Download or read book Adaptive Multilevel Solution of Nonlinear Parabolic PDE Systems written by Jens Lang and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nowadays there is an increasing emphasis on all aspects of adaptively gener ating a grid that evolves with the solution of a PDE. Another challenge is to develop efficient higher-order one-step integration methods which can handle very stiff equations and which allow us to accommodate a spatial grid in each time step without any specific difficulties. In this monograph a combination of both error-controlled grid refinement and one-step methods of Rosenbrock-type is presented. It is my intention to impart the beauty and complexity found in the theoretical investigation of the adaptive algorithm proposed here, in its realization and in solving non-trivial complex problems. I hope that this method will find many more interesting applications. Berlin-Dahlem, May 2000 Jens Lang Acknowledgements I have looked forward to writing this section since it is a pleasure for me to thank all friends who made this work possible and provided valuable input. I would like to express my gratitude to Peter Deuflhard for giving me the oppor tunity to work in the field of Scientific Computing. I have benefited immensly from his help to get the right perspectives, and from his continuous encourage ment and support over several years. He certainly will forgive me the use of Rosenbrock methods rather than extrapolation methods to integrate in time.
Download or read book Adaptive Numerical Solution of PDEs written by Peter Deuflhard and published by Walter de Gruyter. This book was released on 2012-08-31 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the general topic “Numerical solution of partial differential equations (PDEs)” with a focus on adaptivity of discretizations in space and time. By and large, introductory textbooks like “Numerical Analysis in Modern Scientific Computing” by Deuflhard and Hohmann should suffice as a prerequisite. The emphasis lies on elliptic and parabolic systems. Hyperbolic conservation laws are treated only on an elementary level excluding turbulence. Numerical Analysis is clearly understood as part of Scientific Computing. The focus is on the efficiency of algorithms, i.e. speed, reliability, and robustness, which directly leads to the concept of adaptivity in algorithms. The theoretical derivation and analysis is kept as elementary as possible. Nevertheless required somewhat more sophisticated mathematical theory is summarized in comprehensive form in an appendix. Complex relations are explained by numerous figures and illustrating examples. Non-trivial problems from regenerative energy, nanotechnology, surgery, and physiology are inserted. The text will appeal to graduate students and researchers on the job in mathematics, science, and technology. Conceptually, it has been written as a textbook including exercises and a software list, but at the same time it should be well-suited for self-study.
Download or read book ICIAM 91 written by Robert E. O'Malley and published by SIAM. This book was released on 1992-01-01 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings -- Computer Arithmetic, Algebra, OOP.
Download or read book Parallel Multilevel Methods written by Gerhard Zumbusch and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: Main aspects of the efficient treatment of partial differential equations are discretisation, multilevel/multigrid solution and parallelisation. These distinct topics are covered from the historical background to modern developments. It is demonstrated how the ingredients can be put together to give an adaptive and parallel multilevel approach for the solution of elliptic boundary value problems. Error estimators and adaptive grid refinement techniques for ordinary and for sparse grid discretisations are presented. Different types of additive and multiplicative multilevel solvers are discussed with respect to parallel implementation and application to adaptive refined grids. Efficiency issues are treated both for the sequential multilevel methods and for the parallel version by hash table storage techniques. Finally, space-filling curve enumeration for parallel load balancing and processor cache efficiency are discussed.
Download or read book Domain Decomposition Methods in Scientific and Engineering Computing written by David E. Keyes and published by American Mathematical Soc.. This book was released on 1994 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains proceedings from the Seventh International Conference on Domain Decomposition Methods, held at Pennsylvania State University in October 1993. The term ``domain decomposition'' has for nearly a decade been associated with the partly iterative, partly direct algorithms explored in the proceedings of this conference. Noteworthy trends in the current volume include progress in dealing with so-called ``bad parameters'' in elliptic partial differential equation problems, as well as developments in partial differential equations outside of the elliptically-dominated framework. Also described here are convergence and complexity results for novel discretizations, which bring with them new challenges in the derivation of appropriate operators for coarsened spaces. Implementations and architectural considerations are discussed, as well as partitioning tools and environments. In addition, the book describes a wide array of applications, from semiconductor device simulation to structural mechanics to aerodynamics. Presenting many of the latest results in the field, this book offers readers an up-to-date guide to the many facets of the theory and practice of domain decomposition.
Download or read book Design of Adaptive Finite Element Software written by Alfred Schmidt and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last years, scientific computing has become an important research branch located between applied mathematics and applied sciences and engineering. Highly efficient numerical methods are based on adaptive methods, higher order discretizations, fast linear and non-linear iterative solvers, multi-level algorithms, etc. Such methods are integrated in the adaptive finite element software ALBERTA. It is a toolbox for the fast and flexible implementation of efficient software for real life applications, based on modern algorithms. ALBERTA also serves as an environment for improving existent, or developing new numerical methods in an interplay with mathematical analysis and it allows the direct integration of such new or improved methods in existing simulation software.
Download or read book Numerical Treatment of Coupled Systems written by Wolfgang Hackbusch and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: The coupling considered in this volume may be of physical or numerical nature. Examples of the first kind are the solid-fluid interactions, microelectronic systems, and the coupled modelling in groundwater flow. Examples of the latter kind are the domain or subspace decomposition, the local defect correction method, and the very important FEM-BEM coupling.
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 Space Time Methods written by Ulrich Langer and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-09-23 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides an introduction to modern space-time discretization methods such as finite and boundary elements and isogeometric analysis for time-dependent initial-boundary value problems of parabolic and hyperbolic type. Particular focus is given on stable formulations, error estimates, adaptivity in space and time, efficient solution algorithms, parallelization of the solution pipeline, and applications in science and engineering.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book High Performance Scientific And Engineering Computing written by Michael Breuer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Douglas Adams' book 'Hitchhiker's Guide to the Galaxy', hyper-intelligent beings reached a point in their existence where they wanted to understand the purpose of their own existence and the universe. They built a supercomputer, called Deep Thought, and upon completion, they asked it for the answer to the ultimate question of life, the universe and everything else. The computer worked for several millennia on the answers to all these questions. When the day arrived for hyper-intelligent beings the to receive the answer, they were stunned, shocked and disappointed to hear that the answer was simply 42. The still open questions to scientists and engineers are typically much sim pler and consequently the answers are more reasonable. Furthermore, because human beings are too impatient and not ready to wait for such a long pe riod, high-performance computing techniques have been developed, leading to much faster answers. Based on these developments in the last two decades, scientific and engineering computing has evolved to a key technology which plays an important role in determining, or at least shaping, future research and development activities in many branches of industry. Development work has been going on all over the world resulting in numerical methods that are now available for simulations that were not foreseeable some years ago. However, these days the availability of supercomputers with Teraflop perfor mance supports extensive computations with technical relevance. A new age of engineering has started.
Download or read book Multilevel Finite Element Approximation written by Peter Oswald and published by Teubner Skripten zur Numerik. This book was released on 1994 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes reflect, to a great part, the present research interests of the author but were influenced by the ideas and the work of many colleagues. They are based on lectures given by the author at the Institutes of Mathematics and Informatics at the Technical U niversity of Munich during February /March 1993. I wish to warmly thank ehr. Zenger and R. Hoppe for their generous support and the many discussions I had with them and their younger colleagues during the last year. Part of the results contained in section 4 is the output of these discussions and joint work with M. Griebel. There are many other mathematicians who encouraged me (or personally or by their mathematical work) to step into the field of multilevel methods. I want to acknowledge the support I received from W. Dahmen, R. A. DeVore, P. Deufl hard, W. Hackbusch, H. Trieb el , O. Widlund, H. Yserentant and many others. On the other hand, I should apologize for not mentioning many interesting re search results and names standing for recent developments in the fields which are the subject of these notes. Finally, I want to thank my family, my wife Olga and my daughters Evelyn and Annelie, for their everyday patience and support.
Download or read book Numerical Solution of Partial Differential Equations written by K. W. Morton and published by Cambridge University Press. This book was released on 2005-04-11 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the 2005 second edition of a highly successful and well-respected textbook on the numerical techniques used to solve partial differential equations arising from mathematical models in science, engineering and other fields. The authors maintain an emphasis on finite difference methods for simple but representative examples of parabolic, hyperbolic and elliptic equations from the first edition. However this is augmented by new sections on finite volume methods, modified equation analysis, symplectic integration schemes, convection-diffusion problems, multigrid, and conjugate gradient methods; and several sections, including that on the energy method of analysis, have been extensively rewritten to reflect modern developments. Already an excellent choice for students and teachers in mathematics, engineering and computer science departments, the revised text includes more latest theoretical and industrial developments.
Download or read book Multiscaling in Molecular and Continuum Mechanics Interaction of Time and Size from Macro to Nano written by G.C. Sih and published by Springer Science & Business Media. This book was released on 2007-11-29 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the first time, a book is being edited to address how results from one scale can be shifted or related to another scale, say from macro to micro or vice versa. The new approach retains the use of the equilibrium mechanics within a scale level such that cross scale results can be connected by scale invariant criteria. Engineers in different disciplines should be able to understand and use the results.
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 1985 with total page 1052 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Moving grid Methods for Time dependent Partial Differential Equations written by P. A. Zegeling and published by . This book was released on 1993 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
