MULTISCALE STOCHASTIC REACTION-DIFFUSION ALGORITHMS COMBINING MARKOV CHAIN MODELS WITH STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

Abstract

We analyze two multiscale methods for reaction-diffusion process stochastic simulations. They can be used in systems that contain areas where the concentrations of molecules differ noticeably. Both approaches split an interest region into two subsets, one for stochastic partial differential equations (SPDEs) and the other for continuous-time Markov chain models. The first approach considers a pseudo compartment (also known as an overlap or handshaking zone) in the SPDE portion of the computational domain immediately next to the interface in order to associate Markov chain (compartment-based) models with reaction-diffusion SPDEs.
There is no usage of an overlap zone in the second algorithm. Additional developments of both schemes are showcased,encompassing the scenario of an adaptively selected boundary separating distinct modeling methodologies.