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Peridynamic differential operator fo...

Madenci, Erdogan.

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Peridynamic differential operator for numerical analysis

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Peridynamic differential operator for numerical analysis/ by Erdogan Madenci, Atila Barut, Mehmet Dorduncu.
作者:	Madenci, Erdogan.
其他作者:	Barut, Atila.
出版者:	Cham :Springer International Publishing : : 2019.,
面頁冊數:	xi, 282 p. :ill. (some col.), digital ;24 cm.
內容註:	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.
Contained By:	Springer eBooks
標題:	Differential operators. -
電子資源:	https://doi.org/10.1007/978-3-030-02647-9
ISBN:	9783030026479

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

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

555718
Differential operators.

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

Dewey Class. No.: 515.7242

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100 1 $a Madenci, Erdogan. $3 2055823
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.
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650 1 4 $a Solid Mechanics. $3 3381524
650 2 4 $a Characterization and Evaluation of Materials. $3 890988
650 2 4 $a Computational Science and Engineering. $3 893018
700 1 $a Barut, Atila. $3 3383063
700 1 $a Dorduncu, Mehmet. $3 3383064
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