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Full-Text Articles in Applied Mathematics
A Doubly Nonlocal Laplace Operator And Its Connection To The Classical Laplacian, Petronela Radu, Kelseys Wells
A Doubly Nonlocal Laplace Operator And Its Connection To The Classical Laplacian, Petronela Radu, Kelseys Wells
Department of Mathematics: Faculty Publications
In this paper, motivated by the state-based peridynamic frame- work, we introduce a new nonlocal Laplacian that exhibits double nonlocality through the use of iterated integral operators. The operator introduces addi- tional degrees of exibility that can allow for better representation of physical phenomena at different scales and in materials with different properties. We study mathematical properties of this state-based Laplacian, including connec- tions with other nonlocal and local counterparts. Finally, we obtain explicit rates of convergence for this doubly nonlocal operator to the classical Laplacian as the radii for the horizons of interaction kernels shrink to zero.
Properties And Convergence Of State-Based Laplacians, Kelsey Wells
Properties And Convergence Of State-Based Laplacians, Kelsey Wells
Department of Mathematics: Dissertations, Theses, and Student Research
The classical Laplace operator is a vital tool in modeling many physical behaviors, such as elasticity, diffusion and fluid flow. Incorporated in the Laplace operator is the requirement of twice differentiability, which implies continuity that many physical processes lack. In this thesis we introduce a new nonlocal Laplace-type operator, that is capable of dealing with strong discontinuities. Motivated by the state-based peridynamic framework, this new nonlocal Laplacian exhibits double nonlocality through the use of iterated integral operators. The operator introduces additional degrees of flexibility that can allow better representation of physical phenomena at different scales and in materials with different …