POSITIVITY-PRESERVING LOCAL DISCONTINUOUS GALERKIN METHOD FOR PATTERN FORMATION DYNAMICAL MODEL IN POLYMERIZING ACTIN FLOCKS  

作　　者：Xiuhui Guo Lulu Tian Yang Yang Hui Guo 

机构地区：[1]College of Science,China University of Petroleum,Qingdao 266580,China [2]Department of Mathematical Sciences,Michigan Technological University,Houghton,MI 49931 [3]The College of Science,China University of Petroleum,Qingdao 266580,China

出　　处：《Journal of Computational Mathematics》2023年第4期623-642,共20页计算数学（英文）

基　　金：supported by the Natural Science Foundation of Shandong Province(ZR2021MA001);the Fundamental Research Funds for the Central Universities(20CX05011A);supported by National Natural Science Foundation of China Grant 11801569;supported by NSF grant DMS-1818467 and Simons Foundation 961585.

摘　　要：In this paper,we apply local discontinuous Galerkin(LDG)methods for pattern formation dynamical model in polymerizing actin focks.There are two main dificulties in designing effective numerical solvers.First of all,the density function is non-negative,and zero is an unstable equilibrium solution.Therefore,negative density values may yield blow-up solutions.To obtain positive numerical approximations,we apply the positivitypreserving(PP)techniques.Secondly,the model may contain stif source.The most commonly used time integration for the PP technique is the strong-stability-preserving Runge-Kutta method.However,for problems with stiff source,such time discretizations may require strictly limited time step sizes,leading to large computational cost.Moreover,the stiff source any trigger spurious filament polarization,leading to wrong numerical approximations on coarse meshes.In this paper,we combine the PP LDG methods with the semi-implicit Runge-Kutta methods.Numerical experiments demonstrate that the proposed method can yield accurate numerical approximations with relatively large time steps.

关 键 词：Pattern formation dynamical model Local discontinuous Galerkin method Positive-preserving technique Semi-implicit Runge-Kutta method Stiff source 

分 类 号：O241.82[理学—计算数学]