Download or read book The Adaptive Numerical Solution of Phase Change Problems written by Mairi Laidlaw Robertson and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Estimating the Error of Numerical Solutions of Systems of Reaction Diffusion Equations written by Donald J. Estep and published by American Mathematical Soc.. This book was released on 2000 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is concerned with the computational estimation of the error of numerical solutions of potentially degenerate reaction-diffusion equations. The underlying motivation is a desire to compute accurate estimates as opposed to deriving inaccurate analytic upper bounds. In this paper, we outline, analyze, and test an approach to obtain computational error estimates based on the introduction of the residual error of the numerical solution and in which the effects of the accumulation of errors are estimated computationally. We begin by deriving an a posteriori relationship between the error of a numerical solution and its residual error using a variational argument. This leads to the introduction of stability factors, which measure the sensitivity of solutions to various kinds of perturbations. Next, we perform some general analysis on the residual errors and stability factors to determine when they are defined and to bound their size. Then we describe the practical use of the theory to estimate the errors of numerical solutions computationally. Several key issues arise in the implementation that remain unresolved and we present partial results and numerical experiments about these points. We use this approach to estimate the error of numerical solutions of nine standard reaction-diffusion models and make a systematic comparison of the time scale over which accurate numerical solutions can be computed for these problems. We also perform a numerical test of the accuracy and reliability of the computational error estimate using the bistable equation. Finally, we apply the general theory to the class of problems that admit invariant regions for the solutions, which includes seven of the main examples. Under this additional stability assumption, we obtain a convergence result in the form of an upper bound on the error from the a posteriori error estimate. We conclude by discussing the preservation of invariant regions under discretization.
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.
Download or read book Mathematical Models for Phase Change Problems written by J.F. Rodriques and published by Birkhäuser. This book was released on 2013-03-07 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph collects research and expository articles reflect ing the interaction and the cooperation of different groups in several European institut ions concerning current research on mathematical models for the behaviour of materials with phase change. These papers were presented and discussed in a Workshop held at Obidos, Portugal, du ring the first three days of October, 1988, and grew out of a two year period of intensive exploitation of differ ent abilities and mathematical experiences of the six participating groups, namely, in the University of Augsburg, wh ich was the co ordination center of this project, the Laboratoire Central des Ponts et Chaussees of Paris, the Aristoteles University of Thessaloniki, the University of Florence, the University of Lisbon and the University of Oxford. This project was carried out under the title "Mathemat ical Models of Phase Transitions and Numerical Simulation", in the framework of twinning program for stimulation of cooperation and scientific interchange, sponsored by the European Community. The underlying idea of the project was to create and study the mathematical models arising in applied engineering problems with free boundaries in a broad sense, namely in melting and freezing problems, diffusion-reaction processes, solid-solid phase transition, hysteresis phenomena, "mushy region" descriptions, contact prob lems with friction andjor adhesion, elastoplastic deformations, etc. vi This large spectrum of applied problems have in common the main feature of brusque transitions of their qualitative behaviour that correspond, in general, to non-classical discontinuous monotone or non monotone strong nonlinearities in the mathematical equations
Download or read book Recent Advances in Adaptive Computation written by Zhongci Shi and published by American Mathematical Soc.. This book was released on 2005 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: There has been rapid development in the area of adaptive computation over the past decade. The International Conference on Recent Advances in Adaptive Computation was held at Zhejiang University (Hangzhou, China) to explore these new directions. The conference brought together specialists to discuss modern theories and practical applications of adaptive methods. This volume contains articles reflecting the invited talks given by leading mathematicians at the conference. It is suitable for graduate students and researchers interested in methods of computation.
Download or read book Phase Change with Convection Modelling and Validation written by Tomasz A. Kowalewski and published by Springer. This book was released on 2014-05-04 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique volume offers a review of state-of-the-art modelling methods of phase change problems, numerical and experimental methods used in the field. It combines the experience of theoreticians with those using numerical tools for modelling problems of solidification.
Download or read book Finite Difference Methods in Heat Transfer written by M. Necati Özişik and published by CRC Press. This book was released on 2017-07-12 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite Difference Methods in Heat Transfer presents a clear, step-by-step delineation of finite difference methods for solving engineering problems governed by ordinary and partial differential equations, with emphasis on heat transfer applications. The finite difference techniques presented apply to the numerical solution of problems governed by similar differential equations encountered in many other fields. Fundamental concepts are introduced in an easy-to-follow manner. Representative examples illustrate the application of a variety of powerful and widely used finite difference techniques. The physical situations considered include the steady state and transient heat conduction, phase-change involving melting and solidification, steady and transient forced convection inside ducts, free convection over a flat plate, hyperbolic heat conduction, nonlinear diffusion, numerical grid generation techniques, and hybrid numerical-analytic solutions.
Download or read book Numerical Analysis 1999 written by G.A. Watson and published by CRC Press. This book was released on 2000-03-27 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Of considerable importance to numerical analysts, this text contains the proceedings of the 18th Dundee Biennial Conference on Numerical Analysis, featuring eminent analysts and current topics. The papers cover everything from partial differential equations to linear algebra and approximation theory and contain contributions from the leading experts in the field. The applications range from image processing and molecular dynamics to superconductivity. If you rely on numerical methods, Numerical Analysis 1999 will serve as an essential guide to the direction of current research.
Download or read book Models of Phase Transitions written by Augusto Visintin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: ... "What do you call work?" "Why ain't that work?" Tom resumed his whitewashing, and answered carelessly: "Well. lI1a), he it is, and maybe it aill't. All I know, is, it suits Tom Sawvc/:" "Oil CO/lll!, IIOW, Will do not mean to let 011 that you like it?" The brush continued to move. "Likc it? Well, I do not see wlzy I oughtn't to like it. Does a hoy get a chance to whitewash a fence every day?" That put the thing ill a Ilew light. Ben stopped nibhling the apple ... (From Mark Twain's Adventures of Tom Sawyer, Chapter II.) Mathematics can put quantitative phenomena in a new light; in turn applications may provide a vivid support for mathematical concepts. This volume illustrates some aspects of the mathematical treatment of phase transitions, namely, the classical Stefan problem and its generalizations. The in tended reader is a researcher in application-oriented mathematics. An effort has been made to make a part of the book accessible to beginners, as well as physicists and engineers with a mathematical background. Some room has also been devoted to illustrate analytical tools. This volume deals with research I initiated when I was affiliated with the Istituto di Analisi Numerica del C.N.R. in Pavia, and then continued at the Dipartimento di Matematica dell'Universita di Trento. It was typeset by the author in plain TEX
Download or read book One dimensional Stefan Problems written by James M. Hill and published by Longman Scientific and Technical. This book was released on 1987 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book European Symposium on Computer Aided Process Engineering 12 written by J. Grievink and published by Elsevier. This book was released on 2002-04-29 with total page 1059 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains 182 papers presented at the 12th Symposium of Computer Aided Process Engineering (ESCAPE-12), held in The Hague, The Netherlands, May 26-29, 2002. The objective of ESCAPE-12 is to highlight advances made in the development and use of computing methodologies and information technology in the area of Computer Aided Process Engineering and Process Systems Engineering. The Symposium addressed six themes: (1) Integrated Product&Process Design; (2) Process Synthesis & Plant Design; (3) Process Dynamics & Control; (4) Manufacturing & Process Operations; (5) Computational Technologies; (6) Sustainable CAPE Education and Careers for Chemical Engineers. These themes cover the traditional core activities of CAPE, and also some wider conceptual perspectives, such as the increasing interplay between product and process design arising from the often complex internal structures of modern products; the integration of production chains creating the network structure of the process industry and optimization over life span dimensions, taking sustainability as the ultimate driver.
Download or read book Applied mechanics reviews written by and published by . This book was released on 1948 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1994 with total page 836 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Recent Trends in Nanotechnology for Sustainable Living and Environment written by Rabibrata Mukherjee and published by Springer Nature. This book was released on 2023-06-26 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the select proceedings of International Conference on Nanotechnology for Sustainable Living and Environment (ICON-NSLE 2022). It covers the latest trends in nanotechnology and its applications in various sectors such as energy, environment, food technology, and biomedicine. Various topics covered in this book are nanomaterial preparation and characterization, nanobiotechnology, nanodevices, waste to wealth, pollution abatement, renewable energy, advanced materials, sensors and portable electronics, biomedical applications, food preservation, etc. This book is useful for researchers and professionals working in the area of nanotechnology and environment sustainability.
Download or read book Hydrodynamics written by Harry Schulz and published by BoD – Books on Demand. This book was released on 2011-10-26 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: The constant evolution of the calculation capacity of the modern computers implies in a permanent effort to adjust the existing numerical codes, or to create new codes following new points of view, aiming to adequately simulate fluid flows and the related transport of physical properties. Additionally, the continuous improving of laboratory devices and equipment, which allow to record and measure fluid flows with a higher degree of details, induces to elaborate specific experiments, in order to shed light in unsolved aspects of the phenomena related to these flows. This volume presents conclusions about different aspects of calculated and observed flows, discussing the tools used in the analyses. It contains eighteen chapters, organized in four sections: 1) Smoothed Spheres, 2) Models and Codes in Fluid Dynamics, 3) Complex Hydraulic Engineering Applications, 4) Hydrodynamics and Heat/Mass Transfer. The chapters present results directed to the optimization of the methods and tools of Hydrodynamics.
Download or read book Reviews in Numerical Analysis 1980 86 written by and published by . This book was released on 1987 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: These five volumes bring together a wealth of bibliographic information in the area of numerical analysis. Containing over 17,600 reviews of articles, books, and conference proceedings, these volumes represent all the numerical analysis entries that appeared in Mathematical Reviews between 1980 and 1986. Author and key indexes appear at the end of volume 5.
Download or read book Computational Science ICCS 2022 written by Derek Groen and published by Springer Nature. This book was released on 2022-06-21 with total page 797 pages. Available in PDF, EPUB and Kindle. Book excerpt: The four-volume set LNCS 13350, 13351, 13352, and 13353 constitutes the proceedings of the 22ndt International Conference on Computational Science, ICCS 2022, held in London, UK, in June 2022.* The total of 175 full papers and 78 short papers presented in this book set were carefully reviewed and selected from 474 submissions. 169 full and 36 short papers were accepted to the main track; 120 full and 42 short papers were accepted to the workshops/ thematic tracks. *The conference was held in a hybrid format
