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Handbook of Numerical Methods for Hyperbolic Problems explores the
changes that have taken place in the past few decades regarding
literature in the design, analysis and application of various
numerical algorithms for solving hyperbolic equations. This volume
provides concise summaries from experts in different types of
algorithms, so that readers can find a variety of algorithms under
different situations and readily understand their relative
advantages and limitations.
Handbook on Numerical Methods for Hyperbolic Problems: Applied and
Modern Issues details the large amount of literature in the design,
analysis, and application of various numerical algorithms for
solving hyperbolic equations that has been produced in the last
several decades. This volume provides concise summaries from
experts in different types of algorithms, so that readers can find
a variety of algorithms under different situations and become
familiar with their relative advantages and limitations.
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.
The Institute for Mathematical Sciences at the National University
of Singapore hosted a two-month research program on "Mathematical
Theory and Numerical Methods for Computational Materials Simulation
and Design" from 1 July to 31 August 2009. As an important part of
the program, tutorials and special lectures were given by leading
experts in the fields for participating graduate students and
junior researchers. This invaluable volume collects four expanded
lecture notes with self-contained tutorials. They cover a number of
aspects on multiscale modeling, analysis and simulations for
problems arising from materials science including some critical
components in computational prediction of materials properties such
as the multiscale properties of complex materials, properties of
defects, interfaces and material microstructures under different
conditions, critical issues in developing efficient numerical
methods and analytic frameworks for complex and multiscale
materials models. This volume serves to inspire graduate students
and researchers who choose to embark into original research work in
these fields.
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