2017/09/01 by Stefan Hellander, Andreas Hellander, Hellander, Stefan +3
Decision Sciences · #FOS: Mathematics #Numerical Analysis (math.NA) #Simulation Techniques and Applications
paper · pdf · doi:10.48550/arxiv.1709.00475
openalex publication_date 2017/09/01 · openalex created_date 2022/10/05 · openalex updated_date 2026/08/01
The reaction-diffusion master equation (RDME) is a model that allows for\nefficient on-lattice simulation of spatially resolved stochastic chemical\nkinetics. Compared to off-lattice hard-sphere simulations with Brownian\nDynamics (BD) or Green's Function Reaction Dynamics (GFRD) the RDME can be\norders of magnitude faster if the lattice spacing can be chosen coarse enough.\nHowever, strongly diffusion-controlled reactions mandate a very fine mesh\nresolution for acceptable accuracy. It is common that reactions in the same\nmodel differ in their degree of diffusion control and therefore require\ndifferent degrees of mesh resolution. This renders mesoscopic simulation\ninefficient for systems with multiscale properties. Mesoscopic-microscopic\nhybrid methods address this problem by resolving the most challenging reactions\nwith a microscale, off-lattice simulation. However, all methods to date require\nmanual partitioning of a system, effectively limiting their usefulness as\n'black-box' simulation codes. In this paper we propose a hybrid simulation\nalgorithm with automatic system partitioning based on indirect a priori error\nestimates. We demonstrate the accuracy and efficiency of the method on models\nof diffusion-controlled networks in 3D.\n