Reduced-Order Modeling via Peridynamics with Two-Level Grid Discretization

  • Madenci, Erdogan (University of Arizona)
  • BArut, Atila (Global Engineering Research and Technologies)

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Reduced-order modeling (ROM) aims to decrease the computational cost of high-fidelity numerical simulations while preserving the essential physical behavior of the system. This study presents a peridynamic-based reduced-order modeling framework that simultaneously employs fine and coarse spatial discretizations. A two-level grid strategy is introduced to significantly reduce the size of the resulting system of equations while maintaining high solution accuracy. The proposed approach relies on the peridynamic representation of spatial derivatives and the construction of peridynamic (PD) interpolation functions that link the unknowns defined on the fine grid to those on the coarse grid. The level-1 discretization is coarse and governs the number of independent unknowns in the formulation, thereby controlling the computational cost. The level-2 discretization is fine and is used to accurately evaluate nonlocal integrals and functionals, ensuring numerical precision. The Peridynamic Differential Operator (PDDO) is utilized to compute derivatives of the field variables at both discretization levels. Unknowns associated with the fine grid are expressed explicitly in terms of the coarse-grid unknowns through PD interpolation, enabling a substantial reduction in the number of degrees of freedom while retaining the accuracy associated with the fine discretization. The PDDO-based interpolation provides a consistent and systematic mechanism for transferring information between the two grid levels. By combining fine- and coarse-grid discretizations with PD interpolation, the proposed ROM framework effectively eliminates the computational challenges typically encountered when refining spatial grids. In addition, the peridynamic formulation naturally accommodates material heterogeneity arising from spatial variations in material properties and the presence of inclusions or imperfections. The predictive capability and accuracy of the proposed approach are demonstrated by computing elastic energy, evaluating the partition function, and constructing solutions to Laplace’s equation under different boundary conditions, showing excellent agreement with reference solutions.