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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, 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 |
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Madenci, Erdogan VerfasserIn aut, Peridynamic Differential Operator for Numerical Analysis by Erdogan Madenci, Atila Barut, Mehmet Dorduncu, Cham Springer International Publishing 2019, Online-Ressource (XI, 282 p. 163 illus., 137 illus. in color, online resource), Text txt rdacontent, Computermedien c rdamedia, Online-Ressource cr rdacarrier, SpringerLink Bücher, Springer eBook Collection, 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, 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, Springer eBook Collection. Engineering, Surfaces (Physics), Computer science, Solid Mechanics, Mechanics, Mechanics, Applied, Materials science., Computer mathematics., Barut, Atila VerfasserIn aut, Dorduncu, Mehmet VerfasserIn aut, 9783030026462, 9783030026486, Erscheint auch als Druck-Ausgabe 978-3-030-02646-2, Printed edition 9783030026462, Printed edition 9783030026486, https://doi.org/10.1007/978-3-030-02647-9 X:SPRINGER Verlag lizenzpflichtig Volltext, http://dx.doi.org/10.1007/978-3-030-02647-9 Resolving-System Volltext, https://doi.org/10.1007/978-3-030-02647-9 DE-14, DE-14 epn:358857087X 2020-02-06T11:10:47Z, https://doi.org/10.1007/978-3-030-02647-9 DE-Ch1, DE-Ch1 epn:3371750930 2019-02-01T14:08:40Z, DE-105 epn:3371751171 2019-02-01T14:08:40Z, https://doi.org/10.1007/978-3-030-02647-9 DE-Zwi2, DE-Zwi2 epn:3371751635 2019-02-01T14:08:40Z |
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Madenci, Erdogan, Barut, Atila, Dorduncu, Mehmet, Peridynamic Differential Operator for Numerical Analysis, 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, 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, Surfaces (Physics), Computer science, Solid Mechanics, Mechanics, Mechanics, Applied, Materials science., Computer mathematics. |
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Peridynamic Differential Operator for Numerical Analysis |
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Peridynamic Differential Operator for Numerical Analysis |
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Peridynamic Differential Operator for Numerical Analysis by Erdogan Madenci, Atila Barut, Mehmet Dorduncu |
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Peridynamic Differential Operator for Numerical Analysis by Erdogan Madenci, Atila Barut, Mehmet Dorduncu |
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Peridynamic Differential Operator for Numerical Analysis by Erdogan Madenci, Atila Barut, Mehmet Dorduncu |
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Peridynamic Differential Operator for Numerical Analysis |
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peridynamic differential operator for numerical analysis |
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Peridynamic Differential Operator for Numerical Analysis |
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Surfaces (Physics), Computer science, Solid Mechanics, Mechanics, Mechanics, Applied, Materials science., Computer mathematics. |
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Surfaces (Physics), Computer science, Solid Mechanics, Mechanics, Mechanics, Applied, Materials science., Computer mathematics. |
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