Fast Radial Basis Functions For Engineering Applications
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Fast Radial Basis Functions for Engineering Applications
Author: Marco Evangelos Biancolini
language: en
Publisher: Springer
Release Date: 2018-03-29
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.
Radial Basis Functions
Author: Martin D. Buhmann
language: en
Publisher: Cambridge University Press
Release Date: 2003-07-03
The author's aim is to give a thorough treatment from both the theoretical and practical implementation viewpoints. For example, he emphasises the many positive features of radial basis functions such as the unique solvability of the interpolation problem, the computation of interpolants, their smoothness and convergence and provides a careful classification of the radial basis functions into types that have different convergence
Bioinspired Optimization Methods and Their Applications
This book constitutes the refereed proceedings of the 9th International Conference on Bioinspired Optimization Methods and Their Applications, BIOMA 2020, held in Brussels, Belgium, in November 2020. The 24 full papers presented in this book were carefully reviewed and selected from 68 submissions. The papers in this BIOMA proceedings specialized in bioinspired algorithms as a means for solving the optimization problems and came in two categories: theoretical studies and methodology advancements on the one hand, and algorithm adjustments and their applications on the other. Due to the Corona pandemic BIOMA 2020 was held as a virtual event.