Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Physical Sciences and Mathematics
An Adapative Treecode-Accelerated Boundary Integral Solver For Computing The Electrostatics Of A Biomolecule, Andrew Joseph Szatkowski
An Adapative Treecode-Accelerated Boundary Integral Solver For Computing The Electrostatics Of A Biomolecule, Andrew Joseph Szatkowski
Theses and Dissertations
The Poisson-Boltzmann equation (PBE) is a widely-used model in the calculation of electrostatic potential for solvated biomolecules. PBE is an interface problem defined in the whole space with the interface being a molecular surface of a biomolecule, and has been solved numerically by finite difference, finite element, and boundary integral methods. Unlike the finite difference and finite element methods, the boundary integral method works directly over the whole space without approximating the whole space problem into an artificial boundary value problem. Hence, it is expected to solve PBE in higher accuracy. However, so far, it was only applied to a …
Domain Decomposition Based Hybrid Methods Of Finite Element And Finite Difference And Applications In Biomolecule Simulations, Jinyong Ying
Domain Decomposition Based Hybrid Methods Of Finite Element And Finite Difference And Applications In Biomolecule Simulations, Jinyong Ying
Theses and Dissertations
The dielectric continuum models, such as Poisson Boltzmann equation (PBE), size modified PBE (SMPBE), and nonlocal modified PBE (NMPBE), are important models in predicting the electrostatics of a biomolecule in an ionic solvent. To solve these dielectric continuum models efficiently, in this dissertation, new finite element and finite difference hybrid methods are constructed by Schwartz domain decomposition techniques based on a special seven-box partition of a cubic domain. As one important part of these methods, a finite difference optimal solver --- the preconditioned conjugate gradient method using a multigrid V-cycle preconditioner --- is described in details and proved to have …