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Parallel Multigrid Based Methods For Calculating Electrostatic Potentials By Solving The Full Nonlinear Poisson Boltzmann Equation
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Book Synopsis Parallel Multigrid-based Methods for Calculating Electrostatic Potentials by Solving the Full Nonlinear Poisson-Boltzmann Equation by : Dong Zeng
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:
Book Synopsis Multilevel Methods for the Poisson-Boltzmann Equation by : Michael Jay Holst
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."
Book Synopsis Solving the Nonlinear Poisson-Boltzmann Equation Using Multigrid Methods by : Ilia Antsiferov
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:
Book Synopsis Scientific Computing in Object-oriented Parallel Environments by :
Download or read book Scientific Computing in Object-oriented Parallel Environments written by and published by . This book was released on 1997 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Solving the Poisson-Boltzmann Equation Using Nonlinear Multigrid Methods by : Ilia Antsiferov
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:
Book Synopsis Multigrid Solution of the Poisson-Boltzmann Equation by : Michael Holst
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."
Book Synopsis Molecular Biophysics Technical Report by :
Download or read book Molecular Biophysics Technical Report written by and published by . This book was released on 1993 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Cumulated Index Medicus written by and published by . This book was released on 1995 with total page 1496 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Reduced Basis Methods for Partial Differential Equations by : Alfio Quarteroni
Download or read book Reduced Basis Methods for Partial Differential Equations written by Alfio Quarteroni and published by Springer. This book was released on 2015-08-19 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a basic introduction to reduced basis (RB) methods for problems involving the repeated solution of partial differential equations (PDEs) arising from engineering and applied sciences, such as PDEs depending on several parameters and PDE-constrained optimization. The book presents a general mathematical formulation of RB methods, analyzes their fundamental theoretical properties, discusses the related algorithmic and implementation aspects, and highlights their built-in algebraic and geometric structures. More specifically, the authors discuss alternative strategies for constructing accurate RB spaces using greedy algorithms and proper orthogonal decomposition techniques, investigate their approximation properties and analyze offline-online decomposition strategies aimed at the reduction of computational complexity. Furthermore, they carry out both a priori and a posteriori error analysis. The whole mathematical presentation is made more stimulating by the use of representative examples of applicative interest in the context of both linear and nonlinear PDEs. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text. The book will be ideal for upper undergraduate students and, more generally, people interested in scientific computing. All these pseudocodes are in fact implemented in a MATLAB package that is freely available at https://github.com/redbkit
Book Synopsis Parallel Multigrid Waveform Relaxation for Parabolic Problems by : Stefan Vandewalle
Download or read book Parallel Multigrid Waveform Relaxation for Parabolic Problems written by Stefan Vandewalle and published by Teubner Skripten zur Numerik. This book was released on 1993 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wetenschap is meer dan het object dat zij bestudeert. Wetenschap is ook de weg naar de ontdekking, en bovendien, wetenschap is ook het verhaaJ van de ontdekkingsreis. -Po Thielen Focus research, Nr 10-11, juli 1991. The numerical solution of a parabolic partial differential equation is usually calcu lated by using a time-stepping method. This precludes the efficient use of parallelism and vectorization, unless the problem to be solved at each time-level is very large. This monograph investigates the use of an algorithm that overcomes the limitations of the standard schemes by calculating the solution at many time-levels, or along a continuous time-window simultaneously. The algorithm is based on waveform relazation, a highly parallel technique for solving very large systems of ordinary differential equations, and multigrid, a very fast method for solving elliptic partial differential equations. The resulting multigrid waveform relazation method is applicable to both initial boundary value and time-periodic parabolic problems. We analyse in this book theoretical and practical aspects of the multigrid waveform relaxation algorithm. Its implementation on a distributed memory message-passing computer and its computational complexity (arithmetic complexity, communication complexity and potential for vectorization) are studied. The method has been im plemented and extensively tested on a hypercube multiprocessor with vector nodes. Results of numerical experiments are given, which illustrate a severalfold performance gain when compared to parallel implementations of a variety of standard initial bound ary value and time-periodic solvers.
Book Synopsis Proceedings of the National Academy of Sciences of the United States of America by : National Academy of Sciences (U.S.)
Download or read book Proceedings of the National Academy of Sciences of the United States of America written by National Academy of Sciences (U.S.) and published by . This book was released on 2001 with total page 1108 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Proceedings of the National Academy of Sciences (PNAS) publishes research reports, commentaries, reviews, colloquium papers, and actions of the Academy. PNAS is a multidisciplinary journal that covers the biological, physical, and social sciences.
Book Synopsis Reviews in Computational Chemistry, Volume 19 by : Kenny B. Lipkowitz
Download or read book Reviews in Computational Chemistry, Volume 19 written by Kenny B. Lipkowitz and published by John Wiley & Sons. This book was released on 2003-10-21 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: Auch Band 19 dieser seit Jahren bewährten und erfolgreichen Reihe führt Neueinsteiger in moderne Forschungsgebiete der Computerchemie ein und hilft Fachleuten, auf dem Laufenden zu bleiben. - international renommierte Fachleute diskutieren Themen aus den Bereichen Molecular modeling, Quantenchemie, computergestütztes Moleküldesign (CAMD), Molekülmechanik und -dynamik sowie QSAR (Quantitative Struktur-Reaktivitäts-Beziehungen) - ausführliche Autoren- und Sachregister erleichtern die Orientierung - Beiträge sind allgemein verständlich geschrieben und enthalten nur das notwendige Minimum an mathematischen Formalismen; dadurch ist die Reihe auch geeignet für Leser, die sich nicht hauptsächlich mit den genannten Fachgebieten beschäftigen
Book Synopsis Using Pseudo Transient Continuation and the Finite Element Method to Solve the Nonlinear Poisson-Boltzmann Equation by :
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.
Book Synopsis The Robust Multigrid Technique by : Sergey I. Martynenko
Download or read book The Robust Multigrid Technique written by Sergey I. Martynenko and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-09-25 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a detailed description of a robust pseudomultigrid algorithm for solving (initial-)boundary value problems on structured grids in a black-box manner. To overcome the problem of robustness, the presented Robust Multigrid Technique (RMT) is based on the application of the essential multigrid principle in a single grid algorithm. It results in an extremely simple, very robust and highly parallel solver with close-to-optimal algorithmic complexity and the least number of problem-dependent components. Topics covered include an introduction to the mathematical principles of multigrid methods, a detailed description of RMT, results of convergence analysis and complexity, possible expansion on unstructured grids, numerical experiments and a brief description of multigrid software, parallel RMT and estimations of speed-up and efficiency of the parallel multigrid algorithms, and finally applications of RMT for the numerical solution of the incompressible Navier Stokes equations. Potential readers are graduate students and researchers working in applied and numerical mathematics as well as multigrid practitioners and software programmers. Contents Introduction to multigrid Robust multigrid technique Parallel multigrid methods Applications of multigrid methods in computational fluid dynamics
Book Synopsis Multi-Grid Methods and Applications by : Wolfgang Hackbusch
Download or read book Multi-Grid Methods and Applications written by Wolfgang Hackbusch and published by Springer. This book was released on 2003-04-17 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multi-grid methods are the most efficient tools for solving elliptic boundary value problems. The reader finds here an elementary introduction to multi-grid algorithms as well as a comprehensive convergence analysis. One section describes special applications (convection-diffusion equations, singular perturbation problems, eigenvalue problems, etc.). The book also contains a complete presentation of the multi-grid method of the second kind, which has important applications to integral equations (e.g. the "panel method") and to numerous other problems. Readers with a practical interest in multi-grid methods will benefit from this book as well as readers with a more theoretical interest.
Book Synopsis Certified Reduced Basis Methods for Parametrized Partial Differential Equations by : Jan S Hesthaven
Download or read book Certified Reduced Basis Methods for Parametrized Partial Differential Equations written by Jan S Hesthaven and published by Springer. This book was released on 2015-08-20 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.
Book Synopsis Multigrid Methods II by : Wolfgang Hackbusch
Download or read book Multigrid Methods II written by Wolfgang Hackbusch and published by Lecture Notes in Mathematics. This book was released on 1986-12 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt:
