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Wave Packets and Their Bifurcations in Geophysical Fluid Dynamics
The material in this book is based predominantly on my recent work. It is the first monograph on the subject, though some support material may overlap other monographs. The investigation of wave packets and their bi furcations is very interesting, and useful theoretically and in practice, not only in geophysical fluid dynamics, which is the field to which the theory is being applied here, but also in other fields in mathematics and the natural sciences. I hope that the applied mathematician will find reading this book worthwhile, especially the material on the behavior of highly nonlinear dy namic systems. However, it is my belief that applying the concepts and methods developed here to othe...
Mathematics for Large Scale Computing
During recent years a great deal of interest has been devoted to large scale computing applications. This has occurred in great part because of the introduction of advanced high performance computer architectures. The book contains survey articles as well as chapters on specific research applications, development and analysis of numerical algorithms, and performance evaluation of algorithms on advanced architectures. The effect of specialized architectural features on the performance of large scale computation is also considered by several authors. Several areas of applications are represented, including the numerical solution of partial differential equations, iterative techniques for large structured problems, the numerical solution of boundary value problems for ordinary differential equations, numerical optimization, and numerical quadrature. Mathematical issues in computer architecture are also presented, including the description of grey codes for generalized hypercubes. The results presented in this volume give, in our opinion, a representative picture of today’s state of the art in several aspects of large scale computing.
Parallel Algorithms for Numerical Linear Algebra
This is the first in a new series of books presenting research results and developments concerning the theory and applications of parallel computers, including vector, pipeline, array, fifth/future generation computers, and neural computers.All aspects of high-speed computing fall within the scope of the series, e.g. algorithm design, applications, software engineering, networking, taxonomy, models and architectural trends, performance, peripheral devices.Papers in Volume One cover the main streams of parallel linear algebra: systolic array algorithms, message-passing systems, algorithms for parallel shared-memory systems, and the design of fast algorithms and implementations for vector supercomputers.
Parallel Algorithms for Matrix Computations
Mathematics of Computing -- Parallelism.
Numerical Methods in Turbulence Simulation
Numerical Methods in Turbulence Simulation provides detailed specifications of the numerical methods needed to solve important problems in turbulence simulation. Numerical simulation of turbulent fluid flows is challenging because of the range of space and time scales that must be represented. This book provides explanations of the numerical error and stability characteristics of numerical techniques, along with treatments of the additional numerical challenges that arise in large eddy simulations. Chapters are written as tutorials by experts in the field, covering specific both contexts and applications. Three classes of turbulent flow are addressed, including incompressible, compressible a...
Wave Propagation and Stability for Finite Difference Schemes
This dissertation investigates the behavior of finite difference models of linear hyperbolic partial differential equations. Whereas a hyperbolic equation is nondispersive and nondissipative, difference models are invariably dispersive, and often dissipative too. We set about analyzing them by means of existing techniques from the theory of dispersive wave propagation, making extensive use in particular of the concept of group velocity, the velocity at which energy propagates. The first three chapters present a general analysis of wave propagation in difference models. We describe systematically the effects of dispersion on numerical errors, for both smooth and parasitic waves. The reflection and transmission of waves at boundaries and interfaces are then studied at length. The key point for this is a distinction introduced here between leftgoing and rightgoing signals, which is based not on the characteristics of the original equation, but on the group velocities of the numerical model. The last three chapters examine stability for finite difference models of initial boundary value problems.
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