Positivity-Preserving Local Discontinuous Galerkin Method for Pattern Formation Dynamical Model in Polymerizing Actin Flocks
Year: 2023
Author: Xiuhui Guo, Lulu Tian, Yang Yang, Hui Guo
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 4 : pp. 623–642
Abstract
In this paper, we apply local discontinuous Galerkin (LDG) methods for pattern formation dynamical model in polymerizing actin flocks. There are two main difficulties 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 positivity-preserving (PP) techniques. Secondly, the model may contain stiff 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2108-m2021-0143
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 4 : pp. 623–642
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Pattern formation dynamical model Local discontinuous Galerkin method Positive-preserving technique Semi-implicit Runge-Kutta method Stiff source.