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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 …
An A Posteriori Error Estimator For The C0 Interior Penalty Approximations Of Fourth Order Elliptic Boundary Value Problem On Quadrilateral Meshes, Mohammad Arifur Rahman
An A Posteriori Error Estimator For The C0 Interior Penalty Approximations Of Fourth Order Elliptic Boundary Value Problem On Quadrilateral Meshes, Mohammad Arifur Rahman
Open Access Theses & Dissertations
Numerical solutions of fourth order elliptic problems with finite element methods has been the topic of research in computational mechanics for over 50 years. Traditional approaches to solve these problems include using C1 conforming finite element methods which demand the C1 continuity of the underlying shape functions, which is computationally very expensive. In this work, we will present the C0 Interior Penalty Galerkin approximation of the fourth order elliptic problems which relies only on continuous i.e., C0 shape functions, which is much cheaper to implement. The spatial discretization is based on quadrilateral meshes and the underlying C0 shape functions are …