A meshless, high-order integral equation method for smooth surfaces, with application to biomolecular electrostatics

In this thesis, we develop methods for efficient simulation of biomolecular electrostatics based on Poisson-Boltzmann equation. Current techniques using finite-difference solution of differential formulation have many drawbacks. We present an integral formulation that resolves these difficulties and enables an efficient implementation using a recently developed fast solver. The new approach can solve practical engineering problems with good accuracy, but only with an aid of a high quality mesh generator, and sometimes require a large number of panels to discretize a surface. To this end, a novel approach to discretize singular integral equations is proposed. Unlike the traditional boundary element method using panel discretization, the new method is meshless and capable of achieving spectral convergence: numerical errors decrease exponentially fast with increasing size of basis set. We will describe a number of techniques in our approach, including the use of global, high order basis, quadrature-based panel integration, and innovative surface representation. The biomolecular problem is particularly suited for this method because molecular surfaces are typically smooth and can be represented globally using spherical harmonics.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2006

Author dc:creator

• Kuo, Shih-Hsien, Ph. D. Massachusetts Institute of Technology

Advisor dc:contributor.advisor

• Jacob K. White.

• Electrical Engineering and Computer Science.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/38226

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/38226