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Volume 41, Issue 4
Positivity-Preserving Local Discontinuous Galerkin Method for Pattern Formation Dynamical Model in Polymerizing Actin Flocks

Xiuhui Guo, Lulu Tian, Yang Yang & Hui Guo

DOI: 10.4208/jcm.2108-m2021-0143

J. Comp. Math., 41 (2023), pp. 623-642.

Published online: 2023-02

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  • 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.

  • Keywords

Pattern formation dynamical model, Local discontinuous Galerkin method, Positive-preserving technique, Semi-implicit Runge-Kutta method, Stiff source.

  • AMS Subject Headings

65M15, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

20090004@s.upc.edu.cn (Xiuhui Guo)

Tianll@upc.edu.cn (Lulu Tian)

yyang7@mtu.edu (Yang Yang)

sdugh@163.com (Hui Guo)

  • BibTex
  • RIS
  • TXT
@Article{JCM-41-623, author = {Guo , XiuhuiTian , LuluYang , Yang and Guo , Hui}, title = {Positivity-Preserving Local Discontinuous Galerkin Method for Pattern Formation Dynamical Model in Polymerizing Actin Flocks}, journal = {Journal of Computational Mathematics}, year = {2023}, volume = {41}, number = {4}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2108-m2021-0143}, url = {http://global-sci.org/intro/article_detail/jcm/21408.html} }
TY - JOUR T1 - Positivity-Preserving Local Discontinuous Galerkin Method for Pattern Formation Dynamical Model in Polymerizing Actin Flocks AU - Guo , Xiuhui AU - Tian , Lulu AU - Yang , Yang AU - Guo , Hui JO - Journal of Computational Mathematics VL - 4 SP - 623 EP - 642 PY - 2023 DA - 2023/02 SN - 41 DO - http://doi.org/10.4208/jcm.2108-m2021-0143 UR - https://global-sci.org/intro/article_detail/jcm/21408.html KW - Pattern formation dynamical model, Local discontinuous Galerkin method, Positive-preserving technique, Semi-implicit Runge-Kutta method, Stiff source. AB -

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.

Guo , XiuhuiTian , LuluYang , Yang and Guo , Hui. (2023). Positivity-Preserving Local Discontinuous Galerkin Method for Pattern Formation Dynamical Model in Polymerizing Actin Flocks. Journal of Computational Mathematics. 41 (4). 623-642. doi:10.4208/jcm.2108-m2021-0143
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