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Author : Ilia Antsiferov
Publisher :
ISBN 13 :
Total Pages : 126 pages
Book Rating : 4.:/5 (234 download)
Download or read book Solving the Nonlinear Poisson-Boltzmann Equation Using Multigrid Methods written by Ilia Antsiferov and published by . This book was released on 2006 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ilia Antsiferov
Publisher :
ISBN 13 :
Total Pages : 63 pages
Book Rating : 4.:/5 (951 download)
Download or read book Solving the Poisson-Boltzmann Equation Using Nonlinear Multigrid Methods written by Ilia Antsiferov and published by . This book was released on 2006 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Dong Zeng
Publisher :
ISBN 13 :
Total Pages : 164 pages
Book Rating : 4.:/5 (497 download)
Download or read book Parallel Multigrid-based Methods for Calculating Electrostatic Potentials by Solving the Full Nonlinear Poisson-Boltzmann Equation written by Dong Zeng and published by . This book was released on 2000 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Michael Jay Holst
Publisher :
ISBN 13 :
Total Pages : 564 pages
Book Rating : 4.:/5 (31 download)
Download or read book Multilevel Methods for the Poisson-Boltzmann Equation written by Michael Jay Holst and published by . This book was released on 1993 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multilevel convergence theory is discussed, and we adapt and apply some recent results to the Galerkin-based methods. Numerical results arepresented for several test problems, including a nonlinear PBE calculation of the electrostatic potential of Superoxide Dismutase, an enzymewhich has recently been linked to Lou Gehrig's disease. We present a collection of performance statistics and benchmarks for the linear andnonlinear methods on a number of sequential and parallel computers, and discuss the software developed in the course of the research."
Author : Michael Holst
Publisher :
ISBN 13 :
Total Pages : 26 pages
Book Rating : 4.:/5 (31 download)
Download or read book Multigrid Solution of the Poisson-Boltzmann Equation written by Michael Holst and published by . This book was released on 1992 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "A multigrid method is presented for the numerical solution of the linearized Poisson-Boltzmann equation arising in molecular biophysics. The equation is discretized with the finite volume method, and the numerical solution of the discrete equations is accomplished with multiple grid techniques originally developed for two-dimensional interface problems occurring in reactor physics. A detailed analysis of the resulting method is presented for several computer architectures, including comparisons to diagonally scaled CG, ICCG, vectorized ICCG and MICCG, and to SOR provided with an optimal relaxation parameter. Our results indicate that the multigrid method is superior to the preconditioned CG methods and SOR, and that the advantage of multigrid grows with the problem size."
Author : Krishna Prasad M. Varadarajan
Publisher :
ISBN 13 :
Total Pages : 54 pages
Book Rating : 4.:/5 (291 download)
Download or read book Solution of Poisson Equation Using Multigrid Methods written by Krishna Prasad M. Varadarajan and published by . This book was released on 1992 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 8 pages
Book Rating : 4.:/5 (727 download)
Download or read book Numerical Methods for Molecular Dynamics. Progress Report written by and published by . This book was released on 1991 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: This report summarizes our research progress to date on the use of multigrid methods for three-dimensional elliptic partial differential equations, with particular emphasis on application to the Poisson-Boltzmann equation of molecular biophysics. This research is motivated by the need for fast and accurate numerical solution techniques for three-dimensional problems arising in physics and engineering. In many applications these problems must be solved repeatedly, and the extremely large number of discrete unknowns required to accurately approximate solutions to partial differential equations in three-dimensional regions necessitates the use of efficient solution methods. This situation makes clear the importance of developing methods which are of optimal order (or nearly so), meaning that the number of operations required to solve the discrete problem is on the order of the number of discrete unknowns. Multigrid methods are generally regarded as being in this class of methods, and are in fact provably optimal order for an increasingly large class of problems. The fundamental goal of this research is to develop a fast and accurate numerical technique, based on multi-level principles, for the solutions of the Poisson-Boltzmann equation of molecular biophysics and similar equations occurring in other applications. An outline of the report is as follows. We first present some background material, followed by a survey of the literature on the use of multigrid methods for solving problems similar to the Poisson-Boltzmann equation. A short description of the software we have developed so far is then given, and numerical results are discussed. Finally, our research plans for the coming year are presented.
Author : Kah Loon Chan
Publisher :
ISBN 13 :
Total Pages : 264 pages
Book Rating : 4.:/5 (958 download)
Download or read book Solving Poisson Equation Using Multigrid Method (W-Cycle) written by Kah Loon Chan and published by . This book was released on 2006 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multigrid Algorithms for Solving the Linear Boltzmann Equation Using First-order System Least-squares Finite Element Methods written by and published by . This book was released on 2000 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Solving the linear Boltzmann equation in neutron scattering phenomena presents many challenges to standard numerical schemes in computational physics. For an SN discretization, the so-called ray effects pollute the numerical solution. This pollution can be viewed mathematically as ''contamination'' from a poorly chosen approximating basis set for the angle component of the discretization-i.e., collocation in angle is equivalent to discretization with delta basis functions, which form a poor approximating basis set. Fortunately, a PN discretization, which uses a better approximating basis set (i.e., spherical harmonics), eliminates these ray effects. Unfortunately, solving for the moments or PN equations is difficult. Moments couple strongly with each other, creating a strongly coupled system of partial differential equations (pde's) ; numerical algorithms for solving such strongly coupled systems are difficult to develop. In this paper, novel algorithms for solving this coupled system are presented. In particular, algorithms for solving the PN discretization of the linear Boltzmann equation using a first-order system least-squares (FOSLS) methodology (c.f. [1]) are presented.
Author : Wang Chean Tan
Publisher :
ISBN 13 :
Total Pages : 232 pages
Book Rating : 4.:/5 (958 download)
Download or read book Solving Poisson Equation Using Multigrid Method V Cycle written by Wang Chean Tan and published by . This book was released on 2006 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Benjamin Quanah Parker
Publisher :
ISBN 13 :
Total Pages : 104 pages
Book Rating : 4.:/5 (894 download)
Download or read book Multigrid Solution of the Debye-Hückel Equation written by Benjamin Quanah Parker and published by . This book was released on 2013 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Multigrid algorithms are fast solvers for elliptic partial differential equations. In this thesis, we apply multigrid methods to the model of protein charge-regulation of Hollenbeck, et al. The model of protein charge-regulation requires computing work of charging matrices for two low dielectric spheres in a salt solution, which in turn requires many solutions of the linearized Poisson-Boltzmann equation, or the Debye-Hückel equation. We use multigrid methods to reduce the run time of computing solutions to the Debye-Hückel equation, and compare the results of some simple and more complicated examples. Using the work of Brandt and others, we also construct an interpolation scheme that takes the potentially complicated behavior of the coefficient into account."--Abstract.
Author : V.V. Aristov
Publisher : Springer Science & Business Media
ISBN 13 : 9780792368311
Total Pages : 328 pages
Book Rating : 4.3/5 (683 download)
Download or read book Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows written by V.V. Aristov and published by Springer Science & Business Media. This book was released on 2001-01-31 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with the methods of solving the nonlinear Boltz mann equation and of investigating its possibilities for describing some aerodynamic and physical problems. This monograph is a sequel to the book 'Numerical direct solutions of the kinetic Boltzmann equation' (in Russian) which was written with F. G. Tcheremissine and published by the Computing Center of the Russian Academy of Sciences some years ago. The main purposes of these two books are almost similar, namely, the study of nonequilibrium gas flows on the basis of direct integration of the kinetic equations. Nevertheless, there are some new aspects in the way this topic is treated in the present monograph. In particular, attention is paid to the advantages of the Boltzmann equation as a tool for considering nonequi librium, nonlinear processes. New fields of application of the Boltzmann equation are also described. Solutions of some problems are obtained with higher accuracy. Numerical procedures, such as parallel computing, are in vestigated for the first time. The structure and the contents of the present book have some com mon features with the monograph mentioned above, although there are new issues concerning the mathematical apparatus developed so that the Boltzmann equation can be applied for new physical problems. Because of this some chapters have been rewritten and checked again and some new chapters have been added.
Author : Choong Yee Wong
Publisher :
ISBN 13 :
Total Pages : 182 pages
Book Rating : 4.:/5 (958 download)
Download or read book Solving Poisson Equation Using Different Relaxation Method in Multigrid written by Choong Yee Wong and published by . This book was released on 2006 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Siwen Wang
Publisher :
ISBN 13 :
Total Pages : 100 pages
Book Rating : 4.:/5 (125 download)
Download or read book Regularization Methods on Solving Poisson's Equation and Poisson Boltzmann Equation with Singular Charge Sources and Diffuse Interfaces written by Siwen Wang and published by . This book was released on 2021 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical treatment of singular charges is a grand challenge in solving Poisson-Boltzmann (PB) equation for analyzing electrostatic interactions between the solute biomolecules and the surrounding solvent with ions. For diffuse interface models in which solute and solvent are separated by a smooth boundary, no effective algorithm for singular charges has been developed, because the fundamental solution with a space dependent dielectric function is intractable. In this research work, regularization formulations are introduced to capture the singularity analytically, which are the first of their kind for diffuse interface Poisson's equation and PB models. The success lies in a dual decomposition -- besides decomposing the potential into Coulomb and reaction field components, the dielectric function is also split into a constant base plus space changing part. Using the constant dielectric base, the Coulomb potential is represented analytically via Green's functions. After removing the singularity, the reaction field potential satisfies a regularized PB equation with a smooth source. Some diffuse interface models including a Gaussian convolution surface (GCS) are also introduced. The GCS efficiently generates a diffuse interface for three-dimensional realistic biomolecules. The performance of the proposed regularization is examined by considering both analytical and GCS diffuse interfaces, and compared with the trilinear method. Moreover, the proposed GCS-regularization algorithm is validated by calculating electrostatic free energies for a set of proteins and by estimating salt affinities for seven protein complexes. The results are consistent with experimental data and estimates of sharp interface PB models.
Author : Jenny Gu
Publisher : John Wiley & Sons
ISBN 13 : 1118210565
Total Pages : 1105 pages
Book Rating : 4.1/5 (182 download)
Download or read book Structural Bioinformatics written by Jenny Gu and published by John Wiley & Sons. This book was released on 2011-09-20 with total page 1105 pages. Available in PDF, EPUB and Kindle. Book excerpt: Structural Bioinformatics was the first major effort to show the application of the principles and basic knowledge of the larger field of bioinformatics to questions focusing on macromolecular structure, such as the prediction of protein structure and how proteins carry out cellular functions, and how the application of bioinformatics to these life science issues can improve healthcare by accelerating drug discovery and development. Designed primarily as a reference, the first edition nevertheless saw widespread use as a textbook in graduate and undergraduate university courses dealing with the theories and associated algorithms, resources, and tools used in the analysis, prediction, and theoretical underpinnings of DNA, RNA, and proteins. This new edition contains not only thorough updates of the advances in structural bioinformatics since publication of the first edition, but also features eleven new chapters dealing with frontier areas of high scientific impact, including: sampling and search techniques; use of mass spectrometry; genome functional annotation; and much more. Offering detailed coverage for practitioners while remaining accessible to the novice, Structural Bioinformatics, Second Edition is a valuable resource and an excellent textbook for a range of readers in the bioinformatics and advanced biology fields. Praise for the previous edition: "This book is a gold mine of fundamental and practical information in an area not previously well represented in book form." —Biochemistry and Molecular Education "... destined to become a classic reference work for workers at all levels in structural bioinformatics...recommended with great enthusiasm for educators, researchers, and graduate students." —BAMBED "...a useful and timely summary of a rapidly expanding field." —Nature Structural Biology "...a terrific job in this timely creation of a compilation of articles that appropriately addresses this issue." —Briefings in Bioinformatics
Download or read book Using Pseudo Transient Continuation and the Finite Element Method to Solve the Nonlinear Poisson-Boltzmann Equation written by and published by . This book was released on 2000 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The nonlinear Poisson-Boltzmann (PB) equation is solved using Pseudo Transient Continuation. The PB solver is constructed by modifying the nonlinear diffusion module of a 3D, massively parallel, unstructured-grid, finite element, radiation-hydrodynamics code. The solver also computes the electrostatic energy and evaluates the force on a user-specified contour. Either Dirichlet or mixed boundary conditions are allowed. The latter specifies surface charges, approximates far-field conditions, or linearizes conditions ''regulating'' the surface charge. The code may be run in either Cartesian, cylindrical, or spherical coordinates. The potential and force due to a conical probe interacting with a flat plate is computed and the result compared with direct force measurements by chemical force microscopy.
Author : Paul L. A. Popelier
Publisher : World Scientific
ISBN 13 : 1848167245
Total Pages : 375 pages
Book Rating : 4.8/5 (481 download)
Download or read book Solving the Schrdinger Equation written by Paul L. A. Popelier and published by World Scientific. This book was released on 2011 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Schrdinger equation is the master equation of quantum chemistry. The founders of quantum mechanics realised how this equation underpins essentially the whole of chemistry. However, they recognised that its exact application was much too complicated to be solvable at the time. More than two generations of researchers were left to work out how to achieve this ambitious goal for molecular systems of ever-increasing size. This book focuses on non-mainstream methods to solve the molecular electronic Schrdinger equation. Each method is based on a set of core ideas and this volume aims to explain these ideas clearly so that they become more accessible. By bringing together these non-standard methods, the book intends to inspire graduate students, postdoctoral researchers and academics to think of novel approaches. Is there a method out there that we have not thought of yet? Can we design a new method that combines the best of all worlds?
