國立高雄大學圖資館 |

Language: English

Back

Peridynamic differential operator fo...

Barut, Atila.

Peridynamic differential operator for numerical analysis

Record Type:	Electronic resources : Monograph/item
Title/Author:	Peridynamic differential operator for numerical analysisby Erdogan Madenci, Atila Barut, Mehmet Dorduncu.
Author:	Madenci, Erdogan.
other author:	Barut, Atila.
Published:	Cham :Springer International Publishing :2019.
Description:	xi, 282 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Differential operators.
Online resource:	https://doi.org/10.1007/978-3-030-02647-9
ISBN:	9783030026479$q(electronic bk.)

Peridynamic differential operator for numerical analysis
Madenci, Erdogan.

Peridynamic differential operator for numerical analysis[electronic resource] /by Erdogan Madenci, Atila Barut, Mehmet Dorduncu. - Cham :Springer International Publishing :2019. - xi, 282 p. :ill. (some col.), digital ;24 cm.

1 Introduction -- 2 Peridynamic Differential Operator -- 3 Numerical Implementation -- 4 Interpolation, Regression and Smoothing -- 5 Ordinary Differential Equations -- 6 Partial Differential Equations -- 7 Coupled Field Equations -- 8 Integro-Differential Equations -- 9 Weak Form of Peridynamics -- 10 Peridynamic Least Squares Minimization.

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.

ISBN: 9783030026479$q(electronic bk.)

Standard No.: 10.1007/978-3-030-02647-9doiSubjects--Topical Terms:

185325
Differential operators.

LC Class. No.: QA329.4 / .M334 2019

Dewey Class. No.: 515.7242

Peridynamic differential operator for numerical analysis
LDR:02815nmm a2200325 a 4500 001 555535
003 DE-He213
005 20190703103108.0
006 m d
007 cr nn 008maaau
008 191121s2019 gw s 0 eng d
020 $a 9783030026479$q(electronic bk.)
020 $a 9783030026462$q(paper)
024 7 $a 10.1007/978-3-030-02647-9 $2 doi
035 $a 978-3-030-02647-9
040 $a GP $c GP
041 0 $a eng
050 4 $a QA329.4 $b .M334 2019
072 7 $a TGMD $2 bicssc
072 7 $a SCI096000 $2 bisacsh
072 7 $a TGMD $2 thema
082 0 4 $a 515.7242 $2 23
090 $a QA329.4 $b .M181 2019
100 1 $a Madenci, Erdogan. $3 260790
245 1 0 $a Peridynamic differential operator for numerical analysis $h [electronic resource] / $c by Erdogan Madenci, Atila Barut, Mehmet Dorduncu.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2019.
300 $a xi, 282 p. : $b ill. (some col.), digital ; $c 24 cm.
505 0 $a 1 Introduction -- 2 Peridynamic Differential Operator -- 3 Numerical Implementation -- 4 Interpolation, Regression and Smoothing -- 5 Ordinary Differential Equations -- 6 Partial Differential Equations -- 7 Coupled Field Equations -- 8 Integro-Differential Equations -- 9 Weak Form of Peridynamics -- 10 Peridynamic Least Squares Minimization.
520 $a 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.
650 0 $a Differential operators. $3 185325
650 0 $a Numerical analysis. $3 182073
650 1 4 $a Solid Mechanics. $3 825700
650 2 4 $a Characterization and Evaluation of Materials. $3 273978
650 2 4 $a Computational Science and Engineering. $3 274685
700 1 $a Barut, Atila. $3 837698
700 1 $a Dorduncu, Mehmet. $3 837699
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
856 4 0 $u https://doi.org/10.1007/978-3-030-02647-9
950 $a Engineering (Springer-11647)