Comprehensive Exam - Denis Mulumba

Presented by Denis Mulumba
Computing PhD, Computational Math, Science, and Engineering emphasis

Location: Riverfront Hall (RFH) 102B or register via Zoom

Advancements in Solving the Generalized Poisson and Poisson-Boltzmann Equations for Continuum Solvation Models

Abstract: Understanding molecular interactions in different solvents is a complex task in computational chemistry. However, the development of continuum solvation models has helped to reduce the computational expenses of explicit models. This has led to various applications such as drug design, materials science, and understanding biological mechanisms. This study focuses on the evolution of continuum solvation models and the role played by the Generalized Poisson Equation (GPe) and Poisson-Boltzmann Equation (PBe) in bridging the gap between theory and computational techniques. The study examines four seed papers to provide an understanding of how solutes interact with solvents and the mathematical interpretation that comes with it. In addition, the study explores various methodological advances such as the Self-consistent and Preconditioned Conjugate Gradient (PCG) methods, the Polarizable Multipole Poisson-Boltzmann (PMPB) model, which integrates the Atomic Multipole Optimized Energies for Biomolecular Applications (AMOEBA) force field to improve the accuracy of the solution, and the domain decomposition approach which accelerates the solution electrostatic models. These methods treat the dielectric function as a continuous function and also consider the polarizability effects in the system. Moreover, the study discusses the Immersed Interface Method (IIM), a technique that solves the GPe and PBe while treating the dielectric function as a function with discontinuities. The IIM is a powerful tool that has been used to solve complex problems in various fields.

Committee:  Dr. Oliviero Andreussi, Dr. Grady Wright, and Dr. Donna Calhoun (CompEE)