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Volume 25, Issue 3
Discontinuous Bubble Immersed Finite Element Method for Poisson-Boltzmann Equation

In Kwon & Do Y. Kwak

DOI: 10.4208/cicp.OA-2018-0014

Commun. Comput. Phys., 25 (2019), pp. 928-946.

Published online: 2018-11

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  • 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.

  • Keywords

Biomolecular electrostatics, Poisson-Boltzmann equation, immersed finite element method, discontinuous bubble function, linearization.

  • AMS Subject Headings

65F10, 65N30, 65Z05, 92C40

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{CiCP-25-928, author = {In Kwon and Do Y. Kwak}, title = {Discontinuous Bubble Immersed Finite Element Method for Poisson-Boltzmann Equation}, journal = {Communications in Computational Physics}, year = {2018}, volume = {25}, number = {3}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0014}, url = {http://global-sci.org/intro/article_detail/cicp/12834.html} }
TY - JOUR T1 - Discontinuous Bubble Immersed Finite Element Method for Poisson-Boltzmann Equation AU - In Kwon & Do Y. Kwak JO - Communications in Computational Physics VL - 3 SP - 928 EP - 946 PY - 2018 DA - 2018/11 SN - 25 DO - http://doi.org/10.4208/cicp.OA-2018-0014 UR - https://global-sci.org/intro/article_detail/cicp/12834.html KW - Biomolecular electrostatics, Poisson-Boltzmann equation, immersed finite element method, discontinuous bubble function, linearization. AB -

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.

In Kwon and Do Y. Kwak. (2018). Discontinuous Bubble Immersed Finite Element Method for Poisson-Boltzmann Equation. Communications in Computational Physics. 25 (3). 928-946. doi:10.4208/cicp.OA-2018-0014
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