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

100%

Xie Y., Cheng J., Lu B., Zhang L.

Molecular Based Mathematical Biology

2013

tom 1

90-108

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.

Inverse problem for a physiologically structured population model with variable-effort harvesting

76%

Andrusyak R. V.

Open Mathematics

2017

tom 15

nr 1

433-445

We consider the inverse problem of determining how the physiological structure of a harvested population evolves in time, and of finding the time-dependent effort to be expended in harvesting, so that the weighted integral of the density, which may be, for example, the total number of individuals or the total biomass, has prescribed dynamics. We give conditions for the existence of a unique, global, weak solution to the problem. Our investigation is carried out using the method of characteristics and a generalization of the Banach fixed-point theorem.

Ograniczanie wyników

1 Molecular Based Mathematical Biology

1 Open Mathematics

1 Andrusyak R. V.

1 Cheng J.

1 Lu B.

1 Xie Y.

1 Zhang L.

1 2017

1 2013

Wyniki wyszukiwania

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

Inverse problem for a physiologically structured population model with variable-effort harvesting