Domain decomposition methods are designed to allow the effective numerical solution of partial differential equations on parallel computer architectures. They comprise a relatively new field of study but have already found important applications in many branches of physics and engineering. In this book the authors illustrate the basic mathematical concepts behind domain decomposition, looking at a large variety of boundary value problems. Contents include symmetric elliptic equations, advection-diffusion equations, the elasticity problem, the Stokes problem for incompressible and compressible fluids, the time-harmonic Maxwell equations, parabolic and hyperbolic equations, and suitable couplings of heterogeneous equations.

Domain Decomposition Methods for Partial Differential Equations (Numerical Mathematics and Scientific Computation)

Computers & Technology

Quarteroni, Alfio

Valli, Alberto

Programming

Oxford University Press

Mathematical and numerical modelling of the human cardiovascular system has attracted remarkable research interest due to its intrinsic mathematical difficulty and the increasing impact of cardiovascular diseases worldwide. This book addresses the two principal components of the cardiovascular system: arterial circulation and heart function. It systematically describes all aspects of the problem, stating the basic physical principles, analysing the associated mathematical models that comprise PDE and ODE systems, reviewing sound and efficient numerical methods for their approximation, and simulating both benchmark problems and clinically inspired problems. Mathematical modelling itself imposes tremendous challenges, due to the amazing complexity of the cardiovascular system and the need for computational methods that are stable, reliable and efficient. The final part is devoted to control and inverse problems, including parameter estimation, uncertainty quantiﬁcation and the development of reduced-order models that are important when solving problems with high complexity, which would otherwise be out of reach.

Mathematical Modelling of the Human Cardiovascular System: Data, Numerical Approximation, Clinical Applications (Cambridge Monographs on Applied and Computational Mathematics, Series Number 33)

Science & Math

Manzoni, Andrea

Dede', Luca

Vergara, Christian

Mathematics

Cambridge University Press

<div> In this book we describe the magic world of mathematical models: starting from real-life problems, we formulate them in terms of equations, transform equations into algorithms and algorithms into programs to be executed on computers. A broad variety of examples and exercises illustrate that properly designed models can, e.g.: predict the way the number of dolphins in the Aeolian Sea will change as food availability and fishing activity vary; describe the blood flow in a capillary network; calculate the PageRank of websites. This book also includes a chapter with an elementary introduction to Octave, an&nbsp;open-source programming language widely used in the scientific community. Octave&nbsp;functions and scripts for dealing with the problems presented in the text can be&nbsp;downloaded from https://paola-gervasio.unibs.it/quarteroni-gervasio This book is addressed to any student interested in learning how to construct and apply mathematical models. </div> <div> </div>

A Primer on Mathematical Modelling (UNITEXT)

Springer

Optimal Control of Partial Differential Equations: Analysis, Approximation, and Applications (Applied Mathematical Sciences, 207)

This is a book on optimal control problems (OCPs) for partial differential equations (PDEs) that evolved from a series of courses taught by the authors in the last few years at Politecnico di Milano, both at the undergraduate and graduate levels. The book covers the whole range spanning from the setup and the rigorous theoretical analysis of OCPs, the derivation of the system of optimality conditions, the proposition of suitable numerical methods, their formulation, their analysis, including their application to a broad set of problems of practical relevance.The first introductory chapter addresses a handful of representative OCPs and presents an overview of the associated mathematical issues. The rest of the book is organized into three parts: part I provides preliminary concepts of OCPs for algebraic and dynamical systems; part II addresses OCPs involving linear PDEs (mostly elliptic and parabolic type) and quadratic cost functions; part III deals with more general classes of OCPs that stand behind the advanced applications mentioned above.\nStarting from simple problems that allow a “hands-on” treatment, the reader is progressively led to a general framework suitable to face a broader class of problems. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text. 
The three parts of the book are suitable to readers with variable mathematical backgrounds, from advanced undergraduate to Ph.D. levels and beyond. We believe that applied mathematicians, computational scientists, and engineers may find this book useful for a constructive approach toward the solution of OCPs in the context of complex applications.

Salsa, Sandro

This is a book on optimal control problems (OCPs) for partial differential equations (PDEs) that evolved from a series of courses taught by the authors in the last few years at Politecnico di Milano, both at the undergraduate and graduate levels. The book covers the whole range spanning from the setup and the rigorous theoretical analysis of OCPs, the derivation of the system of optimality conditions, the proposition of suitable numerical methods, their formulation, their analysis, including their application to a broad set of problems of practical relevance. The first introductory chapter addresses a handful of representative OCPs and presents an overview of the associated mathematical issues. The rest of the book is organized into three parts: part I provides preliminary concepts of OCPs for algebraic and dynamical systems; part II addresses OCPs involving linear PDEs (mostly elliptic and parabolic type) and quadratic cost functions; part III deals with more general classes ofOCPs that stand behind the advanced applications mentioned above. Starting from simple problems that allow a "hands-on" treatment, the reader is progressively led to a general framework suitable to face a broader class of problems. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text. The three parts of the book are suitable to readers with variable mathematical backgrounds, from advanced undergraduate to Ph.D. levels and beyond. We believe that applied mathematicians, computational scientists, and engineers may find this book useful for a constructive approach toward the solution of OCPs in the context of complex applications.

Modeling Reality with Mathematics

Simulating the behavior of a human heart, predicting tomorrow's weather, optimizing the aerodynamics of a sailboat, finding the ideal cooking time for a hamburger: to solve these problems, cardiologists, meteorologists, sportsmen, and engineers can count on math help. This book will lead you to the discovery of a magical world, made up of equations, in which a huge variety of important problems for our life can find useful answers.

Computer Science

Product Description Covid-19 has shown us the importance of mathematical and statistical models to interpret reality, provide forecasts, and explore future scenarios.Algorithms, artificial neural networks, and machine learning help us discover the opportunities and pitfalls of a world governed by mathematics and artificial intelligence. From the Back Cover Covid-19 has shown us the importance of mathematical and statistical models to interpret reality, provide forecasts, and explore future scenarios.Algorithms, artificial neural networks, and machine learning help us discover the opportunities and pitfalls of a world governed by mathematics and artificial intelligence. About the Author Alfio Quarteroni is Professor of Numerical Analysis and Director of MOX at the Politecnico of Milan (Italy). Formerly he was Director of the Chair of Modelling and Scientific Computing at the EPFL (Swiss Federal Institute of Technology), Lausanne (Switzerland), from 1998 until the end of 2017. He is the founder (and first director) of MOX at Politecnico of Milan (2002) and MATHICSE at EPFL, Lausanne (2010). He is co-founder (and President) of MOXOFF, a spin-off company at Politecnico of Milan (2010). He is the author of 25 books, editor of 9 books, author of more than 300 papers published in international Scientific Journals and Conference Proceedings, member of the editorial board of 25 International Journals and Editor in Chief of two book series published by Springer. He has been an invited or plenary speaker in more than 300 International Conferences and Academic Departments, in particular he has been invited speaker at ICM 2002 in Beijing and plenary speaker at ICM 2006 in Madrid. Among his awards and honors are the NASA Group Achievement Award for the pioneering work in Computational Fluid Dynamics in 1992, the Fanfullino della Riconoscenza 2006, Città di Lodi, the Premio Capo D'Orlando 2006, the Ghislieri prize, 2013, the International Galileo Galilei prize for Sciences 2015, The Euler lecture in 2017. He is the Recipient of two ERC Advanced Grants: “MATHCARD”, 2008, and “i-HEART”, 2017, and of two ERC PoC (Proof of Concept) grants in 2012 and 2015, Recipient of the Galileian Chair from the Scuola Normale Superiore, Pisa, Italy ,2001, doctor Honoris Causa in Naval Engineering from Universi ty of Trieste, Italy, 2003, SIAM Fellow (first row) since 2009, IACM (International Association of Computational Mechanics) Fellow since 2004. He is a member of the Italian Academy of Science, the European Academy of Science, and the Academia Europaea, the IMU Circle, and the Lisbon Academy of Science.His research interests concern Mathematical Modelling, Numerical Analysis, Scientific Computing, and Application to fluid mechanics, geophysics, medicine and the improvement of sports performance. His research Group at EPFL has contributed to the preliminary design of Solar Impulse, the Swiss long-range experimental solar-powered aircraft project; his research group at EPFL has carried out the mathematical simulation for the optimisation of performances of the Alinghi yacht, the winner of two editions (2003 and 2007) of the America’s Cup.

Algorithms for a New World: When Big Data and Mathematical Models Meet

This book provides a basic introduction to reduced basis (RB) methods for problems involving the repeated solution of partial differential equations (PDEs) arising from engineering and applied sciences, such as PDEs depending on several parameters and PDE-constrained optimization. 
The book presents a general mathematical formulation of RB methods, analyzes their fundamental theoretical properties, discusses the related algorithmic and implementation aspects, and highlights their built-in algebraic and geometric structures. 
More specifically, the authors discuss alternative strategies for constructing accurate RB spaces using greedy algorithms and proper orthogonal decomposition techniques, investigate their approximation properties and analyze offline-online decomposition strategies aimed at the reduction of computational complexity. Furthermore, they carry out both a priori and a posteriori error analysis. 
The whole mathematical presentation is made more stimulating by the use of representative examples of applicative interest in the context of both linear and nonlinear PDEs. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text. The book will be ideal for upper undergraduate students and, more generally, people interested in scientific computing.
All these pseudocodes are in fact implemented in a MATLAB package that is freely available at https://github.com/redbkit

Reduced Basis Methods for Partial Differential Equations: An Introduction (UNITEXT, 92)

In this text, we introduce the basic concepts for the numerical modeling 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.

Numerical Models for Differential Problems (MS&A, 16)

See the best price to sell, buy, or rent books by Quarteroni, Alfio. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Quarteroni, Alfio

See the best price to sell, buy, or rent books by Quarteroni, Alfio. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Domain Decomposition Methods for Partial Differential Equations (Numerical Mathematics and Scientific Computation)

Mathematical Modelling of the Human Cardiovascular System: Data, Numerical Approximation, Clinical Applications (Cambridge Monographs on Applied and Computational Mathematics, Series Number 33)

A Primer on Mathematical Modelling (UNITEXT)

Optimal Control of Partial Differential Equations: Analysis, Approximation, and Applications (Applied Mathematical Sciences, 207)

Optimal Control of Partial Differential Equations: Analysis, Approximation, and Applications (Applied Mathematical Sciences, 207)

Modeling Reality with Mathematics

Modeling Reality with Mathematics

Algorithms for a New World: When Big Data and Mathematical Models Meet

Reduced Basis Methods for Partial Differential Equations: An Introduction (UNITEXT, 92)

Numerical Models for Differential Problems (MS&A, 16)