Patrick Ciarlet's Books

The Finite Element Method

From Theory to Practice

By: Patrick Ciarlet,Eric Luneville

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The Finite Element Method

From Theory to Practice

By: Patrick Ciarlet,Eric Luneville

The finite element method, which emerged in the 1950s to deal with structural mechanics problems, has since undergone continuous development. Using partial differential equation models, it is now present in such fields of application as mechanics, physics, chemistry, economics, finance and biology. It is also used in most scientific computing software, and many engineers become adept at using it in their modeling and numerical simulation activities. This book presents all the essential elements of the finite element method in a progressive and didactic way: the theoretical foundations, practical considerations of implementation, algorithms, as well as numerical illustrations created in MATLAB. Original exercises with detailed answers are provided at the end of each chapter.

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Page Count

404

Publisher

John Wiley & Sons

Published Date

ISBN 10

1786307685

ISBN 13

9781786307682

Mathematical Foundations of Computational Electromagnetism

By: Franck Assous,Patrick Ciarlet,Simon Labrunie

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Mathematical Foundations of Computational Electromagnetism

By: Franck Assous,Patrick Ciarlet,Simon Labrunie

This book presents an in-depth treatment of various mathematical aspects of electromagnetism and Maxwell's equations: from modeling issues to well-posedness results and the coupled models of plasma physics (Vlasov-Maxwell and Vlasov-Poisson systems) and magnetohydrodynamics (MHD). These equations and boundary conditions are discussed, including a brief review of absorbing boundary conditions. The focus then moves to well‐posedness results. The relevant function spaces are introduced, with an emphasis on boundary and topological conditions. General variational frameworks are defined for static and quasi-static problems, time-harmonic problems (including fixed frequency or Helmholtz-like problems and unknown frequency or eigenvalue problems), and time-dependent problems, with or without constraints. They are then applied to prove the well-posedness of Maxwell’s equations and their simplified models, in the various settings described above. The book is completed with a discussion of dimensionally reduced models in prismatic and axisymmetric geometries, and a survey of existence and uniqueness results for the Vlasov-Poisson, Vlasov-Maxwell and MHD equations. The book addresses mainly researchers in applied mathematics who work on Maxwell’s equations. However, it can be used for master or doctorate-level courses on mathematical electromagnetism as it requires only a bachelor-level knowledge of analysis.

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Page Count

460

Publisher

Springer

Published Date

ISBN 10

3319708422

ISBN 13

9783319708423

Meshing, Geometric Modeling and Numerical Simulation, Volume 2

Metrics, Meshes and Mesh Adaptation

By: Paul Louis George,Houman Borouchaki,Frederic Alauzet,Patrick Laug,Adrien Loseille,Loic Marechal

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Meshing, Geometric Modeling and Numerical Simulation, Volume 2

Metrics, Meshes and Mesh Adaptation

By: Paul Louis George,Houman Borouchaki,Frederic Alauzet,Patrick Laug,Adrien Loseille,Loic Marechal

Triangulations, and more precisely meshes, are at the heart of many problems relating to a wide variety of scientific disciplines, and in particular numerical simulations of all kinds of physical phenomena. In numerical simulations, the functional spaces of approximation used to search for solutions are defined from meshes, and in this sense these meshes play a fundamental role. This strong link between meshes and functional spaces leads us to consider advanced simulation methods in which the meshes are adapted to the behaviors of the underlying physical phenomena. This book presents the basic elements of this vision of meshing. These mesh adaptations are generally governed by a posteriori error estimators representing an increase of the error with respect to a size or metric. Independently of this metric of calculation, compliance with a geometry can also be calculated using a so-called geometric metric. The notion of mesh thus finds its meaning in the metric of its elements.

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Page Count

385

Publisher

John Wiley & Sons

Published Date

ISBN 10

1119384362

ISBN 13

9781119384366

Augmented Lagrangian and Operator Splitting Methods in Nonlinear Mechanics

By: Roland Glowinski,Patrick Le Tallec

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Augmented Lagrangian and Operator Splitting Methods in Nonlinear Mechanics

By: Roland Glowinski,Patrick Le Tallec

This volume deals with the numerical simulation of the behavior of continuous media by augmented Lagrangian and operator-splitting methods.

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Page Count

301

Publisher

SIAM

Published Date

ISBN 10

0898712300

ISBN 13

9780898712308

Finite Element Approximation of Contact and Friction in Elasticity

By: Franz Chouly,Patrick Hild,Yves Renard

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Finite Element Approximation of Contact and Friction in Elasticity

By: Franz Chouly,Patrick Hild,Yves Renard

This book presents the mathematics behind the formulation, approximation, and numerical analysis of contact and friction problems. It also provides a survey of recent developments in the numerical approximation of such problems as well as several remaining unsolved issues. Particular focus is placed on the Signorini problem and on frictionless unilateral contact in small strain. The final chapters cover more complex, applications-oriented problems, such as frictional contact, multi-body contact, and large strain. Finite Element Approximation of Contact and Friction in Elasticity will be a valuable resource for researchers in the area. It may also be of interest to those studying scientific computing and computational mechanics.

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Page Count

306

Publisher

Springer Nature

Published Date

ISBN 10

3031314239

ISBN 13

9783031314230

Integration Algorithms and Classical Mechanics

By: Jerrold E. Marsden,George William Patrick,W. F. Shadwick

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Integration Algorithms and Classical Mechanics

By: Jerrold E. Marsden,George William Patrick,W. F. Shadwick

Dedicated to the late Juan Carlos Simo, this volume contains the proceedings of a workshop held at the Fields Institute in October 1993. The articles focus on current algorithms for the integration of mechanical systems, from systems in celestial mechanics to coupled rigid bodies to fluid mechanics. The scope of the articles ranges from symplectic integration methods to energy-momentum methods and related themes.

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