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A Primer on Radial Basis Functions with Applications to the Geosciences
Adapted from a series of lectures given by the authors, this monograph focuses on radial basis functions (RBFs), a powerful numerical methodology for solving PDEs to high accuracy in any number of dimensions. This method applies to problems across a wide range of PDEs arising in fluid mechanics, wave motions, astro- and geosciences, mathematical biology, and other areas and has lately been shown to compete successfully against the very best previous approaches on some large benchmark problems. Using examples and heuristic explanations to create a practical and intuitive perspective, the authors address how, when, and why RBF-based methods work. The authors trace the algorithmic evolution of ...
Fractal Analysis
Fractal analysis has entered a new era. The applications to different areas of knowledge have been surprising. Let us begin with the fractional calculus-fractal geometry relationship, which allows for modeling with extreme precision of phenomena such as diffusion in porous media with fractional partial differential equations in fractal objects. Where the order of the equation is the same as the fractal dimension, this allows us to make calculations with enormous precision in diffusion phenomena-particularly in the oil industry, for new spillage prevention. Main applications to industry, design of fractal antennas to receive all frequencies and that is used in all cell phones, spacecraft, radars, image processing, measure, porosity, turbulence, scattering theory. Benoit Mandelbrot, creator of fractal geometry, would have been surprised by the use of fractal analysis presented in this book: "Part I: Petroleum Industry and Numerical Analysis"; "Part II: Fractal Antennas, Spacecraft, Radars, Image Processing, and Measure"; and "Part III: Scattering Theory, Porosity, and Turbulence." It's impossible to picture today's research without fractal analysis.
A Practical Guide to Pseudospectral Methods
This book explains how, when and why the pseudospectral approach works.
Recent Developments in Numerical Methods and Software for ODEs/DAEs/PDEs
Ordinary differential equations (ODEs), differential-algebraic equations (DAEs) and partial differential equations (PDEs) are among the forms of mathematics most widely used in science and engineering. Each of these equation types is a focal point for international collaboration and research. This book contains papers by recognized numerical analysts who have made important contributions to the solution of differential systems in the context of realistic applications, and who now report the latest results of their work in numerical methods and software for ODEs/DAEs/PDEs. The papers address parallelization and vectorization of numerical methods, the numerical solution of ODEs/DAEs/PDEs, and the use of these numerical methods in realistic scientific and engineering applications.
Boundary-Layer Separation
The IUTAM Symposium on Boundary-Layer Separation, suggested by the UK National Committee of Theoretical and Applied Mechanics and supported by the International Union of Theoretical and Applied Mechanics, was held at University College London on August 26-28, 1986. The proposed theme and scope of the Symposium were designed to help to bring about the necessary interaction between experimentalists, computationalists and theoreticians for the furthering of understanding in this challenging subject. The talks and discussions were aimed at representing the very wide range and application of separating-flow phenomena, which often substantially affect the whole of fluid dynamics at medium to large...
Training Cognition
Training is both a teaching and a learning experience, and just about everyone has had that experience. Training involves acquiring knowledge and skills. This newly acquired training information is meant to be applicable to specific activities, tasks, and jobs. In modern times, where jobs are increasingly more complex, training workers to perform successfully is of more importance than ever. The range of contexts in which training is required includes industrial, corporate, military, artistic, and sporting, at all levels from assembly line to executive function. The required training can take place in a variety of ways and settings, including the classroom, the laboratory, the studio, the pl...
Solving Problems in Multiply Connected Domains
Whenever two or more objects or entities—be they bubbles, vortices, black holes, magnets, colloidal particles, microorganisms, swimming bacteria, Brownian random walkers, airfoils, turbine blades, electrified drops, magnetized particles, dislocations, cracks, or heterogeneities in an elastic solid—interact in some ambient medium, they make holes in that medium. Such holey regions with interacting entities are called multiply connected. This book describes a novel mathematical framework for solving problems in two-dimensional, multiply connected regions. The framework is built on a central theoretical concept: the prime function, whose significance for the applied sciences, especially for...
High-Order Methods for Incompressible Fluid Flow
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