GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Description of molecular surface shape using Fourier descriptors
Journal of Molecular Graphics
Journal of Computational Chemistry
Journal of Computational Chemistry
The electric potential of a macromolecule in a solvent: A fundamental approach
Journal of Computational Physics
SIAM Journal on Scientific Computing
Parametrization of closed surfaces for 3-D shape description
Computer Vision and Image Understanding
Locally corrected multidimensional quadrature rules for singular functions
SIAM Journal on Scientific Computing
IES3: a fast integral equation solver for efficient 3-dimensional extraction
ICCAD '97 Proceedings of the 1997 IEEE/ACM international conference on Computer-aided design
High-order Nyström schemes for efficient 3-D capacitance extraction
Proceedings of the 1998 IEEE/ACM international conference on Computer-aided design
A multiscale method for fast capacitance extraction
Proceedings of the 36th annual ACM/IEEE Design Automation Conference
Large-scale capacitance calculation
Proceedings of the 37th Annual Design Automation Conference
Journal of Computational Physics
Field Computation by Moment Methods
Field Computation by Moment Methods
Spherical Harmonic Molecular Surfaces
IEEE Computer Graphics and Applications
Fast methods for simulation of biomolecule electrostatics
Proceedings of the 2002 IEEE/ACM international conference on Computer-aided design
Proceedings of the 40th annual Design Automation Conference
A precorrected-FFT method for electrostatic analysis of complicated 3-D structures
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Algorithms in FastStokes and Its Application to Micromachined Device Simulation
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Fast integral equation methods for the modified Helmholtz equation
Journal of Computational Physics
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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 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.