Usage of Parallel Algorithms Based on CUDA Technology for Realisation of Reaction-Diffusion Models of Two-Dimensional Cellular Ensemble
Penenko A.V., Troeglazova T.S., Zubairova U.S., Bayshibaev D.Zh., Nikolaev S.V.
Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Novosibirsk 630090, Russia,
Novosibirsk State University, Novosibirsk 630090, Russia
D. Serikbayev East-Kazakhstan state technical university, Ust-Kamenogorsk 070004, Kazakhstan
Institute of Cytology & Genetics, SB RAS, Novosibirsk 630090, Russia
Abstract. In the framework of the morphogen theory the growth and differentiation of cellular tissue can be described by mathematical models of reaction-diffusion containing a system of differential equations with partial derivatives. Taking into account the cellular structure of the tissue, such models are reduced to a system of ordinary differential equations. When modeling a real size tissue containing 104-106 cells, the dimension of the system of equations makes actual use of high-performance computing to solve the problem in an acceptable time. In this work, we consider the direct problem solving algorithm based on splitting tasks by biophysical processes and explicit computational schemes for the implementation of individual processes. The paper demonstrates the effectiveness of this scheme for calculations on graphics accelerators in the framework of high performance computing CUDA.
Key words: morphogenesis, reaction-diffusion model, high performance computing, splitting scheme, graphics accelerators.