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"Proceedings of the Workshop on Adaptive Computational Methods for Partial Differential Equations, Rensselaer Polytechnic Institute, October 13-15, 1988"--T.p. verso.
This book leads readers from a basic foundation to an advanced-level understanding of fluid and solid mechanics. Perfect for graduate or PhD mathematical-science students looking for help in understanding the fundamentals of the topic, it also explores more specific areas such as multi-deck theory, time-mean turbulent shear flows, non-linear free surface flows, and internal fluid dynamics.Fluid and Solid Mechanics is the second volume of the LTCC Advanced Mathematics Series. This series is the first to provide advanced introductions to mathematical science topics to advanced students of mathematics. Edited by the three joint heads of the London Taught Course Centre for PhD Students in the Mathematical Sciences (LTCC), each book supports readers in broadening their mathematical knowledge outside of their immediate research disciplines while also covering specialized key areas.
Very light, very strong. extremely reliable -aircraft and aerospace engineers are. and have to be. very demanding partners in the materials community. The results of their research and development work is not only crucial for one special area of applications. but can also lead the way to new solutions in many other areas of advanced technology. Springer-Verlag and the undersigned editor are pleased to present in this volume. an overview of the many facets of materials science and technology which have been the objective of intensive and systematic research work during past decades in the laboratories of the German Aerospace Research Establishment. Its contents shows clearly the interrelations between goals defined by the user. fundamentals provided by the scientists and viable solutions developed by the practical engineer. The particular personal touch which has been given to this volume by its authors in dedicating it as a farewell present to Professor Wolfgang Bunk. inspiring sci entist and director of the DLR Intitute of Materials Research for more than 20 years. has obviously given an added value to this important publication. Surely. this truly cooperative endeavour will render a valuable service to a large interna tional community of interested readers. many of them having personal links to the Institute. its director and its staff.
Authored by well-known researchers, this book presents its material as accessible surveys, giving readers access to comprehensive coverage of results scattered throughout the literature. A unique source of information for graduate students and researchers in mathematics and theoretical physics, and engineers interested in the subject.
List of participants; Elliptic equations; Parabolic equations; Hyperbolic equations.
Topics contained in this volume include the reliability of computations; a posteriori error estimation; adaptive h-, p-, and r-refinement; method of lines and local refinement methods for time-dependent problems; parallel solution techniques; and applications of adaptive methods to problems in elasticity, fluid mechanics, and combustion. Issues of reliability, presented in the contributions by Babuska and Szabo', note the importance of specifying computational accuracy in relation to the idealizations of the mathematical model. Thus, one should envision a sequence of computations where the enhancements and refinements are added to the physical mode as the computational procedure is enriched. These ideas are a relatively new and important innovation in the field. The contributions of Berger and Hassanzadeh et al. discuss parallel adaptive procedures, which is another aspect of the field that has emerged since the early conferences and workshops. (KR).
A practical handbook for understanding and using fast adaptive composite grid (FAC) methods for discretization and solution of partial differential equations (PDEs). Contains fundamental concepts. These so-called FAC are characterized by their use of a composite grid, which is nominally the union of various uniform grids. FAC is capable of producing a composite grid with tailored resolution, and a corresponding solution with commensurate accuracy, at a cost proportional to the number of composite grid points. Moreover, special asynchronous versions of the fast adaptive composite grid methods (AFAC) studied here have seemingly optimal complexity in a parallel computing environment. Most of the methods treated in this book were discovered only within the last decade, and in many cases their development is still in its infancy. While this is not meant to be comprehensive, it does provide a theoretical and practical guide to multilevel adaptive methods and relevant discretization techniques.
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