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An Adaptive Grid Algorithm For One Dimensional Nonlinear Equations
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Book Synopsis An Adaptive Grid Algorithm for One-Dimensional Nonlinear Equations by : National Aeronautics and Space Adm Nasa
Download or read book An Adaptive Grid Algorithm for One-Dimensional Nonlinear Equations written by National Aeronautics and Space Adm Nasa and published by . This book was released on 2018-11-13 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Richards' equation, which models the flow of liquid through unsaturated porous media, is highly nonlinear and difficult to solve. Step gradients in the field variables require the use of fine grids and small time step sizes. The numerical instabilities caused by the nonlinearities often require the use of iterative methods such as Picard or Newton interation. These difficulties result in large CPU requirements in solving Richards equation. With this in mind, adaptive and multigrid methods are investigated for use with nonlinear equations such as Richards' equation. Attention is focused on one-dimensional transient problems. To investigate the use of multigrid and adaptive grid methods, a series of problems are studied. First, a multigrid program is developed and used to solve an ordinary differential equation, demonstrating the efficiency with which low and high frequency errors are smoothed out. The multigrid algorithm and an adaptive grid algorithm is used to solve one-dimensional transient partial differential equations, such as the diffusive and convective-diffusion equations. The performance of these programs are compared to that of the Gauss-Seidel and tridiagonal methods. The adaptive and multigrid schemes outperformed the Gauss-Seidel algorithm, but were not as fast as the tridiagonal method. The adaptive grid scheme solved the problems slightly faster than the multigrid method. To solve nonlinear problems, Picard iterations are introduced into the adaptive grid and tridiagonal methods. Burgers' equation is used as a test problem for the two algorithms. Both methods obtain solutions of comparable accuracy for similar time increments. For the Burgers' equation, the adaptive grid method finds the solution approximately three times faster than the tridiagonal method. Finally, both schemes are used to solve the water content formulation of the Richards' equation. For this problem, the adaptive grid method obtains a more accurate solution in fewer work units and ...
Book Synopsis An Adaptive Grid Algorithm for One-dimensional Nonlinear Equations by : William Edward Gutierrez
Download or read book An Adaptive Grid Algorithm for One-dimensional Nonlinear Equations written by William Edward Gutierrez and published by . This book was released on 1990 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Adaptive Methods — Algorithms, Theory and Applications by : W. Hackbusch
Download or read book Adaptive Methods — Algorithms, Theory and Applications written by W. Hackbusch and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: The GAMM Committee for "Efficient Numerical Methods for Partial Differential Equations" organizes workshops on subjects concerning the algorithmical treat ment of partial differential equations. The topics are discretization methods like the finite element and finite volume method for various types of applications in structural and fluid mechanics. Particular attention is devoted to advanced solu tion techniques. th The series of such workshops was continued in 1993, January 22-24, with the 9 Kiel-Seminar on the special topic "Adaptive Methods Algorithms, Theory and Applications" at the Christian-Albrechts-University of Kiel. The seminar was attended by 76 scientists from 7 countries and 23 lectures were given. The list of topics contained general lectures on adaptivity, special discretization schemes, error estimators, space-time adaptivity, adaptive solvers, multi-grid me thods, wavelets, and parallelization. Special thanks are due to Michael Heisig, who carefully compiled the contribu tions to this volume. November 1993 Wolfgang Hackbusch Gabriel Wittum v Contents Page A. AUGE, G. LUBE, D. WEISS: Galerkin/Least-Squares-FEM and Ani- tropic Mesh Refinement. 1 P. BASTIAN, G. WmUM : Adaptive Multigrid Methods: The UG Concept. 17 R. BEINERT, D. KRONER: Finite Volume Methods with Local Mesh Alignment in 2-D. 38 T. BONK: A New Algorithm for Multi-Dimensional Adaptive Nume- cal Quadrature. 54 F.A. BORNEMANN: Adaptive Solution of One-Dimensional Scalar Conservation Laws with Convex Flux. 69 J. CANU, H. RITZDORF : Adaptive, Block-Structured Multigrid on Local Memory Machines. 84 S. DAHLKE, A. KUNaTH: Biorthogonal Wavelets and Multigrid. 99 B. ERDMANN, R.H.W. HOPPE, R.
Book Synopsis A Piecewise Uniform Adaptive Grid Algorithm for Nonlinear Dispersive Wave Equations by : E. S. Fraga
Download or read book A Piecewise Uniform Adaptive Grid Algorithm for Nonlinear Dispersive Wave Equations written by E. S. Fraga and published by . This book was released on 1987 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fundamentals of Grid Generation by : Stanley Steinberg
Download or read book Fundamentals of Grid Generation written by Stanley Steinberg and published by CRC Press. This book was released on 2020-12-17 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamentals of Grid Generation is an outstanding text/reference designed to introduce students in applied mathematics, mechanical engineering, and aerospace engineering to structured grid generation. It provides excellent reference material for practitioners in industry, and it presents new concepts to researchers. Readers will learn what boundary-conforming grids are, how to generate them, and how to devise their own methods. The text is written in a clear, intuitive style that doesn't get bogged down in unnecessary abstractions. Topics covered include planar, surface, and 3-D grid generation; numerical techniques; solution adaptivity; the finite volume approach to discretization of hosted equations; concepts from elementary differential geometry; and the transformation of differential operators to general coordinate systems. The book also reviews the literature on algebraic, conformal, orthogonal, hyperbolic, parabolic, elliptic, biharmonic, and variational approaches to grid generation. This unique volume closes with the author's original methods of variational grid generation.
Book Synopsis A Multigrid Tutorial by : William L. Briggs
Download or read book A Multigrid Tutorial written by William L. Briggs and published by SIAM. This book was released on 2000-01-01 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition preserves the introductory spirit of the first edition while roughly doubling the amount of material covered. The topics of the first edition have been enhanced with additional discussion, new numerical experiments, and improved figures. New topics in the second edition include nonlinear equations, Neumann boundary conditions, variable mesh and variable coefficient problems, anisotropic problems, algebraic multigrid (AMG), adaptive methods, and finite elements. This introductory book is ideally suited as a companion textbook for graduate numerical analysis courses. It is written for computational mathematicians, engineers, and other scientists interested in learning about multigrid.
Book Synopsis Government Reports Annual Index by :
Download or read book Government Reports Annual Index written by and published by . This book was released on 1994 with total page 1442 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sections 1-2. Keyword Index.--Section 3. Personal author index.--Section 4. Corporate author index.-- Section 5. Contract/grant number index, NTIS order/report number index 1-E.--Section 6. NTIS order/report number index F-Z.
Book Synopsis Grid Generation and Adaptive Algorithms by : Marshall W. Bern
Download or read book Grid Generation and Adaptive Algorithms written by Marshall W. Bern and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications GRID GENERATION AND ADAPTIVE ALGORITHMS is based on the proceedings of a workshop with the same title. The work shop was an integral part of the 1996-97 IMA program on "MATHEMAT ICS IN HIGH-PERFORMANCE COMPUTING. " I would like to thank Marshall Bern (Xerox, Palo Alto Research Cen ter), Joseph E. Flaherty (Department of Computer Science, Rensselaer Polytechnic Institute), and Mitchell Luskin (School of Mathematics, Uni versity of Minnesota), for their excellent work as organizers of the meeting and for editing the proceedings. I also take this opportunity to thank the National Science Founda tion (NSF), Department of Energy (DOE), and the Army Research Office (ARO), whose financial support made the workshop possible. Willard Miller, Jr. , Professor and Director v PREFACE Scientific and engineering computation has become so complex that traditional numerical computation on uniform meshes is generally not pos sible or too expensive. Mesh generation must reflect both the domain geometry and the expected solution characteristics. Meshes should, fur thermore, be related to the solution through computable estimates of dis cretization errors. This, suggests an automatic and adaptive process where an initial mesh is enriched with the goal of computing a solution with prescribed accuracy specifications in an optimal manner. While automatic mesh generation procedures and adaptive strategies are becoming available, major computational challenges remain. Three-dimensional mesh genera tion is still far from automatic.
Book Synopsis Adaptive Method of Lines by : A, Vande Wouwer
Download or read book Adaptive Method of Lines written by A, Vande Wouwer and published by CRC Press. This book was released on 2001-04-18 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: The general Method of Lines (MOL) procedure provides a flexible format for the solution of all the major classes of partial differential equations (PDEs) and is particularly well suited to evolutionary, nonlinear wave PDEs. Despite its utility, however, there are relatively few texts that explore it at a more advanced level and reflect the method's
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1987 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Digital Simulation in Electrochemistry by : Dieter Britz
Download or read book Digital Simulation in Electrochemistry written by Dieter Britz and published by Springer. This book was released on 2016-05-09 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explains how the partial differential equations (pdes) in electroanalytical chemistry can be solved numerically. It guides the reader through the topic in a very didactic way, by first introducing and discussing the basic equations along with some model systems as test cases systematically. Then it outlines basic numerical approximations for derivatives and techniques for the numerical solution of ordinary differential equations. Finally, more complicated methods for approaching the pdes are derived. The authors describe major implicit methods in detail and show how to handle homogeneous chemical reactions, even including coupled and nonlinear cases. On this basis, more advanced techniques are briefly sketched and some of the commercially available programs are discussed. In this way the reader is systematically guided and can learn the tools for approaching his own electrochemical simulation problems. This new fourth edition has been carefully revised, updated and extended compared to the previous edition (Lecture Notes in Physics Vol. 666). It contains new material describing migration effects, as well as arrays of ultramicroelectrodes. It is thus the most comprehensive and didactic introduction to the topic of electrochemical simulation.
Book Synopsis Acta Numerica 2009 by : Arieh Iserles
Download or read book Acta Numerica 2009 written by Arieh Iserles and published by Cambridge University Press. This book was released on 2009-05-28 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: A high-impact, prestigious, annual publication featuring invited surveys by subject leaders: essential reading for all practitioners and researchers.
Book Synopsis Numerical Analysis by : Andrew R. Mitchell
Download or read book Numerical Analysis written by Andrew R. Mitchell and published by World Scientific. This book was released on 1996 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is intended to mark the 75th birthday of A R Mitchell, of the University of Dundee. It consists of a collection of articles written by numerical analysts having links with Ron Mitchell, as colleagues, collaborators, former students, or as visitors to Dundee. Ron Mitchell is known for his books and articles contributing to the numerical analysis of partial differential equations; he has also made major contributions to the development of numerical analysis in the UK and abroad, and his many human qualitites are such that he is held in high regard and looked on with great affection by the numerical analysis community. The list of contributors is evidence of the esteem in which he is held, and of the way in which his influence has spread through his former students and fellow workers. In addition to contributions relevant to his own specialist subjects, there are also papers on a wide range of subjects in numerical analysis.
Book Synopsis Monthly Catalog of United States Government Publications by :
Download or read book Monthly Catalog of United States Government Publications written by and published by . This book was released on 1993-10 with total page 1146 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Adaptive Grid Technique for Solution of the Euler Equations by : Dun Charles Liu
Download or read book An Adaptive Grid Technique for Solution of the Euler Equations written by Dun Charles Liu and published by . This book was released on 1987 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Courant–Friedrichs–Lewy (CFL) Condition by : Carlos A. de Moura
Download or read book The Courant–Friedrichs–Lewy (CFL) Condition written by Carlos A. de Moura and published by Springer Science & Business Media. This book was released on 2012-10-28 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises a carefully selected collection of articles emerging from and pertinent to the 2010 CFL-80 conference in Rio de Janeiro, celebrating the 80th anniversary of the Courant-Friedrichs-Lewy (CFL) condition. A major result in the field of numerical analysis, the CFL condition has influenced the research of many important mathematicians over the past eight decades, and this work is meant to take stock of its most important and current applications. The Courant–Friedrichs–Lewy (CFL) Condition: 80 Years After its Discovery will be of interest to practicing mathematicians, engineers, physicists, and graduate students who work with numerical methods.
