A spectrally accurate integral equation solver for molecular surface electrostatics

  • Authors:

  • Shih-Hsien Kuo;Jacob White

  • Affiliations:

  • Massachusetts Institute of Technology, Cambridge, MA;Massachusetts Institute of Technology, Cambridge, MA

  • Venue:
  • Proceedings of the 2006 IEEE/ACM international conference on Computer-aided design
  • Year:
  • 2006

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Abstract

Electrostatic analysis of complicated molecular surfaces arises in a number of nanotechnology applications including: biomolecule design, carbon nanotube simulation, and molecular electron transport. Molecular surfaces are typically smooth, without the corners common in electrical interconnect problems, and are candidates for methods with higher order convergence than that of the commonly used flat panel methods. In this paper we describe and demonstrate a spectrally accurate approach for analyzing molecular surfaces described by a collection of surface points. The method is a synthesis of several techniques, and starts by using least squares to fit a high order spherical harmonic surface representation to the given points. Then this analytic representation is used to construct a differentiable map from the molecular suface to a cube, an orthogonal basis is generated on the rectangular cube surfaces, and a change of variables is used to desingularize the required integrals of products of basis functions and Green's function. Finally, an efficient method for solving the discretized system using a matrix-implicit scheme is described. The combined method is demonstrated on an analytically solvable sphere problem, capacitance calculation of complicated molecular surface, and a coupled Poisson/Poisson-Boltzmann problem associated with a biomolecule. The results demonstrate that for a tolerance of 10-3 this new approach requires one to two orders of magnitude fewer unknowns than a flat panel method.