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Fast Radial Basis Functions for Engineering Applications

  • Marco Evangelos Biancolini

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Marco Evangelos Biancolini
    Pages 1-6
  3. Fast RBF for Engineering Applications

    1. Front Matter
      Pages 7-7
    2. Marco Evangelos Biancolini
      Pages 9-33
    3. Marco Evangelos Biancolini
      Pages 35-62
    4. Marco Evangelos Biancolini
      Pages 63-78
  4. Engineering Applications Examples

    1. Front Matter
      Pages 79-79
    2. Marco Evangelos Biancolini
      Pages 81-92
    3. Marco Evangelos Biancolini
      Pages 93-117
    4. Marco Evangelos Biancolini
      Pages 119-136
    5. Marco Evangelos Biancolini
      Pages 137-174
    6. Marco Evangelos Biancolini
      Pages 225-256
    7. Marco Evangelos Biancolini
      Pages 257-287
    8. Marco Evangelos Biancolini
      Pages 289-327
    9. Marco Evangelos Biancolini
      Pages 329-358

About this book

Introduction

This book presents the first “How To” guide to the use of radial basis functions (RBF). It provides a clear vision of their potential, an overview of ready-for-use computational tools and precise guidelines to implement new engineering applications of RBF.

Radial basis functions (RBF) are a mathematical tool mature enough for useful engineering applications. Their mathematical foundation is well established and the tool has proven to be effective in many fields, as the mathematical framework can be adapted in several ways. A candidate application can be faced considering the features of RBF: 

multidimensional space (including 2D and 3D), numerous radial functions available, global and compact support, interpolation/regression.

This great flexibility makes RBF attractive – and their great potential has only been partially discovered. This is because of the difficulty in taking a first step toward RBF as they are not commonly part of engineers’ cultural background, but also due to the numerical complexity of RBF problems that scales up very quickly with the number of RBF centers. Fast RBF algorithms are available to alleviate this and high-performance computing (HPC) can provide further aid. Nevertheless, a consolidated tradition in using RBF in engineering applications is still missing and the beginner can be confused by the literature, which in many cases is presented with language and symbolisms familiar to mathematicians but which can be cryptic for engineers.

The book is divided in two main sections. The first covers the foundations of RBF, the tools available for their quick implementation and guidelines for facing new challenges; the second part is a collection of practical RBF applications in engineering, covering several topics, including response surface interpolation in n-dimensional spaces, mapping of magnetic loads, mapping of pressure loads, up-scaling of flow fields, stress/strain analysis by experimental displacement fields, implicit surfaces, mesh to cad deformation, mesh morphing for crack propagation in 3D, ice and snow accretion using computational fluid dynamics (CFD) data, shape optimization for external aerodynamics, and use of adjoint data for surface sculpting. For each application, the complete path is clearly and consistently exposed using the systematic approach defined in the first section.

Keywords

Advanced Numerical Methods Engineering Applications High Performance Computing Interpolar and Regression Radial Basis Functions

Authors and affiliations

  • Marco Evangelos Biancolini
    • 1
  1. 1.Department of Enterprise Engineering “Mario Lucertini”University of Rome “Tor Vergata”RomeItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-75011-8
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-75009-5
  • Online ISBN 978-3-319-75011-8
  • Buy this book on publisher's site