
@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},
} 
