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

dc.contributorHalpern, David
dc.contributorAmes, Brendan
dc.contributorSharif, Muhammad
dc.contributorRasoulzadeh, Mojdeh
dc.contributor.advisorZhao, Shan
dc.contributor.authorAhmed Ullah, Sheik
dc.contributor.otherUniversity of Alabama Tuscaloosa
dc.date.accessioned2020-01-16T15:04:09Z
dc.date.available2020-01-16T15:04:09Z
dc.date.issued2019
dc.descriptionElectronic Thesis or Dissertationen_US
dc.description.abstractThe 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.en_US
dc.format.extent71 p.
dc.format.mediumelectronic
dc.format.mimetypeapplication/pdf
dc.identifier.otheru0015_0000001_0003459
dc.identifier.otherAhmedUllah_alatus_0004D_13915
dc.identifier.urihttp://ir.ua.edu/handle/123456789/6516
dc.languageEnglish
dc.language.isoen_US
dc.publisherUniversity of Alabama Libraries
dc.relation.hasversionborn digital
dc.relation.ispartofThe University of Alabama Electronic Theses and Dissertations
dc.relation.ispartofThe University of Alabama Libraries Digital Collections
dc.rightsAll rights reserved by the author unless otherwise indicated.en_US
dc.subjectApplied mathematics
dc.titlePseudo-transient ghost fluid methods for the Poisson-Boltzmann equation with a two-component regularizationen_US
dc.typethesis
dc.typetext
etdms.degree.departmentUniversity of Alabama. Department of Mathematics
etdms.degree.disciplineMathematics
etdms.degree.grantorThe University of Alabama
etdms.degree.leveldoctoral
etdms.degree.namePh.D.
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