An Ewald summation based multipole method

We present a method for evaluating Coulomb interactions in periodic molecular systems. The real space term in Ewald summation is accelerated using a tree code in which interactions between clusters and distant particles are approximated by multipole expansions. The performance is reported for water systems. © 2000 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69692/2/JCPSA6-113-9-3492-1.pd

Integral equation method for the 1D steady-state Poisson-Nernst-Planck equations

An integral equation method is presented for the 1D steady-state Poisson-Nernst-Planck equations modeling ion transport through membrane channels. The differential equations are recast as integral equations using Green's 3rd identity yielding a fixed-point problem for the electric potential gradient and ion concentrations. The integrals are discretized by a combination of midpoint and trapezoid rules and the resulting algebraic equations are solved by Gummel iteration. Numerical tests for electroneutral and non-electroneutral systems demonstrate the method's 2nd order accuracy and ability to resolve sharp boundary layers. The method is applied to a 1D model of the K$^+$ ion channel with a fixed charge density that ensures cation selectivity. In these tests, the proposed integral equation method yields potential and concentration profiles in good agreement with published results.Comment: 15 pages, 7 figure

Improvements to the APBS biomolecular solvation software suite

The Adaptive Poisson-Boltzmann Solver (APBS) software was developed to solve the equations of continuum electrostatics for large biomolecular assemblages that has provided impact in the study of a broad range of chemical, biological, and biomedical applications. APBS addresses three key technology challenges for understanding solvation and electrostatics in biomedical applications: accurate and efficient models for biomolecular solvation and electrostatics, robust and scalable software for applying those theories to biomolecular systems, and mechanisms for sharing and analyzing biomolecular electrostatics data in the scientific community. To address new research applications and advancing computational capabilities, we have continually updated APBS and its suite of accompanying software since its release in 2001. In this manuscript, we discuss the models and capabilities that have recently been implemented within the APBS software package including: a Poisson-Boltzmann analytical and a semi-analytical solver, an optimized boundary element solver, a geometry-based geometric flow solvation model, a graph theory based algorithm for determining p$K_a$ values, and an improved web-based visualization tool for viewing electrostatics

A Vortex Sheet/Point Vortex Dynamical Model For Unsteady Separated Flows

This paper presents a hybrid vortex sheet/point vortex method for modeling unsteady separated flows. We use vortex sheets to capture the dynamics of the shear layers immediately behind a wing in motion. The sheets provide a natural way of capturing vortex shedding, a feature missing from many point vortex models. We overcome the high computational cost traditionally associated with vortex sheet methods by approximating the spiraling cores of the sheets using point vortices with time-varying circulation. Circulation is continuously truncated from the tips of the vortex sheets and fed into their associated point vortices. To compensate for the discontinuous force response that results from this redistribution of vorticity, we adjust the velocity of the variable strength point vortices. We demonstrate the viability of the method by modeling the impulsive translation of a wing at a fixed angle of attack. We show that the proposed model correctly predicts the dynamics of large-scale vortical structures in the flow by comparing the distribution of vorticity from results of high-fidelity simulation, a model using only vortex sheets, and the proposed model. For the test cases attempted, the hybrid model predicts similar force responses to those of the sheet-only model, while being orders of magnitude faster