Nonlocal modeling, analysis, and computation
by Du, Qiang
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. 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 w…
Read More ↓Title Statements
- Full title :Nonlocal modeling, analysis, and computation / Qiang Du (Columbia University, New York, New York).
Summary
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. 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.
Read More ↓Edition Statements
- Publication Date:2018
Publication Statements
- Publisher(s):Society for Industrial and Applied Mathematics
- Place of Publication:Philadelphia
- Language:eng
- Publication Date:2018
The Physical Object
- Description:1 online resource.
Edition Identifiers
- ISBN:9781611975628, 161197562X, 9781611975611, 1611975611
- oclc:on1080249000
- LC Classification:QA611.28
- Dewey Decimal:514/.32
Table of Contents
Nonlocal modeling : A new perspective and overview -- Nonlocal models : An introduction and examples -- Nonlocal vector calculus and variational problems -- Numerical discretization of nonlocal models -- Nonlocal and local coupling -- Nonlocal-in-time dynamics -- Epilogue : An invitation to nonlocal modeling.
Read More ↓Subjects
Writers
More from this Series
No reviews yet. Be the first to rate this work.
Related Works
more →
Applied longitudinal data analysis: modeling change and event occurrence
Singer, Judith D.
Object-oriented modeling and design
Econometric models, techniques and applications
Intriligator, Michael David,, economie
Notes and problems in applied general equilibrium economics
Stochastic models
Integrated environmental modelling: design and tools
Brouwer, F.M., (Florinus Mijnlief)
Experimental design techniques in statistical practice: a practical software-based approach
Gardiner, William P.
Rate & Review