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This paper discusses a novel approach to employ the absorbing boundary condition in conjunction with the finite-element method (FEM) in biomolecular electrostatics. The introduction of Bayliss-Turkel absorbing boundary operators in electromagnetic scattering problem has been incorporated by few researchers. However, in the area of biomolecular electrostatics, this boundary condition has not been investigated yet. The objective of this paper is twofold. First, to solve nonlinear Poisson-Boltzmann equation using Newton's method and second, to find an efficient and acceptable solution with minimum number of unknowns. In this work, a Galerkin finite-element formulation is used along with a Bayliss-Turkel absorbing boundary operator that explicitly accounts for the open field problem by mapping the Sommerfeld radiation condition from the far field to near field. While the Bayliss-Turkel condition works well when the artificial boundary is far from the scatterer, an acceptable tolerance of error can be achieved with the second order operator. Numerical results on test case with simple sphere show that the treatment is able to reach the same level of accuracy achieved by the analytical method while using a lower grid density. Bayliss-Turkel absorbing boundary condition (BTABC) combined with the FEM converges to the exact solution of scattering problems to within discretization error.
Poisson equation, bioelectric phenomena, Boltzmann equation, electrostatics, finite element analysis, Galerkin method, molecular biophysics, Newton method, nonlinear equations,discretization error, biomolecular electrostatics, electromagnetic scattering problem, nonlinear Poisson-Boltzmann equation, Newton method, Galerkin finite-element method, Bayliss-Turkel absorbing boundary operator, open field problem, Sommerfeld radiation condition, artificial boundary, analytical method, grid density, Bayliss-Turkel absorbing boundary condition, exact solution,Electrostatics, Boundary conditions, Mathematical model, Finite element analysis, Equations, Solvents, Electric potential,Nonlinear Poisson-Boltzmann equation, diffuse layer, finite-element method,
"A New Approach to Implement Absorbing Boundary Condition in Biomolecular Electrostatics", IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 10, no. , pp. 799-804, May-June 2013, doi:10.1109/TCBB.2013.96
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