These proceedings originated from a conference commemorating the 50th anniversary of the publication of Richard Courant's seminal paper, Variational Methods for Problems of Equilibrium and Vibration. These papers address fundamental questions in numerical analysis and the special problems that occur in applying the finite element method to various fields of science and engineering.

This book is addressed to young researchers and engineers in the fields of Computational Science and Artificial Intelligence, ranging from innovative computational methods to digital machine learning tools and their coupling used for solving challenging industrial and societal problems.This book provides the latest knowledge from jointly academic and industries experts in Computational Science and Artificial Intelligence fields for exploring possibilities and identifying challenges of applying Computational Sciences and AI methods and tools in industrial and societal sectors.

Transforming the Socio Economy with Digital Innovation explores the impacts of digital innovation on socioeconomic phenomena, resilience and governance. The book examines the limitation of using GDP as a measure of economic growth in digital societies, stressing how the Internet promotes a "free" culture that cannot be captured through GDP data. The book synthesizes multi-dimensional research consisting of digital platform ecosystems observations, theoretical appraisals, statistical methods development, in-depth empirical analysis, and database construction for analysis and outcomes compilation. Utilizing analysis from more than 500 global ICT leaders, this book identifies potential challenges and solutions for academic analysis, economic planning and policymaking.

The present monograph is intended to provide a comprehensive and accessible introduction to the optimization of elliptic systems. This area of mathematical research, which has many important applications in science and technology. has experienced an impressive development during the past two decades. There are already many good textbooks dealing with various aspects of optimal design problems. In this regard, we refer to the works of Pironneau [1984], Haslinger and Neittaanmaki [1988], [1996], Sokolowski and Zolksio [1992], Litvinov [2000], Allaire [2001], Mohammadi and Pironneau [2001], Delfour and Zolksio [2001], and Makinen and Haslinger [2003]. Already Lions [I9681 devoted a major part of his classical monograph on the optimal control of partial differential equations to the optimization of elliptic systems. Let us also mention that even the very first known problem of the calculus of variations, the brachistochrone studied by Bernoulli back in 1696. is in fact a shape optimization problem. The natural richness of this mathematical research subject, as well as the extremely large field of possible applications, has created the unusual situation that although many important results and methods have already been est- lished, there are still pressing unsolved questions. In this monograph, we aim to address some of these open problems; as a consequence, there is only a minor overlap with the textbooks already existing in the field.

This book studies electron resonant tunneling in two- and three-dimensional quantum waveguides of variable cross-sections in the time-independent approach. Mathematical models are suggested for the resonant tunneling and develop asymptotic and numerical approaches for investigating the models. Also, schemes are presented for several electronics devices based on the phenomenon of resonant tunneling. Compared to its first edition, this book includes four new chapters, redistributes the content between chapters and modifies the estimates of the remainders in the asymptotics of resonant tunneling characteristics. The book is addressed to mathematicians, physicists, and engineers interested in waveguide theory and its applications in electronics.

This book studies electron resonant tunneling in two- and three-dimensional quantum waveguides of variable cross-sections in the time-independent approach. Mathematical models are suggested for the resonant tunneling and develop asymptotic and numerical approaches for investigating the models. Also, schemes are presented for several electronics devices based on the phenomenon of resonant tunneling. Compared to its first edition, this book includes four new chapters, redistributes the content between chapters and modifies the estimates of the remainders in the asymptotics of resonant tunneling characteristics. The book is addressed to mathematicians, physicists, and engineers interested in waveguide theory and its applications in electronics.

This book discusses the stability of axially moving materials, which are encountered in process industry applications such as papermaking. A special emphasis is given to analytical and semianalytical approaches. As preliminaries, we consider a variety of problems across mechanics involving bifurcations, allowing to introduce the techniques in a simplified setting. In the main part of the book, the fundamentals of the theory of axially moving materials are presented in a systematic manner, including both elastic and viscoelastic material models, and the connection between the beam and panel models. The issues that arise in formulating boundary conditions specifically for axially moving materials are discussed. Some problems involving axially moving isotropic and orthotropic elastic plates are analyzed. Analytical free-vibration solutions for axially moving strings with and without damping are derived. A simple model for fluid--structure interaction of an axially moving panel is presented in detail. This book is addressed to researchers, industrial specialists and students in the fields of theoretical and applied mechanics, and of applied and computational mathematics.

This book gathers the outcomes of the second ECCOMAS CM3 Conference series on transport, which addressed the main challenges and opportunities that computation and big data represent for transport and mobility in the automotive, logistics, aeronautics and marine-maritime fields. Through a series of plenary lectures and mini-forums with lectures followed by question-and-answer sessions, the conference explored potential solutions and innovations to improve transport and mobility in surface and air applications. The book seeks to answer the question of how computational research in transport can provide innovative solutions to Green Transportation challenges identified in the ambitious Horizon 2020 program. In particular, the respective papers present the state of the art in transport modeling, simulation and optimization in the fields of maritime, aeronautics, automotive and logistics research. In addition, the content includes two white papers on transport challenges and prospects. Given its scope, the book will be of interest to students, researchers, engineers and practitioners whose work involves the implementation of Intelligent Transport Systems (ITS) software for the optimal use of roads, including safety and security, traffic and travel data, surface and air traffic management, and freight logistics.

This book discusses the stability of axially moving materials, which are encountered in process industry applications such as papermaking. A special emphasis is given to analytical and semianalytical approaches. As preliminaries, we consider a variety of problems across mechanics involving bifurcations, allowing to introduce the techniques in a simplified setting. In the main part of the book, the fundamentals of the theory of axially moving materials are presented in a systematic manner, including both elastic and viscoelastic material models, and the connection between the beam and panel models. The issues that arise in formulating boundary conditions specifically for axially moving materials are discussed. Some problems involving axially moving isotropic and orthotropic elastic plates are analyzed. Analytical free-vibration solutions for axially moving strings with and without damping are derived. A simple model for fluid--structure interaction of an axially moving panel is presented in detail. This book is addressed to researchers, industrial specialists and students in the fields of theoretical and applied mechanics, and of applied and computational mathematics.

This book gathers the outcomes of the second ECCOMAS CM3 Conference series on transport, which addressed the main challenges and opportunities that computation and big data represent for transport and mobility in the automotive, logistics, aeronautics and marine-maritime fields. Through a series of plenary lectures and mini-forums with lectures followed by question-and-answer sessions, the conference explored potential solutions and innovations to improve transport and mobility in surface and air applications. The book seeks to answer the question of how computational research in transport can provide innovative solutions to Green Transportation challenges identified in the ambitious Horizon 2020 program. In particular, the respective papers present the state of the art in transport modeling, simulation and optimization in the fields of maritime, aeronautics, automotive and logistics research. In addition, the content includes two white papers on transport challenges and prospects. Given its scope, the book will be of interest to students, researchers, engineers and practitioners whose work involves the implementation of Intelligent Transport Systems (ITS) software for the optimal use of roads, including safety and security, traffic and travel data, surface and air traffic management, and freight logistics.

This volume contains selected papers in three closely related areas: mathematical modeling in mechanics, numerical analysis, and optimization methods. The papers are based upon talks presented on the International Conference for Mathematical Modeling and Optimization in Mechanics, held in Jyvaskyla, Finland, March 6-7, 2014 dedicated to Prof. N. Banichuk on the occasion of his 70th birthday. The articles are written by well-known scientists working in computational mechanics and in optimization of complicated technical models. Also, the volume contains papers discussing the historical development, the state of the art, new ideas, and open problems arising in modern continuum mechanics and applied optimization problems. Several papers are concerned with mathematical problems in numerical analysis, which are also closely related to important mechanical models. The main topics treated include: * Computer simulation methods in mechanics, physics, and biology; * Variational problems and methods; minimization algorithms; * Optimal control problems with distributed and discrete control; * Shape optimization and shape design problems in science and engineering; * Sensitivity analysis and parameters optimization of complex systems.

This volume contains thirteen articles on advances in applied mathematics and computing methods for engineering problems. Six papers are on optimization methods and algorithms with emphasis on problems with multiple criteria; four articles are on numerical methods for applied problems modeled with nonlinear PDEs; two contributions are on abstract estimates for error analysis; finally one paper deals with rare events in the context of uncertainty quantification. Applications include aerospace, glaciology and nonlinear elasticity.

Hereinis a selection of contributions from speakers at two conferences on applied mathematics held in June 2012 at the University of Jyvaskyla, Finland. The first conference, Optimization and PDEs with Industrial Applications celebrated the seventieth birthday of Professor Jacques Periaux of theUniversity of Jyvaskyla and Polytechnic University of Catalonia (Barcelona Tech) and the second conference, Optimization and PDEs with Applications celebrated the seventy-fifth birthday of Professor Roland Glowinski of the University of Houston.

This work should be of interest to researchers and practitioners as well as advanced students or engineers in computational and applied mathematics or mechanics."

This volume provides universal methodologies accompanied by Matlab software to manipulate numerous signal and image processing applications. It is done with discrete and polynomial periodic splines. Various contributions of splines to signal and image processing from a unified perspective are presented. This presentation is based on Zak transform and on Spline Harmonic Analysis (SHA) methodology. SHA combines approximation capabilities of splines with the computational efficiency of the Fast Fourier transform. SHA reduces the design of different spline types such as splines, spline wavelets (SW), wavelet frames (SWF) and wavelet packets (SWP) and their manipulations by simple operations. Digital filters, produced by wavelets design process, give birth to subdivision schemes. Subdivision schemes enable to perform fast explicit computation of splines' values at dyadic and triadic rational points. This is used for signals and images up sampling. In addition to the design of a diverse library of splines, SW, SWP and SWF, this book describes their applications to practical problems. The applications include up sampling, image denoising, recovery from blurred images, hydro-acoustic target detection, to name a few. The SWF are utilized for image restoration that was degraded by noise, blurring and loss of significant number of pixels. The book is accompanied by Matlab based software that demonstrates and implements all the presented algorithms. The book combines extensive theoretical exposure with detailed description of algorithms, applications and software. The Matlab software can be downloaded from http://extras.springer.com

This book deals with theoretical aspects of modelling the mechanical behaviour of manufacturing, processing, transportation or other systems in which the processed or supporting material is travelling through the system. Examples of such applications include paper making, transmission cables, band saws, printing presses, manufacturing of plastic films and sheets, and extrusion of aluminium foil, textiles and other materials.

The work focuses on out-of-plane dynamics and stability analysis for isotropic and orthotropic travelling elastic and viscoelastic materials, with and without fluid-structure interaction, using analytical and semi-analytical approaches. Also topics such as fracturing and fatigue are discussed in the context of moving materials. The last part of the book deals with optimization problems involving physical constraints arising from the stability and fatigue analyses, including uncertainties in the parameters.

The book is intended for researchers and specialists in the field, providing a view of the mechanics of axially moving materials. It can also be used as a textbook for advanced courses on this specific topic. Considering topics related to manufacturing and processing, the book can also be applied in industrial mathematics.
"

The importance of accuracy verification methods was understood at the very beginning of the development of numerical analysis. Recent decades have seen a rapid growth of results related to adaptive numerical methods and a posteriori estimates. However, in this important area there often exists a noticeable gap between mathematicians creating the theory and researchers developing applied algorithms that could be used in engineering and scientific computations for guaranteed and efficient error control.

The goals of the book are to (1) give a transparent explanation of the underlying mathematical theory in a style accessible not only to advanced numerical analysts but also to engineers and students; (2) present detailed step-by-step algorithms that follow from a theory; (3) discuss their advantages and drawbacks, areas of applicability, give recommendations and examples.

"

The position taken in this collection of pedagogically written essays is that conjugate gradient algorithms and finite element methods complement each other extremely well.

Via their combinations practitioners have been able to solve complicated, direct and inverse, multidemensional problems modeled by ordinary or partial differential equations and inequalities, not necessarily linear, optimal control and optimal design being part of these problems.

The aim of this book is to present both methods in the context of complicated problems modeled by linear and nonlinear partial differential equations, to provide an in-depth discussion on their implementation aspects. The authors show that conjugate gradient methods and finite element methods apply to the solution of real-life problems. They address graduate students as well as experts in scientific computing.

One service mathematics has rendered the 'Et moi, .... si favait su comment en revenir, je n'y seTais point alle.' human race. It has put common sense back Jules Verne where it belongs. on the topmost shelf next to the dusty canister labelled 'discarded n- sense', The series is divergent; therefore we may be Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One scrvice logic has rendered com puter science .. .'; 'One service category theory has rendcred mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'e"tre of this scries."

Structural optimization is currently attracting considerable attention. Interest in - search in optimal design has grown in connection with the rapid development of aeronautical and space technologies, shipbuilding, and design of precision mach- ery. A special ?eld in these investigations is devoted to structural optimization with incomplete information (incomplete data). The importance of these investigations is explained as follows. The conventional theory of optimal structural design - sumes precise knowledge of material parameters, including damage characteristics and loadings applied to the structure. In practice such precise knowledge is seldom available. Thus, it is important to be able to predict the sensitivity of a designed structure to random ?uctuations in the environment and to variations in the material properties. To design reliable structures it is necessary to apply the so-called gu- anteed approach, based on a "worst case scenario" or a more optimistic probabilistic approach, if we have additional statistical data. Problems of optimal design with incomplete information also have consid- able theoretical importance. The introduction and investigations into new types of mathematical problems are interesting in themselves. Note that some ga- theoretical optimization problems arise for which there are no systematic techniques of investigation. This monograph is devoted to the exposition of new ways of formulating and solving problems of structural optimization with incomplete information. We recall some research results concerning the optimum shape and structural properties of bodies subjected to external loadings.

The present volume is comprised of contributions solicited from invitees to conferences held at the University of Houston, University of Jyv] askyl] a, and Xi'an Jiaotong University honoring the 70th birthday of Professor Roland Glowinski. Although scientists convened on three di?erent continents, the - itors prefer to view the meetings as single event. The three locales signify the fact Roland has friends, collaborators and admirers across the globe. The contents span a wide range of topics in contemporary applied mathematics rangingfrompopulationdynamics, to electromagnetics, to ?uidmechanics, to the mathematics of ?nance among others. However, they do not fully re?ect the breath and diversity of Roland's scienti?c interest. His work has always been at the intersection mathematics and scienti?c computing and their - plication to mechanics, physics, aeronautics, engineering sciences and more recently biology. He has made seminal contribution in the areas of methods for science computation, ?uid mechanics, numerical controls for distributed parameter systems, and solid and structural mechanics as well as shape - timization, stellar motion, electron transport, and semiconductor modeling. Two central themes arise from the corpus of Roland's work. The ?rst is that numerical methods should take advantage of the mathematical properties of themodel. Theyshouldbeportableandcomputablewithcomputingresources of the foreseeable future as well as with contemporary resources. The second theme is that whenever possible one should validate numerical with expe- mental data. The volume is written at an advanced scienti?c level and no e?ort has been made to make it self contained."

For more than 250 years partial di?erential equations have been clearly the most important tool available to mankind in order to understand a large variety of phenomena, natural at ?rst and then those originating from - man activity and technological development. Mechanics, physics and their engineering applications were the ?rst to bene't from the impact of partial di?erential equations on modeling and design, but a little less than a century ago the Schr] odinger equation was the key opening the door to the application of partial di?erential equations to quantum chemistry, for small atomic and molecular systems at ?rst, but then for systems of fast growing complexity. The place of partial di?erential equations in mathematics is a very particular one: initially, the partial di?erential equations modeling natural phenomena were derived by combining calculus with physical reasoning in order to - press conservation laws and principles in partial di?erential equation form, leading to the wave equation, the heat equation, the equations of elasticity, the Euler and Navier-Stokes equations for ?uids, the Maxwell equations of electro-magnetics, etc. It is in order to solve 'constructively' the heat equation that Fourier developed the series bearing his name in the early 19th century; Fourier series (and later integrals) have played (and still play) a fundamental roleinbothpureandappliedmathematics, includingmanyareasquiteremote from partial di?erential equations. On the other hand, several areas of mathematics such as di?erential ge- etry have bene?ted from their interactions with partial di?erential equations."

The aim of this book is to present the mathematical theory and the know-how to make computer programs for the numerical approximation of Optimal Control of PDE's. The computer programs are presented in a straightforward generic language. As a consequence they are well structured, clearly explained and can be translated easily into any high level programming language. Applications and corresponding numerical tests are also given and discussed. To our knowledge, this is the first book to put together mathematics and computer programs for Optimal Control in order to bridge the gap between mathematical abstract algorithms and concrete numerical ones.
The text is addressed to students and graduates in Mathematics, Mechanics, Applied Mathematics, Numerical Software, Information Technology and Engineering. It can also be used for Master and Ph.D. programs.

Mathematical modeling plays an essential role in science and engineering. Costly and time consuming experiments (if they can be done at all) are replaced by computational analysis. In industry, commercial codes are widely used. They are flexible and can be adjusted for solving specific problems of interest. Solving large problems with tens or hundreds of thousands unknowns becomes routine. The aim of analysis is to predict the behavior of the engineering and physical reality usually within the constraints of cost and time. Today, human cost and time are more important than computer cost. This trend will continue in the future. Agreement between computational results and reality is related to two factors, namely mathematical formulation of the problems and the accuracy of the numerical solution. The accuracy has to be understood in the context of the aim of the analysis. A small error in an inappropriate norm does not necessarily mean that the computed results are usable for practical purposes.

The present monograph is intended to provide a comprehensive and accessible introduction to the optimization of elliptic systems. This area of mathematical research, which has many important applications in science and technology. has experienced an impressive development during the past two decades. There are already many good textbooks dealing with various aspects of optimal design problems. In this regard, we refer to the works of Pironneau [1984], Haslinger and Neittaanmaki [1988], [1996], Sokolowski and Zolksio [1992], Litvinov [2000], Allaire [2001], Mohammadi and Pironneau [2001], Delfour and Zolksio [2001], and Makinen and Haslinger [2003]. Already Lions [I9681 devoted a major part of his classical monograph on the optimal control of partial differential equations to the optimization of elliptic systems. Let us also mention that even the very first known problem of the calculus of variations, the brachistochrone studied by Bernoulli back in 1696. is in fact a shape optimization problem. The natural richness of this mathematical research subject, as well as the extremely large field of possible applications, has created the unusual situation that although many important results and methods have already been est- lished, there are still pressing unsolved questions. In this monograph, we aim to address some of these open problems; as a consequence, there is only a minor overlap with the textbooks already existing in the field.

During the last few years, a new area of creative media industry, namely Serious Games, has started to emerge around the world. The term serious games has become more popular for example in the fields of education, business, welfare and safety. Despite this, there has been no single definition of serious games. A key question, what the concept itself means, has stayed unsolved though most have agreed on a definition that serious games are games or game-like interactive systems developed with game technology and design principles for a primary purpose other than pure entertainment. In this book, serious games are understood as games which aim at providing an engaging, self-reinforcing context in which to motivate and educate the players. Serious games can be of any genre, use any game technology, and be developed for any platform. They can be entertaining, but usually they teach the user something. The central aim of serious games is to raise quality of life and well-being. As part of interactive media industry, the serious games field focuses on designing and using digital games for real-life purposes and for the everyday life of citizens in information societies. The field of serious games focuses on such areas as education, business, welfare, military, traffic, safety, travelling and tourism.

The present volume is comprised of contributions solicited from invitees to conferences held at the University of Houston, University of Jyv] askyl] a, and Xi'an Jiaotong University honoring the 70th birthday of Professor Roland Glowinski. Although scientists convened on three di?erent continents, the - itors prefer to view the meetings as single event. The three locales signify the fact Roland has friends, collaborators and admirers across the globe. The contents span a wide range of topics in contemporary applied mathematics rangingfrompopulationdynamics, to electromagnetics, to ?uidmechanics, to the mathematics of ?nance among others. However, they do not fully re?ect the breath and diversity of Roland's scienti?c interest. His work has always been at the intersection mathematics and scienti?c computing and their - plication to mechanics, physics, aeronautics, engineering sciences and more recently biology. He has made seminal contribution in the areas of methods for science computation, ?uid mechanics, numerical controls for distributed parameter systems, and solid and structural mechanics as well as shape - timization, stellar motion, electron transport, and semiconductor modeling. Two central themes arise from the corpus of Roland's work. The ?rst is that numerical methods should take advantage of the mathematical properties of themodel. Theyshouldbeportableandcomputablewithcomputingresources of the foreseeable future as well as with contemporary resources. The second theme is that whenever possible one should validate numerical with expe- mental data. The volume is written at an advanced scienti?c level and no e?ort has been made to make it self contained."