Fast Radial Basis Functions for Engineering Applications
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
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Fast Radial Basis Functions for Engineering Applications
Fast Radial Basis Functions for Engineering Applications
Marco Evangelos Biancolini
Fast Radial Basis Functions for Engineering Applications
123
Marco Evangelos Biancolini Department of Enterprise Engineering “Mario Lucertini” University of Rome “Tor Vergata” Rome Italy
ISBN 978-3-319-75009-5 ISBN 978-3-319-75011-8 https://doi.org/10.1007/978-3-319-75011-8
(eBook)
Library of Congress Control Number: 2018930106 © Springer International Publishing AG, part of Springer Nature 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by the registered company Springer International Publishing AG part of Springer Nature The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
This book is the result of the industrial and academic research path that I started to follow since 2007. At that time, I had a cooperation in place with a Formula 1 top team. When the need for a software tool suitable for advanced and high-performance mesh morphing, namely such to enable the update of the nodal positions of large computational grids in order to accommodate shape variations, was expressed, I considered many options. Among them, the use of a structural solution using finite elements method (FEM) produced very good results. However, I was looking for a meshless approach capable to fast propagate the action defined on the surface mesh into the volume mesh regardless of the mesh elements’ typology and the presence of interfaces between different partitions when processing meshes ready for parallel computing. So I did some attempts adopting the boundary elements method (BEM) which allows to define a deformation field as a point function. My first readings about RBF were related to the wide literature of meshless methods for the solution of
