Morales 17, 08029 Barcelona, España Printed on elemental chlorine-free paper
Typesetting: Mª Jesús Samper, CIMNE, Barcelona, Spain Lecture Notes Series Manager: Adriana Hanganu, CIMNE, Barcelona, Spain Cover page: Pallí Disseny i Comunicació, Printed by: Artes Gráficas Torres S.L. Catalogue record for this book is available from the Library of Congress Basis and Solids, 2009Įugenio Oñate International Center for Numerical Methods in Engineering (CIMNE) School of Civil Engineering Universitat Politècnica de Catalunya (UPC) Barcelona, Spain Oñate, Structural Analysis with the Finite Element Method. of Jyväskylä, Finland Bernhard Schrefler, Università degli Studi di Padova, Padova, Italy Genki Yagawa, Tokyo University, Tokyo, Japan Mingwu Yuan, Peking University, China Idelsohn, CIMNE-ICREA, Barcelona, Spain Pierre Ladeveze, ENS de Cachan-LMT-Cachan, France Wing Kam Liu, Northwestern University, Evanston, USA Xavier Oliver, Universitat Politècnica de Catalunya (UPC), Barcelona, Spain Manolis Papadrakakis, National Technical University of Athens, Greece Jacques Périaux, CIMNE-UPC Barcelona, Spain & Univ. Hughes, The University of Texas at Austin, Austin, USA Sergio R.
Series Editor Eugenio Oñate International Center for Numerical Methods in Engineering (CIMNE) School of Civil Engineering Universitat Politècnica de Catalunya (UPC), Barcelona, Spain Editorial Board Francisco Chinesta, Ecole Nationale Supérieure d'Arts et Métiers, Paris, France Charbel Farhat, Stanford University, Stanford, USA Carlos Felippa, University of Colorado at Boulder, Colorado, USA Antonio Huerta, Universitat Politècnica de Catalunya (UPC), Barcelona, Spain Thomas J.R. The books will be also useful for practising engineers and scientists interested in state of the art information on the theory and application of numerical methods. Some books define the current state of a field to a highly specialised readership others are accessible to final year undergraduates, but essentially the emphasis is on accessibility and clarity. The main intended audience is the first year graduate student. Advances in finite element, finite volume, finite differences, discrete and particle methods and their applications to classical single discipline fields and new multidisciplinary domains are examples of the topics covered by the series. The books will focus on subjects in which numerical methods play a fundamental role for solving problems in engineering and applied sciences. Lecture Notes on Numerical Methods in Engineering and Sciences Aims and Scope of the Series This series publishes text books on topics of general interest in the field of computational engineering sciences.
The results of the paper are applicable to the design of suboptimal controllers and filters for nonlinear quantum systems.Structural Analysis with the Finite Element Method Linear Statics We demonstrate the proposed Hamiltonian-based Gaussian linearization for the quantum Duffing oscillator whose Hamiltonian is a quadro-quartic polynomial of the momentum and position operators. This approximation is carried out in a mean square optimal sense with respect to a Gaussian reference quantum state and leads to a self-consistent linearization procedure where the mean vector and quantum covariance matrix of the system observables evolve in time according to the effective linear dynamics. The linearization proceeds by approximating the actual Hamiltonian of the quantum system by a quadratic function of its observables which corresponds to the Hamiltonian of a quantum harmonic oscillator. This paper extends the energy-based version of the stochastic linearization method, known for classical nonlinear systems, to open quantum systems with canonically commuting dynamic variables governed by quantum stochastic differential equations with non-quadratic Hamiltonians.