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Numerical Implementation

  • Erdogan Madenci
  • Atila Barut
  • Mehmet Dorduncu
Chapter

Abstract

Recasting the local differentiation by employing the nonlocal PDDO requires spatial integration which is not always amenable to analytical methods. Therefore, the integration is performed by using a meshless quadrature technique due to its simplicity. The domain is divided into a finite number of cells, each with a specific entity. The discretization may have a uniform or nonuniform structure. Prior to discretizing the differential equation and boundary conditions/initial conditions, the family (interaction domain) of each collocation point is formed, and its degree of interaction (weight function) with the family members is specified. Associated with a particular point, the integration is performed by summing the entity of the points within each family. The size of the family and the weight function can be different for each point. The size of the family may be established based on the computational efficiency; however, it should capture the characteristics of the differential equation.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Erdogan Madenci
    • 1
  • Atila Barut
    • 1
  • Mehmet Dorduncu
    • 1
  1. 1.Aerospace and Mechanical Engineering DepartmentUniversity of ArizonaTucsonUSA

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