LEADER 04239nam 22006615 450 001 9910337629803321 005 20200707004007.0 010 $a9783030026479 010 $a3030026477 024 7 $a10.1007/978-3-030-02647-9 035 $a(CKB)4100000007522566 035 $a(DE-He213)978-3-030-02647-9 035 $a(MiAaPQ)EBC5922788 035 $a(PPN)233801928 035 $a(MiAaPQ)EBC31886925 035 $a(Au-PeEL)EBL31886925 035 $a(OCoLC)1083523407 035 $a(EXLCZ)994100000007522566 100 $a20190117d2019 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aPeridynamic Differential Operator for Numerical Analysis /$fby Erdogan Madenci, Atila Barut, Mehmet Dorduncu 205 $a1st ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019. 215 $a1 online resource (XI, 282 p. 163 illus., 137 illus. in color.) 311 08$a9783030026462 311 08$a3030026469 327 $a1 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. . 330 $aThis 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. 606 $aMechanics 606 $aMechanics, Applied 606 $aMaterials science 606 $aComputer science$xMathematics 606 $aSolid Mechanics$3https://scigraph.springernature.com/ontologies/product-market-codes/T15010 606 $aCharacterization and Evaluation of Materials$3https://scigraph.springernature.com/ontologies/product-market-codes/Z17000 606 $aComputational Science and Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/M14026 615 0$aMechanics. 615 0$aMechanics, Applied. 615 0$aMaterials science. 615 0$aComputer science$xMathematics. 615 14$aSolid Mechanics. 615 24$aCharacterization and Evaluation of Materials. 615 24$aComputational Science and Engineering. 676 $a515.7242 676 $a515.7242 700 $aMadenci$b Erdogan$4aut$4http://id.loc.gov/vocabulary/relators/aut$0628410 702 $aBarut$b Atila$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aDorduncu$b Mehmet$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910337629803321 996 $aPeridynamic Differential Operator for Numerical Analysis$92004568 997 $aUNINA