Nonlocal Modeling, Analysis, and Computation - CBMS-NSF Regional Conference Series in Applied Mathematics (Paperback)Qiang Du (author)
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Nonlocal Modeling, Analysis, and Computation includes motivational examples of nonlocal models, basic building blocks of nonlocal vector calculus, elements of theory for well-posedness and nonlocal spaces, connections to and coupling with local models, convergence and compatibility of numerical approximations, and various applications, such as nonlocal dynamics of anomalous diffusion and nonlocal peridynamic models of elasticity and fracture mechanics.
A particular focus is on nonlocal systems with a finite range of interaction to illustrate their connection to traditional local systems represented by partial differential equations and fractional PDEs. These models are designed to represent nonlocal interactions explicitly and to remain valid for complex systems involving possible singular solutions and they have the potential to be alternatives to as well as bridges to existing local continuum and discrete models.
The author discusses ongoing studies of nonlocal models to encourage the discovery of new mathematical theory for nonlocal continuum models and offer new perspectives on existing discrete models and local continuum models and the connections between them.
Publisher: Society for Industrial & Applied Mathematics,U.S.
Number of pages: 168
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