Radial Basis Function Methods For Large Scale Wave Propagation
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Author | : Jun-Pu Li |
Publisher | : Bentham Science Publishers |
Total Pages | : 183 |
Release | : 2021-12-24 |
Genre | : Science |
ISBN | : 1681088991 |
This book details the development of techniques and ideas from the radial basis function. It begins with a mathematical description of the basic concept of radial function method with chapters progressively delving into the derivation and construction of radial basis functions for large-scale wave propagation problems including singularity problems, high-frequency wave problems and large-scale computation problems. This reference, written by experts in numerical analysis, demonstrates how the functions arise naturally in mathematical analyses of structures responding to external loads. Readers are also equipped with mathematical knowledge about the radial basis function for understanding key algorithms required for practical solutions. Key features: - Introduces basic concepts of radial basis function methods - Provides detailed derivations of several radial basis functions - Explains complex problems using simple language - Contains a wide range of numerical examples to demonstrate applications of relevant functions - Combines the radial basis function with other known numerical methods (boundary element methods and differential equations). - Includes references and appropriate chapter appendices - Includes MATLAB codes for origin intensity factors and nearly singular factors for radial basis calculations The book is designed to make information about radial basis function methods more accessible to research scientists, professional engineers and postgraduate students, with a specific focus on large-scale wave propagation problems.
Author | : Cheng, A. H-D |
Publisher | : WIT Press |
Total Pages | : 313 |
Release | : 2019-09-13 |
Genre | : Mathematics |
ISBN | : 1784663417 |
Originating from the 42nd conference on Boundary Elements and other Mesh Reduction Methods (BEM/MRM), the research presented in this book consist of high quality papers that report on advances in techniques that reduce or eliminate the type of meshes associated with such methods as finite elements or finite differences.
Author | : Bengt Fornberg |
Publisher | : SIAM |
Total Pages | : 226 |
Release | : 2015-09-30 |
Genre | : Science |
ISBN | : 161197402X |
?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 RBFs, starting with brief introductions to finite difference (FD) and pseudospectral (PS) methods and following a logical progression to global RBFs and then to RBF-generated FD (RBF-FD) methods. The RBF-FD method, conceived in 2000, has proven to be a leading candidate for numerical simulations in an increasingly wide range of applications, including seismic exploration for oil and gas, weather and climate modeling, and electromagnetics, among others.? This is the first survey in book format of the RBF-FD methodology and is suitable as the text for a one-semester first-year graduate class.
Author | : Detlef H. Mache |
Publisher | : Springer Science & Business Media |
Total Pages | : 300 |
Release | : 2006-03-30 |
Genre | : Mathematics |
ISBN | : 3764373563 |
This volume contains contributions from international experts in the fields of constructive approximation. This area has reached out to encompass the computational and approximation-theoretical aspects of various interesting fields in applied mathematics.
Author | : Amir Sharifahmadian |
Publisher | : Butterworth-Heinemann |
Total Pages | : 364 |
Release | : 2015-11-24 |
Genre | : Technology & Engineering |
ISBN | : 0128026650 |
Numerical Models for Submerged Breakwaters: Coastal Hydrodynamics and Morphodynamics discusses the practice of submerged breakwaters, an increasingly popular tool used as a coastal defense system because of their amenity and aesthetics as compared to common emerged beach protection measures. The book is the perfect guide for experienced professionals who wish to keep abreast of the latest best practices or those who are entering the field and need a reference, explaining new and traditional numerical methodologies for designing submerged breakwaters and measuring their performance. In addition, the book provides case studies, examples, and practical methods for data selection and pre-processing, model setup, calibration, and analysis. - Case studies and worked-out examples illustrate different concepts and methods - Offers practical methods for Data Selection and Pre-Processing - Provides simplified prediction tools for practical applications
Author | : L. C. Wrobel |
Publisher | : John Wiley & Sons |
Total Pages | : 480 |
Release | : 2002-04-22 |
Genre | : Technology & Engineering |
ISBN | : 9780471720393 |
The boundary element method (BEM) is a modern numerical techniquewhich has enjoyed increasing popularity over the last two decades,and is now an established alternative to traditional computationalmethods of engineering analysis. The main advantage of the BEM isits unique ability to provide a complete solution in terms ofboundary values only, with substantial savings in modelling effort. This two-volume book set is designed to provide the readers with acomprehensive and up-to-date account of the boundary element methodand its application to solving engineering problems. Each volume isa self-contained book including a substantial amount of materialnot previously covered by other text books on the subject. Volume 1covers applications to heat transfer, acoustics, electrochemistryand fluid mechanics problems, while volume 2 concentrates on solidsand structures, describing applications to elasticity, plasticity,elastodynamics, fracture mechanics and contact analysis. The earlychapters are designed as a teaching text for final yearundergraduate courses. Both volumes reflect the experience of theauthors over a period of more than twenty years of boundary element research. This volume, Applications in Thermo-Fluids and Acoustics, provides acomprehensive presentation of the BEM from fundamentals to advancedengineering applications and encompasses: Steady and transient heat transfer Potential and viscous fluid flows Frequency and time-domain acoustics Corrosion and other electrochemical problems. A unique feature of this book is an in-depth presentation of BEMformulations in all the above fields, including detaileddiscussions of the basic theory, numerical algorithms and practicalengineering applications of the method. Written by an internationally recognised authority in the field,this is essential reading for postgraduates, researchers andpractitioners in civil, mechanical and chemical engineering andapplied mathematics.
Author | : Gregory E Fasshauer |
Publisher | : World Scientific Publishing Company |
Total Pages | : 537 |
Release | : 2015-07-30 |
Genre | : Mathematics |
ISBN | : 9814630152 |
In an attempt to introduce application scientists and graduate students to the exciting topic of positive definite kernels and radial basis functions, this book presents modern theoretical results on kernel-based approximation methods and demonstrates their implementation in various settings. The authors explore the historical context of this fascinating topic and explain recent advances as strategies to address long-standing problems. Examples are drawn from fields as diverse as function approximation, spatial statistics, boundary value problems, machine learning, surrogate modeling and finance. Researchers from those and other fields can recreate the results within using the documented MATLAB code, also available through the online library. This combination of a strong theoretical foundation and accessible experimentation empowers readers to use positive definite kernels on their own problems of interest.
Author | : Rodolphe L. Motard |
Publisher | : Springer Science & Business Media |
Total Pages | : 329 |
Release | : 2013-11-27 |
Genre | : Science |
ISBN | : 1461527082 |
Increasing emphasis on safety, productivity and quality control has provided an impetus to research on better methodologies for fault diagnosis, modeling, identification, control and optimization ofchemical process systems. One of the biggest challenges facing the research community is the processing of raw sensordata into meaningful information. Wavelet analysis is an emerging field of mathematics that has provided new tools and algorithms suited for the type of problems encountered in process monitoring and control. The concept emerged in the geophysical field as a result ofthe need for time-frequency analytical techniques. It has since been picked up by mathematicians and recognized as a unifying theory for many ofthe methodologies employed in the past in physics and signal processing. l Meyer states: "Wavelets are without doubt an exciting and intuitive concept. The concept brings with it a new way of thinking, which is absolutely essential and was entirely missing in previously existing algorithms. " The unification ofthe theory from these disciplines has led to applications of wavelet transforms in many areas ofscience and engineering including: • pattern recognition • signal analysis • time-frequency decomposition • process signal characterization and representation • process system modeling and identification • control system design, analysis and implementation • numerical solution ofdifferential equations • matrix manipulation About a year ago, in talking to various colleagues and co-workers, it became clear that a number of chemical engineers were fascinated with this new concept.
Author | : |
Publisher | : |
Total Pages | : 456 |
Release | : 1995 |
Genre | : Aeronautics |
ISBN | : |
Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Author | : Bengt Fornberg |
Publisher | : SIAM |
Total Pages | : 226 |
Release | : 2015-09-30 |
Genre | : Science |
ISBN | : 1611974046 |
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 RBFs, starting with brief introductions to finite difference (FD) and pseudospectral (PS) methods and following a logical progression to global RBFs and then to RBF-generated FD (RBF-FD) methods. The RBF-FD method, conceived in 2000, has proven to be a leading candidate for numerical simulations in an increasingly wide range of applications, including seismic exploration for oil and gas, weather and climate modeling, and electromagnetics, among others. This is the first survey in book format of the RBF-FD methodology and is suitable as the text for a one-semester first-year graduate class.