We have developed a multiscale method coupling the mesoscopic and microscopic scales. On the mesoscopic scale, systems are modeled as discrete jump processes on a structured or unstructured grid, while on the microscopic scale, molecules are modeled by hard spheres diffusing in continuous space.
Microscopic simulations are accurate but computationally expensive. In this paper we try to automatically detect which parts of a system that need high accuracy to be accurately resolved, and which parts can be simulated on the coarser mesoscopic scale. We also extend a previously developed hybrid algorithm (http://epubs.siam.org/doi/abs/10.1137/110832148), to improve its convergence properties.
This new algorithm makes it possible to simulate larger systems with greater accuracy than before, thus significantly widening the scope of problems that can be simulated at the particle level.
The manuscript has been submitted and is under review. It is available on Arxiv at https://arxiv.org/abs/1709.00475