Peridynamic Least Square Minimization
This chapter presents the PD least square minimization (LSM) to construct the analytical expressions in integral form for PD approximation of a field variable and its derivatives on the basis of TSE and the moving LSM of error. Similar to the PDDO, it is also based on the concept of PD interactions. Unlike the PDDO, it does not require the construction of PD functions at each point.
- Bevington PR, Robinson DK (2003) Data Reduction and Error Analysis for the Physical Sciences. McGraw-Hill, New YorkGoogle Scholar
- Madenci E, Dorduncu M, Gu X., (2018) Peridynamic least squares minimization. Computer Methods in Applied Mechanics and Engineering (under review)Google Scholar
- Nealen A (2004) An as-short-as-possible introduction to the least squares, weighted least squares and moving least squares methods for scattered data approximation and interpolation. URL: http://www.nealen.com/projects
- Randall JL (2005) Finite difference methods for differential equations. A Math 585–586 Lecture Notes, University of WashingtonGoogle Scholar
- Strutz T (2010) Data fitting and uncertainty: A practical introduction to weighted least squares and beyond. Vieweg and TeubnerGoogle Scholar