A Self-Adjusting FEM-BEM Coupling Scheme for the Nonlinear Poisson-Boltzmann Equation
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| Format: | Preprint |
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2025
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| _version_ | 1866918451207995392 |
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| author | Guerrero-Montero, Mauricio Bosy, Michal Cooper, Christopher D. |
| author_facet | Guerrero-Montero, Mauricio Bosy, Michal Cooper, Christopher D. |
| contents | The Poisson-Boltzmann equation is widely used to model molecular electrostatics; however, it is usually solved in linearised form because the sinh nonlinearity is challenging, limiting its applicability in highly charged systems such as nucleic acids. This work presents a solution method for the nonlinear Poisson-Boltzmann equation based on a coupled finite/boundary element scheme that automatically finds an optimal relaxation parameter, ensuring fast and reliable convergence of the nonlinear solver without user intervention. We validated our solver against APBS for a spherical cavity, and used RNA-based structures to perform a thorough study of the different algorithmic choices, and to test our implementation. We found that the best alternative to solve the Poisson-Boltzmann equation was using a Newton-Raphson method where the nonlinearity was gradually introduced with a cubic approximation in the first iteration. Newton-Raphson was also the best method to find the optimal relaxation factor, reducing the number of iterations by 40%. Including other optimisation techniques, we were able to obtain a 1.37x speed-up with respect to the best hand-picked relaxation factor for 1HC8 (molecule with highest charge in our tests), avoiding any trial-and-error process to find the relaxation factor. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_21713 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Self-Adjusting FEM-BEM Coupling Scheme for the Nonlinear Poisson-Boltzmann Equation Guerrero-Montero, Mauricio Bosy, Michal Cooper, Christopher D. Computational Physics 35Q92 J.2 The Poisson-Boltzmann equation is widely used to model molecular electrostatics; however, it is usually solved in linearised form because the sinh nonlinearity is challenging, limiting its applicability in highly charged systems such as nucleic acids. This work presents a solution method for the nonlinear Poisson-Boltzmann equation based on a coupled finite/boundary element scheme that automatically finds an optimal relaxation parameter, ensuring fast and reliable convergence of the nonlinear solver without user intervention. We validated our solver against APBS for a spherical cavity, and used RNA-based structures to perform a thorough study of the different algorithmic choices, and to test our implementation. We found that the best alternative to solve the Poisson-Boltzmann equation was using a Newton-Raphson method where the nonlinearity was gradually introduced with a cubic approximation in the first iteration. Newton-Raphson was also the best method to find the optimal relaxation factor, reducing the number of iterations by 40%. Including other optimisation techniques, we were able to obtain a 1.37x speed-up with respect to the best hand-picked relaxation factor for 1HC8 (molecule with highest charge in our tests), avoiding any trial-and-error process to find the relaxation factor. |
| title | A Self-Adjusting FEM-BEM Coupling Scheme for the Nonlinear Poisson-Boltzmann Equation |
| topic | Computational Physics 35Q92 J.2 |
| url | https://arxiv.org/abs/2511.21713 |