Discontinuous Bubble Immersed Finite Element Method for Poisson-Boltzmann Equation

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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.
Publisher
GLOBAL SCIENCE PRESS
Issue Date
2019-03
Language
English
Article Type
Article
Citation

COMMUNICATIONS IN COMPUTATIONAL PHYSICS, v.25, no.3, pp.928 - 946

ISSN
1815-2406
DOI
10.4208/cicp.OA-2018-0014
URI
http://hdl.handle.net/10203/250344
Appears in Collection
MA-Journal Papers(저널논문)
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