Parallel Adaptive Finite Element Algorithms for Solving the Coupled Electro-diffusion Equations

• Autorzy: Yan Xie , Jie Cheng , Benzhuo Lu , Linbo Zhang
• Języki publikacji: EN

Abstrakty

EN

rithms for solving the 3D electro-diffusion equations such as the Poisson-Nernst-Planck equations and the size-modified Poisson-Nernst-Planck equations in simulations of biomolecular systems in ionic liquid. A set of transformation methods based on the generalized Slotboom variables is used to solve the coupled equations. Calculations of the diffusion-reaction rate coefficients, electrostatic potential and ion concentrations for various systems verify the method’s validity and stability. The iterations between the Poisson equation and the Nernst- Planck equations in the primitive method and in the transformation method are compared to illustrate how the new method accelerates the convergence of the solution. To speed up the convergence, we introduce the DIIS (direct inversion of the iterative subspace) method including Simple Mixing and Anderson Mixing as under-relaxation techniques, the effectiveness of which on acceleration is shown by numerical tests. It is worth noting that the primitive method fails to solve the size-modified Poisson-Nernst-Planck equations for real protein systems but the transformation method succeeds in the simulations of the ACh-AChE reaction system and the DNA fragment. To improve the accuracy of the solution, we introduce high order elements and mesh adaptation based on an a posteriori error estimator. Numerical results indicate that our mesh adaptation process leads to quasi-optimal convergence. We implement our algorithms using the parallel adaptive finite element package PHG [53] and high parallel efficiency is obtained.

Słowa kluczowe

EN

Poisson-Nernst-Planck equations; Adaptive Finite Element Method; DIIS; Parallel Processing; Slotboom variables; PHG

• Wydawca: De Gruyter Open
• Czasopismo: Molecular Based Mathematical Biology
• Rocznik: 2013
• Tom: 1
• Strony: 90-108

Daty

otrzymano

2012-09-25

zaakceptowano

2013-03-19

online

2013-04-24

Twórcy

autor

Yan Xie,

autor

Jie Cheng,

autor

Benzhuo Lu,

autor

Linbo Zhang,

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Identyfikatory

DOI

10.2478/mlbmb-2013-0005