Pseudo-transient ghost fluid methods for the Poisson-Boltzmann equation with a two-component regularization

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dc.contributor Halpern, David
dc.contributor Ames, Brendan
dc.contributor Sharif, Muhammad
dc.contributor Rasoulzadeh, Mojdeh
dc.contributor.advisor Zhao, Shan Ahmed Ullah, Sheik 2020-01-16T15:04:09Z 2020-01-16T15:04:09Z 2019
dc.identifier.other u0015_0000001_0003459
dc.identifier.other AhmedUllah_alatus_0004D_13915
dc.description Electronic Thesis or Dissertation
dc.description.abstract The Poisson Boltzmann equation (PBE) is a well-established implicit solvent continuum model for the electrostatic analysis of solvated biomolecules. The numerical solution of the nonlinear PBE is still a challenge due to its strong singularity by the source terms, dielectrically distinct regions, and exponential nonlinear terms. In this dissertation, a new alternating direction implicit method (ADI) is proposed for solving the nonlinear PBE using a two-component regularization. This scheme inherits all the advantages of the two-component regularization and the pseudo-time solution of the PBE while possesses a novel approach to combine them. A modified Ghost Fluid Method (GFM) has been introduced to incorporate the nonzero jump condition into the ADI framework to construct a new GFM-ADI method. It produced better results in terms of spatial accuracy and stability compared to the existing ADI methods for PBE and it is simpler to implement by circumventing the work necessary to apply the rigorous 3D interface treatments with the regularization. Moreover, the stability of the GFM-ADI method has been significantly improved in comparing with the non-regularized ADI method, so that stable and efficient protein simulations can be carried out with a pretty large time step size. Two locally one-dimensional (LOD) methods have also been developed for the time-dependent regularized PBE, which are unconditionally stable. Finally, for numerical validation, we have evaluated the solvation free energy for a collection of 24 proteins with various sizes and the salt effect on the protein-protein binding energy of protein complexes.
dc.format.extent 71 p.
dc.format.medium electronic
dc.format.mimetype application/pdf
dc.language English
dc.language.iso en_US
dc.publisher University of Alabama Libraries
dc.relation.ispartof The University of Alabama Electronic Theses and Dissertations
dc.relation.ispartof The University of Alabama Libraries Digital Collections
dc.relation.hasversion born digital
dc.rights All rights reserved by the author unless otherwise indicated.
dc.subject.other Applied mathematics
dc.title Pseudo-transient ghost fluid methods for the Poisson-Boltzmann equation with a two-component regularization
dc.type thesis
dc.type text University of Alabama. Department of Mathematics Mathematics The University of Alabama doctoral Ph.D.

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