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@book{Acary.Brogliato2008,
author="Acary, V. and Brogliato, B.",
title="{Numerical methods for nonsmooth dynamical systems. Applications in
mechanics and electronics.}",
language="English",
publisher="{Lecture Notes in Applied and Computational Mechanics 35. Berlin:
Springer. xxi, 525~p. }",
year="2008",
abstract="{This book concerns the numerical simulation of dynamical systems
whose trajectories may be not differentiable. These systems are called
nonsmooth dynamical systems, and they represent an important class of
systems, firstly because of many applications in which nonsmooth models are
useful, secondly because they give rise to new problems in various fields of
mathematics and computational mechanics.
The book is divided into three
parts.
The first part presents the formulation of nonsmooth dynamical
systems, with model problems from mechanics, electricity and control, as
well as useful material from convex and nonsmooth analysis related to
differential inclusions, variational inequalities, and complementarity
systems. The model applications are taken from multibody systems with
contact, impact and friction, and from electrical circuits with piecewise
linear and ideal components.
The second part deals with numerical
time-integration schemes, which can be divided into event-driven schemes and
time-stepping schemes.
The third part is devoted to one-step nonsmooth
problem solvers, and includes techniques suitable for the solution of
variational inequalities, nonlinear programming problems and complementarity
problems. The one-step problems include the nonlinear models known as
holonomic models, which have a long tradition in engineering mechanics (cf.
unilateral contact for static elastic bodies, the holonomic or Hencky model
of plasticity). Nonsmooth modelling in mechanics is based on the seminal
works of J. J. Moreau and T. Rockafellar on convex analysis and its usage in
contact mechanics and elastoplasticity, as well as on later extensions to
nonconvex problems by P. D. Panagiotopoulos. This development has been
documented in a number of research monographs like [{\it R. T. Rockafellar},
Convex Analysis. Princeton Landmarks in Mathematics. Princeton, NJ:
Princeton University Press (1997; Zbl 0932.90001); {\it P. D.
Panagiotopoulos}, Inequality problems in mechanics and applications. Convex
and nonconvex energy functions. Boston-Basel-Stuttgart: Birkh\"{a}user (1985;
Zbl 0579.73014); {\it J. J. Moreau, P. D. Panagiotopoulos}, Nonsmooth
mechanics and applications. CISM Courses and Lectures, 302. Wien etc.:
Springer-Verlag (1988; Zbl 0652.00016)] and in many others.
Practical
applications of nonsmooth mechanics are also presented in research
monographs, see e.g. [{\it F. Pfeiffer, C. Glocker}, Multibody dynamics with
unilateral contacts. CISM Courses and Lectures. 421. Wien etc.:
Springer-Verlag (2000; Zbl 0960.00025)].
The present book is a research
monograph with numerous information and references to original publications
which gives to the book an encyclopaedic nature. The wealth of information
and solution methods mentioned in this book certainly shows that the area of
nonsmooth mechanics has arrived a level of maturity that allows for serious
industrial applications, without loosing its attractiveness for research
purposes. The parallel presentation of nonsmooth models in mechanics and
electronics indicates that the mentioned effects will also be of interest
for people working in mechatronics, microelectromechanics and multiphysics.
The book is intended for graduate students and scientists doing research and
development in mechanics and electrical engineering, designers of modern
electromechanical devices, as well as to researchers from other scientific
communities like applied mathematics, robotics, civil and mechanical
engineering, mechatronics, virtual reality, etc.}",
reviewer="{Georgios E. Stavroulakis (Chania)}",
keywords="{unilateral contact; complementarity problems; mathematical
programming; event-driven schemes; time-stepping schemes}",
classmath="{*74-02 (Research monographs (mechanics of deformable solids))
49-02 (Research monographs (calculus of variations))
74M15 (Contact)
49J40 (Variational methods including variational inequalities)
65Kxx (Numerical methods in mathematical programming and optimization)
74Sxx (Numerical methods in solid mechanics)
}",
}
@book{Davis:2006:DMS:1196434,
author = {Davis, Timothy A.},
title = {Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2)},
year = {2006},
isbn = {0898716136},
publisher = {Society for Industrial and Applied Mathematics},
address = {Philadelphia, PA, USA},
}
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