A fast algorithm for particle simulations
Journal of Computational Physics
The electric potential of a macromolecule in a solvent: A fundamental approach
Journal of Computational Physics
Journal of Computational Chemistry
Multigrid solution of the Poisson-Boltzmann equation
Journal of Computational Chemistry
ACM Transactions on Mathematical Software (TOMS)
SIAM Journal on Applied Mathematics
A fast adaptive multipole algorithm in three dimensions
Journal of Computational Physics
A Matrix Version of the Fast Multipole Method
SIAM Review
Molecular Modeling and Simulation: An Interdisciplinary Guide
Molecular Modeling and Simulation: An Interdisciplinary Guide
A kernel-independent adaptive fast multipole algorithm in two and three dimensions
Journal of Computational Physics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Optimality of Multilevel Preconditioners for Local Mesh Refinement in Three Dimensions
SIAM Journal on Numerical Analysis
Extending the fast multipole method to charges inside or outside a dielectric sphere
Journal of Computational Physics
A boundary element formulation of protein electrostatics with explicit ions
Journal of Computational Physics
Journal of Computational Physics
Image charge approximations of reaction fields in solvents with arbitrary ionic strength
Journal of Computational Physics
A Cartesian treecode for screened coulomb interactions
Journal of Computational Physics
A Sixth-order Image Approximation to the Ionic Solvent Induced Reaction Field
Journal of Scientific Computing
Fast Molecular Solvation Energetics and Forces Computation
SIAM Journal on Scientific Computing
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Journal of Scientific Computing
Journal of Scientific Computing
Journal of Computational Physics
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We review recent developments of fast analytical methods for macroscopic electrostatic calculations in biological applications, including the Poisson-Boltzmann (PB) and the generalized Born models for electrostatic solvation energy. The focus is on analytical approaches for hybrid solvation models, especially the image charge method for a spherical cavity, and also the generalized Born theory as an approximation to the PB model. This review places much emphasis on the mathematical details behind these methods.