Project title: Multiscale Stochastic Reaction-Diffusion Algorithms
Dr. Hye-Won Kang has been awarded an NSF grant ( DMS–1620403) in the amount of $199,993 for the period 2016–2019 by the Division of Mathematical Sciences, Computational Mathematics Program.
The project focuses on the development and the analysis of multiscale numerical algorithms for stochastic reaction-diffusion processes combining different numerical schemes. Markov chain models are widely used to model chemically reacting species with diffusion, but the exact simulation of Markov chain models for large systems are computationally expensive when the systems involve multiscale phenomena. There are many studies to develop and to understand multiscale methods for stochastic reaction-diffusion processes using Markov chain models, but the major drawback in the existing methodologies is that they do not fully account for significant changes in the abundances of chemical species in time and space, which reduce the accuracy of the approximations. In this project, a spatial domain of interest will be divided into several subsets based on the abundance of chemical species and Markov chain models and stochastic partial differential equations will be respectively applied to the different regions.
Dr. Hye-Won Kang has been awarded an NSF grant ( DMS–1620403) in the amount of $199,993 for the period 2016–2019 by the Division of Mathematical Sciences, Computational Mathematics Program.
The project focuses on the development and the analysis of multiscale numerical algorithms for stochastic reaction-diffusion processes combining different numerical schemes. Markov chain models are widely used to model chemically reacting species with diffusion, but the exact simulation of Markov chain models for large systems are computationally expensive when the systems involve multiscale phenomena. There are many studies to develop and to understand multiscale methods for stochastic reaction-diffusion processes using Markov chain models, but the major drawback in the existing methodologies is that they do not fully account for significant changes in the abundances of chemical species in time and space, which reduce the accuracy of the approximations. In this project, a spatial domain of interest will be divided into several subsets based on the abundance of chemical species and Markov chain models and stochastic partial differential equations will be respectively applied to the different regions.
