Year: 2019
Communications in Computational Physics, Vol. 25 (2019), Iss. 3 : pp. 928–946
Abstract
We develop a numerical scheme for nonlinear Poisson-Boltzmann equation. First, we regularize the solution of PBE to remove the singularity. We introduce the discontinuous bubble function to treat the nonhomogeneous jump conditions of the regularized solution. Next, starting with an initial guess, we apply linearization to treat the nonlinearity. Then, we discretize the discontinuous bubble and the bilinear form of PBE. Finally, we solve the discretized linear problem by IFEM. This process is repeated by updating the previous approximation.
We carry out numerical experiments. We observe optimal convergence rate for all examples.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2018-0014
Communications in Computational Physics, Vol. 25 (2019), Iss. 3 : pp. 928–946
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Biomolecular electrostatics Poisson-Boltzmann equation immersed finite element method discontinuous bubble function linearization.