Feature-oriented image enhancement using shock filters
SIAM Journal on Numerical Analysis
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Computing minimal surfaces via level set curvature flow
Journal of Computational Physics
International Journal of Computer Vision
Level set methods: an overview and some recent results
Journal of Computational Physics
Journal of Computational Physics
Subjective Surfaces: A Geometric Model for Boundary Completion
International Journal of Computer Vision
3D Curves Reconstruction Based on Deformable Models
Journal of Mathematical Imaging and Vision
Using the Vector Distance Functions to Evolve Manifolds of Arbitrary Codimension
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
Semi-Implicit Level Set Methods for Curvature and Surface Diffusion Motion
Journal of Scientific Computing
High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces
Journal of Computational Physics
A numerical method for computing minimal surfaces in arbitrary dimension
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Matched interface and boundary (MIB) method for elliptic problems with sharp-edged interfaces
Journal of Computational Physics
Three-dimensional matched interface and boundary (MIB) method for treating geometric singularities
Journal of Computational Physics
Quality meshing of implicit solvation models of biomolecular structures
Computer Aided Geometric Design - Special issue: Applications of geometric modeling in the life sciences
A computational algorithm for minimizing total variation in image restoration
IEEE Transactions on Image Processing
Anisotropic diffusion of multivalued images with applications to color filtering
IEEE Transactions on Image Processing
Color TV: total variation methods for restoration of vector-valued images
IEEE Transactions on Image Processing
A general framework for low level vision
IEEE Transactions on Image Processing
Multiscale molecular dynamics using the matched interface and boundary method
Journal of Computational Physics
Second-order Poisson-Nernst-Planck solver for ion transport
Journal of Computational Physics
Mode Decomposition Evolution Equations
Journal of Scientific Computing
Multiscale geometric modeling of macromolecules I: Cartesian representation
Journal of Computational Physics
Operator splitting ADI schemes for pseudo-time coupled nonlinear solvation simulations
Journal of Computational Physics
Hi-index | 31.47 |
This paper presents a differential geometry based model for the analysis and computation of the equilibrium property of solvation. Differential geometry theory of surfaces is utilized to define and construct smooth interfaces with good stability and differentiability for use in characterizing the solvent-solute boundaries and in generating continuous dielectric functions across the computational domain. A total free energy functional is constructed to couple polar and nonpolar contributions to the solvation process. Geometric measure theory is employed to rigorously convert a Lagrangian formulation of the surface energy into an Eulerian formulation so as to bring all energy terms into an equal footing. By optimizing the total free energy functional, we derive coupled generalized Poisson-Boltzmann equation (GPBE) and generalized geometric flow equation (GGFE) for the electrostatic potential and the construction of realistic solvent-solute boundaries, respectively. By solving the coupled GPBE and GGFE, we obtain the electrostatic potential, the solvent-solute boundary profile, and the smooth dielectric function, and thereby improve the accuracy and stability of implicit solvation calculations. We also design efficient second-order numerical schemes for the solution of the GPBE and GGFE. Matrix resulted from the discretization of the GPBE is accelerated with appropriate preconditioners. An alternative direct implicit (ADI) scheme is designed to improve the stability of solving the GGFE. Two iterative approaches are designed to solve the coupled system of nonlinear partial differential equations. Extensive numerical experiments are designed to validate the present theoretical model, test computational methods, and optimize numerical algorithms. Example solvation analysis of both small compounds and proteins are carried out to further demonstrate the accuracy, stability, efficiency and robustness of the present new model and numerical approaches. Comparison is given to both experimental and theoretical results in the literature.