Numerical Models for Differential Problems

Author: Alfio Quarteroni
Publisher: Springer Science & Business Media
ISBN: 9788847010710
Format: PDF, Docs
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In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics.

Numerical Models for Differential Problems

Author: Alfio Quarteroni
Publisher: Springer Science & Business
ISBN: 8847055229
Format: PDF, Kindle
Download Now
In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics.

New Approaches to Problems in Liquid State Theory

Author: Carlo Caccamo
Publisher: Springer Science & Business Media
ISBN: 9401145644
Format: PDF, ePub
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The theory of simple and complex fluids has made considerable recent progress, due to the emergence of new concepts and theoretical tools, and also to the availability of a large body of new experimental data on increas ingly complex systems, as well as far-reaching methodological developments in numerical simulations. This AS! aimed at providing a comprehensive overview of the most significant theoretical developments, supplemented by a few presentations of cutting-edge simulation and experimental work. The impact of the Institute in the overall landscape of Statistical Mechanics received an important recognition with its inclusion in the list of satellite events of STATPHYS20, the triennal international conference on Statistical Physics held in Paris in July 1998. These Proceedings contain the texts of the 13 Lecture Courses and 9 Invited Seminars delivered at Patti. Two clear trends emerge from these Proceedings: first, the diversity of new and unexpected theoretical results relating to classic models of liq uids, which have recently been subjected to fresh scrutiny; and secondly the parallel emergence of new concepts, models and methods, aimed at investigating complex fluids and phenomena, like the phase behaviour of fluids in pores, macromolecular assemblies, and the glass transition. Many of the new tools have their roots in traditional liquid state theory, and, in conjunction with fresh input from related fields, allow it wider applicability.

An Introduction to Mathematical Modeling

Author: Edward A. Bender
Publisher: Courier Corporation
ISBN: 0486137120
Format: PDF, Mobi
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Accessible text features over 100 reality-based examples pulled from the science, engineering, and operations research fields. Prerequisites: ordinary differential equations, continuous probability. Numerous references. Includes 27 black-and-white figures. 1978 edition.

Integrated Urban Models Volume 2 New Research and Applications of Optimization and Dynamics Routledge Revivals

Author: Stephen H. Putman
Publisher: Routledge
ISBN: 1317748190
Format: PDF, ePub
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Following on from Integrated Models Volume 1: Policy Analysis of Transportation and Lane Use (Routledge Library Editions, 2006), this book bridges the gap between the scholars and the practitioners of transportation and land-use modelling. First published in 1991, chapters discuss model-calibration and model-solution problems, describe a series of numerical and policy analyses, and propose potential directions for location and land-use research. This reissue will be of particular value to undergraduate and postgraduate geography students with an interest in integrated urban modelling; in particular, the research conducted in the field over the past two decades.

Reduced Order Methods for Modeling and Computational Reduction

Author: Alfio Quarteroni
Publisher: Springer
ISBN: 3319020900
Format: PDF
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This monograph addresses the state of the art of reduced order methods for modeling and computational reduction of complex parametrized systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in computational mechanics, bioengineering and computer graphics. Several topics are covered, including: design, optimization, and control theory in real-time with applications in engineering; data assimilation, geometry registration, and parameter estimation with special attention to real-time computing in biomedical engineering and computational physics; real-time visualization of physics-based simulations in computer science; the treatment of high-dimensional problems in state space, physical space, or parameter space; the interactions between different model reduction and dimensionality reduction approaches; the development of general error estimation frameworks which take into account both model and discretization effects. This book is primarily addressed to computational scientists interested in computational reduction techniques for large scale differential problems.