Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Applications of spatial data structures: Computer graphics, image processing, and GIS
Applications of spatial data structures: Computer graphics, image processing, and GIS
The design and analysis of spatial data structures
The design and analysis of spatial data structures
Journal of Computational Chemistry
SIAM Journal on Numerical Analysis
Multilevel methods for the Poisson-Boltzmann equation
Multilevel methods for the Poisson-Boltzmann equation
Adaptive mesh enrichment for the Poisson-Boltzmann equation
Journal of Computational Physics
A second-order-accurate symmetric discretization of the Poisson equation on irregular domains
Journal of Computational Physics
An Object-Oriented Programming Suite for Electrostatic Effects in Biological Molecules
ISCOPE '97 Proceedings of the Scientific Computing in Object-Oriented Parallel Environments
A Level Set Approach for the Numerical Simulation of Dendritic Growth
Journal of Scientific Computing
A Jump Condition Capturing Finite Difference Scheme for Elliptic Interface Problems
SIAM Journal on Scientific Computing
Local level set method in high dimension and codimension
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A Finite Difference Method and Analysis for 2D Nonlinear Poisson-Boltzmann Equations
Journal of Scientific Computing
A second order accurate level set method on non-graded adaptive cartesian grids
Journal of Computational Physics
Geometric integration over irregular domains with application to level-set methods
Journal of Computational Physics
The Finite Element Approximation of the Nonlinear Poisson-Boltzmann Equation
SIAM Journal on Numerical Analysis
Journal of Computational Physics
An efficient fluid-solid coupling algorithm for single-phase flows
Journal of Computational Physics
Journal of Computational Physics
IBM Journal of Research and Development
Hi-index | 31.45 |
We introduce a second-order solver for the Poisson-Boltzmann equation in arbitrary geometry in two and three spatial dimensions. The method differs from existing methods solving the Poisson-Boltzmann equation in the two following ways: first, non-graded Quadtree (in two spatial dimensions) and Octree (in three spatial dimensions) grid structures are used; Second, Neumann or Robin boundary conditions are enforced at the irregular domain's boundary. The irregular domain is described implicitly and the grid needs not to conform to the domain's boundary, which makes grid generation straightforward and robust. The linear system is symmetric, positive definite in the case where the grid is uniform, nonsymmetric otherwise. In this case, the resulting matrix is an M-matrix, thus the linear system is invertible. Convergence examples are given in both two and three spatial dimensions and demonstrate that the solution is second-order accurate and that Quadtree/Octree grid structures save a significant amount of computational power at no sacrifice in accuracy.