KMS Of Academy of mathematics and systems sciences, CAS
| Model reduction-based initialization methods for solving the Poisson-Nernst-Plank equations in three-dimensional ion channel simulations | |
| Zhang, Qianru1,2; Gui, Sheng1,2; Li, Hongliang3,4; Lu, Benzhuo1,2 | |
| 2020-10-15 | |
| Source Publication | JOURNAL OF COMPUTATIONAL PHYSICS
 |
| ISSN | 0021-9991 |
| Volume | 419Pages:18 |
| Abstract | The Poisson-Nernst-Planck (PNP) model is frequently-used in simulating ion transport through ion channel systems. Due to the nonlinearity and coupling of PNP model, choosing appropriate initial values is crucial to obtaining a convergent result or accelerating the convergence rate of finite element solution, especially for large channel systems. Continuation is an effective and commonly adopted strategy to provide good initial guesses for the solution procedure. However, this method needs multiple times to solve the whole system at different conditions. We utilize a reduced model describing a near or partial-equilibrium state as an approximation of the original PNP system (describing a non-equilibrium process in general). Based on the reduced model, we design three initialization methods for the solution of PNP equations under general conditions. These methods provide the initial guess of the PNP system by solving a specifically designed Poisson-Boltzmann-like model, Smoluchowski-Poisson-Boltzmann-like model, and linear approximation model. Simulations of potassium channels 1BL8 and 2JK4 demonstrate that these methods can effectively reduce the number of Gummel iteration steps and the total CPU time in the solution of the PNP equations, and especially do not need the continuation approach anymore. The reason is that these initial guesses can approximate the PNP solution well in the channel region. Besides, our numerical experiments demonstrate that as one of the initialization methods, the linear approximation method can even produce very close results such as current-voltage curves to that from the PNP model when the membrane potential is not high. (C) 2020 Elsevier Inc. All rights reserved. |
| Keyword | Reduced model Poisson-Nernst-Planck Smoluchowski-Poisson-Boltzmann Initialization Linear approximation of PNP model Finite element method |
| DOI | 10.1016/j.jcp.2020.109627 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | Science Challenge Program[TZ2016003-1] ; National Key Research and Development Program of Ministry of Science and Technology[2016YFB0201304] ; China NSF[21573274] ; China NSF[11771435] |
| WOS Research Area | Computer Science ; Physics |
| WOS Subject | Computer Science, Interdisciplinary Applications ; Physics, Mathematical |
| WOS ID | WOS:000629857800007 |
| Publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/58361 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Li, Hongliang; Lu, Benzhuo |
| Affiliation | 1.Chinese Acad Sci, Acad Math & Syst Sci, Natl Ctr Math & Interdisciplinary Sci, State Key Lab Sci & Engn Comp, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Sichuan Normal Univ, Dept Math, Chengdu 610066, Peoples R China 4.China Acad Engn Phys, Inst Elect Engn, Mianyang 621900, Sichuan, Peoples R China |
| Recommended Citation GB/T 7714 | Zhang, Qianru,Gui, Sheng,Li, Hongliang,et al. Model reduction-based initialization methods for solving the Poisson-Nernst-Plank equations in three-dimensional ion channel simulations[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2020,419:18. |
| APA | Zhang, Qianru,Gui, Sheng,Li, Hongliang,&Lu, Benzhuo.(2020).Model reduction-based initialization methods for solving the Poisson-Nernst-Plank equations in three-dimensional ion channel simulations.JOURNAL OF COMPUTATIONAL PHYSICS,419,18. |
| MLA | Zhang, Qianru,et al."Model reduction-based initialization methods for solving the Poisson-Nernst-Plank equations in three-dimensional ion channel simulations".JOURNAL OF COMPUTATIONAL PHYSICS 419(2020):18. |
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