{"title":"Society for Industrial \u0026 Applied Mathematics,U.S.","description":null,"products":[{"product_id":"9781611975611","title":"Nonlocal Modeling, Analysis, and Computation","description":"Studies of complexity, singularity, and anomaly using nonlocal continuum models are steadily gaining popularity. This monograph provides an introduction to basic analytical, computational, and modeling issues and to some of the latest developments in these areas.\u003cbr\u003e\u003cbr\u003e\u003ci\u003eNonlocal Modeling, Analysis, and Computation\u003c\/i\u003e 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.\u003cbr\u003e\u003cbr\u003eA 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.\u003cbr\u003e\u003cbr\u003eThe 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.","brand":"Gardners","offers":[{"title":"Default Title","offer_id":56303948235125,"sku":"9781611975611","price":61.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0612\/7193\/3106\/files\/9781611975611_36f3b4ea-a9fd-45d9-aae4-078bfd8062c6.jpg?v=1786022961"},{"product_id":"9781611976076","title":"Interpolatory Methods for Model Reduction","description":"Dynamical systems are a principal tool in the modeling, prediction, and control of a wide range of complex phenomena. As the need for improved accuracy leads to larger and more complex dynamical systems, direct simulation often becomes the only available strategy for accurate prediction or control, inevitably creating a considerable burden on computational resources. This is the main context where one considers model reduction, seeking to replace large systems of coupled differential and algebraic equations that constitute high fidelity system models with substantially fewer equations that are crafted to control the loss of fidelity that order reduction may induce in the system response. \u003cbr\u003e\u003cbr\u003eInterpolatory methods are among the most widely used model reduction techniques, and \u003ci\u003eInterpolatory Methods for Model Reduction\u003c\/i\u003e is the first comprehensive analysis of this approach available in a single, extensive resource. It introduces state-of-the-art methods reflecting significant developments over the past two decades, covering both classical projection frameworks for model reduction and data-driven, nonintrusive frameworks.\u003cbr\u003e\u003cbr\u003eThis textbook is appropriate for a wide audience of engineers and other scientists working in the general areas of large-scale dynamical systems and data-driven modeling of dynamics.","brand":"Gardners","offers":[{"title":"Default Title","offer_id":56303951217013,"sku":"9781611976076","price":81.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0612\/7193\/3106\/files\/9781611976076_bbec8d9d-b5fb-4074-8570-bd77a3a8140a.jpg?v=1786022962"}],"url":"https:\/\/backstory.london\/collections\/publisher-society-for-industrial-applied-mathematicsus.oembed","provider":"Backstory","version":"1.0","type":"link"}