### A meshless, spectrally accurate, integral equation solver for molecular surface electrostaticsA meshless, spectrally accurate, integral equation solver for molecular surface electrostatics

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 Author Kuo, Shih-Hsien ♦ Tidor, Bruce ♦ White, Jacob Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©2008 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword Poisson-Boltzmann equation ♦ Integral equation ♦ Meshless ♦ Spectral method Abstract The need to determine electrostatic fields in domains bounded by molecular surfaces arises in a number of nanotechnology applications including: biomolecule design, carbon nanotube simulation, and molecular electron transport analysis. Molecular surfaces are typically smooth, without the corners common in electrical interconnect problems, but are often so geometrically complicated that numerical evaluation of the associated electrostatic fields is extremely time-consuming. In this paper we describe and demonstrate a meshless spectrally-accurate integral equation method that $\textit{only}$ requires a description of the molecular surface in the form of a collection of surface points. Our meshless method is a synthesis of techniques, suitably adapted, including: spherical harmonic surface interpolation, spectral-element-like integral equation discretization, integral desingularization via variable transformation, and matrix-implicit iterative matrix solution. The spectral accuracy of this combined method is verified using analytically solvable sphere and ellipsoid problems, and then its accuracy and efficiency is demonstrated numerically by solving capacitance and coupled Poisson/linearized Poisson-Boltzmann problems associated with a commonly used model of a molecule in solution. The results demonstrate that for a tolerance of $10^{™3}$ this new approach reduces the number of unknowns by as much as two orders of magnitude over the more commonly used flat panel methods. ISSN 15504832 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 2008-04-01 Publisher Place New York e-ISSN 15504840 Journal ACM Journal on Emerging Technologies in Computing Systems (JETC) Volume Number 4 Issue Number 2 Page Count 30 Starting Page 1 Ending Page 30

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Source: ACM Digital Library