Peridynamic Differential Operator for Numerical Analysis
暫譯: 數值分析的周邊動力學微分算子

Erdogan Madenci, Atila Barut, Mehmet Dorduncu

  • 出版商: Springer
  • 出版日期: 2019-03-04
  • 售價: $4,130
  • 貴賓價: 9.5$3,924
  • 語言: 英文
  • 頁數: 282
  • 裝訂: Paperback
  • ISBN: 3030026469
  • ISBN-13: 9783030026462
  • 相關分類: 數值分析 Numerical-analysis
  • 海外代購書籍(需單獨結帳)

商品描述

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.

商品描述(中文翻譯)

這本書介紹了周邊動力學(Peridynamic, PD)微分算子,該算子使得局部微分的非局部形式成為可能。PD 是微分與積分之間的橋樑。它提供了複雜場方程的計算解,以及在存在不連續情況下平滑或散佈數據的導數評估。PD 也作為一種自然過濾器,用於平滑噪聲數據和恢復缺失數據。

本書首先概述了 PD 概念、PD 微分算子的推導、其在空間和時間導數的數值實現,以及誤差來源的描述。應用方面涉及數據的插值、回歸和平滑,非線性常微分方程的解,單場和多場偏微分方程及積分微分方程。它描述了 PD 泊松方程和納維方程的弱形式推導,以便直接施加基本和自然邊界條件。它還提出了一種基於最小二乘法的 PD 微分算子的替代方法。

周邊動力學微分算子在數值分析中的應用適合高級學生和研究人員,展示了如何構建所有應用的解。作為補充材料,針對一組選定應用的解算法可用於數值實現的更多細節。