A brief survey of splines and variational methods
Author | : P. M. Prenter |
Publisher | : |
Total Pages | : 154 |
Release | : 1974 |
Genre | : |
ISBN | : 9780798804837 |
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Author | : P. M. Prenter |
Publisher | : |
Total Pages | : 154 |
Release | : 1974 |
Genre | : |
ISBN | : 9780798804837 |
Author | : P. M. Prenter |
Publisher | : Courier Corporation |
Total Pages | : 338 |
Release | : 2013-11-26 |
Genre | : Mathematics |
ISBN | : 0486783499 |
One of the clearest available introductions to variational methods, this text requires only a minimal background in calculus and linear algebra. Its self-contained treatment explains the application of theoretic notions to the kinds of physical problems that engineers regularly encounter. The text’s first half concerns approximation theoretic notions, exploring the theory and computation of one- and two-dimensional polynomial and other spline functions. Later chapters examine variational methods in the solution of operator equations, focusing on boundary value problems in one and two dimensions. Additional topics include least squares and other Galerkin methods. Many helpful definitions, examples, and exercises appear throughout the book. A classic reference in spline theory, this volume will benefit experts as well as students of engineering and mathematics.
Author | : Anatoly Yu. Bezhaev |
Publisher | : Springer Science & Business Media |
Total Pages | : 291 |
Release | : 2013-04-18 |
Genre | : Mathematics |
ISBN | : 147573428X |
This book is a systematic description of the variational theory of splines in Hilbert spaces. All central aspects are discussed in the general form: existence, uniqueness, characterization via reproducing mappings and kernels, convergence, error estimations, vector and tensor hybrids in splines, dimensional reducing (traces of splines onto manifolds), etc. All considerations are illustrated by practical examples. In every case the numerical algorithms for the construction of splines are demonstrated.
Author | : W. D. Hoskins |
Publisher | : |
Total Pages | : 160 |
Release | : 1970 |
Genre | : |
ISBN | : |
Author | : Robert Hermann |
Publisher | : Math Science Press |
Total Pages | : 205 |
Release | : 1994 |
Genre | : Mathematics |
ISBN | : 9780915692460 |
Author | : Sheng-Hong Chen |
Publisher | : Springer |
Total Pages | : 908 |
Release | : 2018-06-21 |
Genre | : Science |
ISBN | : 9811081352 |
This book presents recent research into developing and applying computational tools to estimate the performance and safety of hydraulic structures from the planning and construction stage to the service period. Based on the results of a close collaboration between the author and his colleagues, friends, students and field engineers, it shows how to achieve a good correlation between numerical computation and the actual in situ behavior of hydraulic structures. The book’s heuristic and visualized style disseminates the philosophy and road map as well as the findings of the research. The chapters reflect the various aspects of the three typical and practical methods (the finite element method, the block element method, the composite element method) that the author has been working on and made essential contributions to since the 1980s. This book is an advanced continuation of Hydraulic Structures by the same author, published by Springer in 2015.
Author | : South African Council for Scientific and Industrial Research |
Publisher | : |
Total Pages | : 428 |
Release | : 1973 |
Genre | : Science |
ISBN | : |
Author | : Morten Dæhlen |
Publisher | : |
Total Pages | : 584 |
Release | : 1998 |
Genre | : Mathematics |
ISBN | : |
Contains more than fifty carefully refereed and edited full-length papers on the theory and applications of mathematical methods arising out of the Fourth International Conference on Mathematical Methods in Computer Aided Geometric Design, held in Lillehammer, Norway, in July 1997.
Author | : R. Arcangéli |
Publisher | : Springer |
Total Pages | : 263 |
Release | : 2013-05-08 |
Genre | : Mathematics |
ISBN | : 9781475788426 |
This book is of interest to mathematicians, geologists, engineers and, in general, researchers and post graduate students involved in spline function theory, surface fitting problems or variational methods. From reviews: The book is well organized, and the English is very good. I recommend the book to researchers in approximation theory, and to anyone interested in bivariate data fitting." (L.L. Schumaker, Mathematical Reviews, 2005).
Author | : Felix Wolf |
Publisher | : Springer Nature |
Total Pages | : 139 |
Release | : 2020-11-30 |
Genre | : Technology & Engineering |
ISBN | : 3030619397 |
This book presents a comprehensive mathematical and computational approach for solving electromagnetic problems of practical relevance, such as electromagnetic scattering and the cavity problems. After an in-depth introduction to the mathematical foundations of isogeometric analysis, which discusses how to conduct higher-order simulations efficiently and without the introduction of geometrical errors, the book proves quasi-optimal approximation properties for all trace spaces of the de Rham sequence, and demonstrates inf-sup stability of the isogeometric discretisation of the electric field integral equation (EFIE). Theoretical properties and algorithms are described in detail. The algorithmic approach is, in turn, validated through a series of numerical experiments aimed at solving a set of electromagnetic scattering problems. In the last part of the book, the boundary element method is combined with a novel eigenvalue solver, a so-called contour integral method. An algorithm is presented, together with a set of successful numerical experiments, showing that the eigenvalue solver benefits from the high orders of convergence offered by the boundary element approach. Last, the resulting software, called BEMBEL (Boundary Element Method Based Engineering Library), is reviewed: the user interface is presented, while the underlying design considerations are explained in detail. Given its scope, this book bridges an important gap between numerical analysis and engineering design of electromagnetic devices.