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Peridynamic Differential Operator for Numerical Analysis

  • Erdogan Madenci
  • Atila Barut
  • Mehmet Dorduncu

Table of contents

  1. Front Matter
    Pages i-xi
  2. Erdogan Madenci, Atila Barut, Mehmet Dorduncu
    Pages 1-4
  3. Erdogan Madenci, Atila Barut, Mehmet Dorduncu
    Pages 5-37
  4. Erdogan Madenci, Atila Barut, Mehmet Dorduncu
    Pages 39-56
  5. Erdogan Madenci, Atila Barut, Mehmet Dorduncu
    Pages 57-90
  6. Erdogan Madenci, Atila Barut, Mehmet Dorduncu
    Pages 91-116
  7. Erdogan Madenci, Atila Barut, Mehmet Dorduncu
    Pages 117-157
  8. Erdogan Madenci, Atila Barut, Mehmet Dorduncu
    Pages 159-185
  9. Erdogan Madenci, Atila Barut, Mehmet Dorduncu
    Pages 187-208
  10. Erdogan Madenci, Atila Barut, Mehmet Dorduncu
    Pages 209-246
  11. Erdogan Madenci, Atila Barut, Mehmet Dorduncu
    Pages 247-261
  12. Back Matter
    Pages 263-282

About this book

Introduction

This book introduces the peridynamic (PD) differential operator, which enables the nonlocal form of local differentiation.  PD is a bridge between differentiation and integration.  It provides the computational solution of complex field equations and evaluation of derivatives of smooth or scattered data in the presence of discontinuities.  PD also serves as a natural filter to smooth noisy data and to recover missing data.

This book starts with an overview of the PD concept, the derivation of the PD differential operator, its numerical implementation for the spatial and temporal derivatives, and the description of sources of error.  The applications concern interpolation, regression, and smoothing of data, solutions to nonlinear ordinary differential equations, single- and multi-field partial differential equations and integro-differential equations.  It describes the derivation of the weak form of PD Poisson’s and Navier’s equations for direct imposition of essential and natural boundary conditions.  It also presents an alternative approach for the PD differential operator based on the least squares minimization.

Peridynamic  Differential Operator for Numerical Analysis is suitable for both advanced-level student and researchers, demonstrating how to construct solutions to all of the applications.  Provided as supplementary material, solution algorithms for a set of selected applications are available for more details in the numerical implementation.


Keywords

Peridynamic Differentiation nonlocal transient nonlinear discrete data recovery ordinary differential equations partial integral equations multi-field equations Integro-differential equations Coupled multi-field equations Weak form of peridynamics Peridynamic least square minimization Transient implicit

Authors and affiliations

  • Erdogan Madenci
    • 1
  • Atila Barut
    • 2
  • Mehmet Dorduncu
    • 3
  1. 1.Aerospace and Mechanical Engineering DepartmentUniversity of ArizonaTucsonUSA
  2. 2.Aerospace and Mechanical Engineering DepartmentUniversity of ArizonaTucsonUSA
  3. 3.Aerospace and Mechanical Engineering DepartmentUniversity of ArizonaTucsonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-02647-9
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-030-02646-2
  • Online ISBN 978-3-030-02647-9
  • Buy this book on publisher's site
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