Pollock teaches Scientific Computation at the graduate level, Differential Equations with Matrix Algebra at the undergratudate level, and Applied Mathematics, both at the undergraduate and graduate level. Her research focus is on the design and analysis of efficient and accurate numerical methods for nonlinear and multiscale partial differential equations.
Congratulations to Dr. Pollock upon the successful award of her grant.