In this talk, on two-dimension unstructured triangular meshes, an efficient fully -discrete local discontinuous Galerkin (LDG) method is presented for solving the nonlinear reaction-diffusion systems, which are often used as mathematical models for many biological, physical and chemical sciences. In order to overcome LDG method for the strict time-step restriction Δt = O(h²min) of explicit schemes for stability, the implicit integration factor (IIF) method based on Krylov subspace approximation is introduced into the temporal discretization, in which the time-step can be taken as Δt = O(hmin) . The method can derive the numerical approximations not only for solutions but also for their gradients at the same time comparing other methods for the numerical solutions only. Moreover, the method can compute element by element and avoid solving a global system of nonlinear algebraic equations as the standard implicit schemes do, so that the method can reduce the computational cost greatly. Numerical experiments for the reaction-diffusion equations with exact solutions and the morphogenesis systems from developmental biology are conducted to illustrate the efficient, accurate and advantages of the LDG method coupled with the Krylov IIF time discretization.

Xijun Yu (蔚喜军), Doctor and Professor, graduated in 1993 from Institute of Computational Mathematics and Scientific and Engineering Computing of Chinese Academy of Science. Now Yu is vice-director of Laboratory of Computational Physics (LCP) of Institute of Applied Physics and Computational Mathematics (IAPCM) and Doctoral supervisor of IAPCM, University of Science and Technology of China, Northeast Normal University, member of the editorial board in Chinese Journal of Computational Physics and ACTA Aerodynamica Sinica and Journal of Mathematical Research and Applications (JMRA). Yu has long been engaged in study on the numerical methods of fluid dynamics, especially on the structured and unstructured grid, the high resolution finite volume and finite element method, including numerical mesh generation and adaptive method, multimedia fluid and interface treatment. In the study of finite element numerical method of fluid dynamics, he has achieved the great scientific research achievements. More than 90 papers were published in journals at home and abroad.