News 2020: Mathematics professor receives NSF grant to create algorithms that break down the dynamics in physics, engineering, and biological sciences

Professor Cheng Wang will administer $150,000 of the grant to study highly efficient, structure-preserving numerical schemes for nonlinear gradient equations with singular energy potentials

Professor Cheng Wang (Mathematics) was part of a research team that received a $350,000 National Science Foundation grant for their project "Collaborative Research: Efficient, Accurate, and Structure-Preserving Numerical Methods for Phase Fields-Type Models with Applications".

Wang, who will administer $150,000 of the grant, aims to study highly efficient, structure-preserving numerical schemes for nonlinear gradient equations with singular energy potentials. These proposed numerical schemes would lead to highly efficient solvers to study the complicated long-time dynamics of different models in physics, material engineering, and biological sciences. In particular, this work is expected to have a direct and immediate impact on many scientific disciplines.

According to Wang and his team, the large time scale simulation of these nonlinear gradient flows is vital for understanding phase transformations of materials at the atomic and nanometer scales, the complex processes in biological growth and development, and the complicated topological change involved in two-phase and ternary flows for example.

The grant will produce algorithms and software, which will be available free of cost to future researchers. Ultimately, Wang’s project will influence research in atomic-scale phase transitions; complex biological growth and cancer; and multi-phase active-particle and ionic fluids. Utilizing free resources from high performance-computing programs, the codes developed in this project could be scaled up to conduct real-world three-dimensional simulations.

Wang says that this grant will create a graduate research assistant position at UMassD and offer students the opportunity to receive innovative training in scientific computing, modeling, and numerical analysis.

The lead PI on the project is Professor Steven Wise (Mathematics) of the University of Tennessee.