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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Accesso online: | https://arxiv.org/abs/2309.06862 |
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| _version_ | 1866917630377459712 |
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| author | Jha, Abhinav Stamm, Benjamin |
| author_facet | Jha, Abhinav Stamm, Benjamin |
| contents | In this paper, we develop a domain decomposition method for the nonlinear Poisson-Boltzmann equation based on a solvent-excluded surface widely used in computational chemistry. The model relies on a nonlinear equation defined in $\mathbb{R}^3$ with a space-dependent dielectric permittivity and an ion-exclusion function that accounts for steric effects. Potential theory arguments transform the nonlinear equation into two coupled equations defined in a bounded domain. Then, the Schwarz decomposition method is used to formulate local problems by decomposing the cavity into overlapping balls and only solving a set of coupled sub-equations in each ball. The main novelty of the proposed method is the introduction of a hybrid linear-nonlinear solver used to solve the equation. A series of numerical experiments are presented to test the method and show the importance of the nonlinear model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_06862 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Domain Decomposition Method for Poisson--Boltzmann Equations based on Solvent Excluded Surface Jha, Abhinav Stamm, Benjamin Numerical Analysis Number Theory 65N35, 65N55 In this paper, we develop a domain decomposition method for the nonlinear Poisson-Boltzmann equation based on a solvent-excluded surface widely used in computational chemistry. The model relies on a nonlinear equation defined in $\mathbb{R}^3$ with a space-dependent dielectric permittivity and an ion-exclusion function that accounts for steric effects. Potential theory arguments transform the nonlinear equation into two coupled equations defined in a bounded domain. Then, the Schwarz decomposition method is used to formulate local problems by decomposing the cavity into overlapping balls and only solving a set of coupled sub-equations in each ball. The main novelty of the proposed method is the introduction of a hybrid linear-nonlinear solver used to solve the equation. A series of numerical experiments are presented to test the method and show the importance of the nonlinear model. |
| title | Domain Decomposition Method for Poisson--Boltzmann Equations based on Solvent Excluded Surface |
| topic | Numerical Analysis Number Theory 65N35, 65N55 |
| url | https://arxiv.org/abs/2309.06862 |