Dr. Lili Ju received a research grant from NSF Division of Mathematical Sciences  (DMS-2109633) on “Maximum Bound Principle-Preserving Time Integration Methods for Some Semilinear Parabolic Equations”. The total amount of the award is $150,000 for three years.
 
The project will focus on the algorithms and analysis for a class of equations with applications in fluids dynamics, solid mechanics, materials science, chemistry, and cell biology to image and data sciences. Specifically, a class of semilinear parabolic equations will be considered, and the focus will be on ensuring that the computational solutions possess particular important properties, called the time-invariant maximum bound principle (MBP). Such properties are important for the models of grain growth and coarsening, thin film microstructure, crystal growth, dislocation-solute interactions, and image restoration and deblurring. The project will design and analyze efficient and accurate MBP-preserving time integration methods of high-order accuracies. The project will develop and disseminate software and provide an interdisciplinary training opportunity for graduate students.