This book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physics and engineering problems. The book includes introductory and advanced concepts in measure and integration, as well as an introduction to Sobolev spaces. The problems presented are nonlinear, with non-convex variational formulation. Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to an appropriate weak cluster point of minimizing sequences for the primal one. Indeed, the dual approach more readily facilitates numerical computations for some of the selected models. While intended primarily for applied mathematicians, the text will also be of interest to engineers, physicists, and other researchers in related fields.

This book contains papers presented at the Workshop on the Analysis of Large-scale, High-Dimensional, and Multi-Variate Data Using Topology and Statistics, held in Le Barp, France, June 2013. It features the work of some of the most prominent and recognized leaders in the field who examine challenges as well as detail solutions to the analysis of extreme scale data. The book presents new methods that leverage the mutual strengths of both topological and statistical techniques to support the management, analysis, and visualization of complex data. It covers both theory and application and provides readers with an overview of important key concepts and the latest research trends. Coverage in the book includes multi-variate and/or high-dimensional analysis techniques, feature-based statistical methods, combinatorial algorithms, scalable statistics algorithms, scalar and vector field topology, and multi-scale representations. In addition, the book details algorithms that are broadly applicable and can be used by application scientists to glean insight from a wide range of complex data sets.

This book presents the basic theory and experimental techniques of transport phenomena in materials processing operations. Such fundamental knowledge is highly useful for researchers and engineers in the field to improve the efficiency of conventional processes or develop novel technology. Divided into four parts, the book comprises 11 chapters describing the principles of momentum transfer, heat transfer, and mass transfer in single phase and multiphase systems. Each chapter includes examples with solutions and exercises to facilitate students' learning. Diagnostic problems are also provided at the end of each part to assess students' comprehension of the material. The book is aimed primarily at students in materials science and engineering. However, it can also serve as a useful reference text in chemical engineering as well as an introductory transport phenomena text in mechanical engineering. In addition, researchers and engineers engaged in materials processing operations will find the material useful for the design of experiments and mathematical models in transport phenomena. This volume contains unique features not usually found in traditional transport phenomena texts. It integrates experimental techniques and theory, both of which are required to adequately solve the inherently complex problems in materials processing operations. It takes a holistic approach by considering both single and multiphase systems, augmented with specific practical examples. There is a discussion of flow and heat transfer in microscale systems, which is relevant to the design of modern processes such as fuel cells and compact heat exchangers. Also described are auxiliary relationships including turbulence modeling, interfacial phenomena, rheology, and particulate systems, which are critical to many materials processing operations.

The book contains a selection of high quality papers, chosen among the best presentations during the International Conference on Spectral and High-Order Methods (2014), and provides an overview of the depth and breadth of the activities within this important research area. The carefully reviewed selection of papers will provide the reader with a snapshot of the state-of-the-art and help initiate new research directions through the extensive biography.

Designed to provide tools for independent study, this book contains student-tested mathematical exercises joined with MATLAB programming exercises. Most chapters open with a review followed by theoretical and programming exercises, with detailed solutions provided for all problems including programs. Many of the MATLAB exercises are presented as Russian dolls: each question improves and completes the previous program and results are provided to validate the intermediate programs. The book offers useful MATLAB commands, advice on tables, vectors, matrices and basic commands for plotting. It contains material on eigenvalues and eigenvectors and important norms of vectors and matrices including perturbation theory; iterative methods for solving nonlinear and linear equations; polynomial and piecewise polynomial interpolation; Bezier curves; approximations of functions and integrals and more. The last two chapters considers ordinary differential equations including two point boundary value problems, and deal with finite difference methods for some partial differential equations. The format is designed to assist students working alone, with concise Review paragraphs, Math Hint footnotes on the mathematical aspects of a problem and MATLAB Hint footnotes with tips on programming.

This book is a collection of selected papers presented at the last Scientific Computing in Electrical Engineering (SCEE) Conference, held in Sinaia, Romania, in 2006. The series of SCEE conferences aims at addressing mathematical problems which have a relevance to industry, with an emphasis on modeling and numerical simulation of electronic circuits, electromagnetic fields but also coupled problems and general mathematical and computational methods.

The present book provides an introduction to using space-filling curves (SFC) as tools in scientific computing. Special focus is laid on the representation of SFC and on resulting algorithms. For example, grammar-based techniques are introduced for traversals of Cartesian and octree-type meshes, and arithmetisation of SFC is explained to compute SFC mappings and indexings. The locality properties of SFC are discussed in detail, together with their importance for algorithms. Templates for parallelisation and cache-efficient algorithms are presented to reflect the most important applications of SFC in scientific computing. Special attention is also given to the interplay of adaptive mesh refinement and SFC, including the structured refinement of triangular and tetrahedral grids. For each topic, a short overview is given on the most important publications and recent research activities.

This work provides a short "getting started" guide to Fortran 90/95. The main target audience consists of newcomers to the field of numerical computation within Earth system sciences (students, researchers or scientific programmers). Furthermore, readers accustomed to other programming languages may also benefit from this work, by discovering how some programming techniques they are familiar with map to Fortran 95. The main goal is to enable readers to quickly start using Fortran 95 for writing useful programs. It also introduces a gradual discussion of Input/Output facilities relevant for Earth system sciences, from the simplest ones to the more advanced netCDF library (which has become a de facto standard for handling the massive datasets used within Earth system sciences). While related works already treat these disciplines separately (each often providing much more information than needed by the beginning practitioner), the reader finds in this book a shorter guide which links them. Compared to other books, this work provides a much more compact view of the language, while also placing the language-elements in a more applied setting, by providing examples related to numerical computing and more advanced Input/Output facilities for Earth system sciences. Naturally, the coverage of the programming language is relatively shallow, since many details are skipped. However, many of these details can be learned gradually by the practitioner, after getting an overview and some practice with the language through this book.

Meshfree methods, particle methods, and generalized finite element methods have witnessed substantial development since the mid 1990s. The growing interest in these methods is due in part to the fact that they are extremely flexible numerical tools and can be interpreted in a number of ways. For instance, meshfree methods can be viewed as a natural extension of classical finite element and finite difference methods to scattered node configurations with no fixed connectivity. Furthermore, meshfree methods offer a number of advantageous features which are especially attractive when dealing with multiscale phenomena: a priori knowledge about particular local behavior of the solution can easily be introduced in the meshfree approximation space, and coarse-scale approximations can be seamlessly refined with fine-scale information. This volume collects selected papers presented at the Seventh International Workshop on Meshfree Methods, held in Bonn, Germany in September 2013. They address various aspects of this highly dynamic research field and cover topics from applied mathematics, physics and engineering.

The Leibniz Supercomputing Centre (LRZ) and the Bavarian Competence Network for Technical and Scienti?c High Performance Computing (KONWIHR) publish in the present book results of numerical simulations facilitated by the High P- formance Computer System in Bavaria (HLRB II) within the last two years. The papers were presented at the Fourth Joint HLRB and KONWIHR Review and - sult Workshop in Garching on 8th and 9th December 2009, and were selected from all progress reports of projects that use the HLRB II. Similar to the workshop two years ago, the majority of the contributed papers belong to the area of computational ?uid dynamics (CFD), condensed matter physics, astrophysics, chemistry, computer sciences and high-energy physics. We note a considerable increase of the user c- munity in some areas: Compared to 2007, the number of papers increased from 6 to 12 in condensed matter physics and from 2 to 5 in high-energy physics. Bio s- ences contributed only one paper in 2007, but four papers in 2009. This indicates that the area of application of supercomputers is continuously growing and entering new ?elds of research. The year 2007 saw two major events of particular importance for the LRZ. First, after a substantial upgrade with dual-core processors the SGI Altix 4700 superc- puter reached a peak performance of more than 62 Tera?op/s. And second, the n- pro?t organization Gauss Centre for Supercomputing e. V. (GCS) was founded on April 13th.

This book collects new results, concepts and further developments of NMF. The open problems discussed include, e.g. in bioinformatics: NMF and its extensions applied to gene expression, sequence analysis, the functional characterization of genes, clustering and text mining etc. The research results previously scattered in different scientific journals and conference proceedings are methodically collected and presented in a unified form. While readers can read the book chapters sequentially, each chapter is also self-contained. This book can be a good reference work for researchers and engineers interested in NMF, and can also be used as a handbook for students and professionals seeking to gain a better understanding of the latest applications of NMF.

Any financial asset that is openly traded has a market price. Except for extreme market conditions, market price may be more or less than a "fair" value. Fair value is likely to be some complicated function of the current intrinsic value of tangible or intangible assets underlying the claim and our assessment of the characteristics of the underlying assets with respect to the expected rate of growth, future dividends, volatility, and other relevant market factors. Some of these factors that affect the price can be measured at the time of a transaction with reasonably high accuracy. Most factors, however, relate to expectations about the future and to subjective issues, such as current management, corporate policies and market environment, that could affect the future financial performance of the underlying assets. Models are thus needed to describe the stochastic factors and environment, and their implementations inevitably require computational finance tools.

Computability and complexity theory are two central areas of research in theoretical computer science. This book provides a systematic, technical development of "algorithmic randomness" and complexity for scientists from diverse fields.

The book contains a selection of high quality papers, chosen among the best presentations during the International Conference on Spectral and High-Order Methods (2012), and provides an overview of the depth and breath of the activities within this important research area. The carefully reviewed selection of the papers will provide the reader with a snapshot of state-of-the-art and help initiate new research directions through the extensive bibliography.

The investigation of multiscale problems in multibody system contacts is an interesting and timely topic which has been the subject of intensive research. This IUTAM Symposium facilitated discussions between researchers active in the field. This proceedings volume summarizes contributions of many authors active in the field and gives insight in very different areas of this fascinating research. It reviews the state-of-the-art and identifies future hot topics.

This contributed volume contains a collection of articles on state-of-the-art developments on the construction of theoretical integral techniques and their application to specific problems in science and engineering. Written by internationally recognized researchers, the chapters in this book are based on talks given at the Thirteenth International Conference on Integral Methods in Science and Engineering, held July 21-25, 2014, in Karlsruhe, Germany. A broad range of topics is addressed, from problems of existence and uniqueness for singular integral equations on domain boundaries to numerical integration via finite and boundary elements, conservation laws, hybrid methods, and other quadrature-related approaches. This collection will be of interest to researchers in applied mathematics, physics, and mechanical and electrical engineering, as well as graduate students in these disciplines and other professionals for whom integration is an essential tool.

Scilab and its Scicos block diagram graphical editor, with a special emphasis on modeling and simulation tools. The first part is a detailed Scilab tutorial, and the second is dedicated to modeling and simulation of dynamical systems in Scicos. The concepts are illustrated through numerous examples, and all code used in the book is available to the reader.

This contributed volume presents some recent theoretical advances in mathematics and its applications in various areas of science and technology. Written by internationally recognized scientists and researchers, the chapters in this book are based on talks given at the International Conference on Advances in Applied Mathematics (ICAAM), which took place December 16-19, 2013, in Hammamet, Tunisia. Topics discussed at the conference included spectral theory, operator theory, optimization, numerical analysis, ordinary and partial differential equations, dynamical systems, control theory, probability, and statistics. These proceedings aim to foster and develop further growth in all areas of applied mathematics.

This book represents the refereed proceedings of the Ninth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at the University of Warsaw (Poland) in August 2010. These biennial conferences are major events for Monte Carlo and the premiere event for quasi-Monte Carlo research. The proceedings include articles based on invited lectures as well as carefully selected contributed papers on all theoretical aspects and applications of Monte Carlo and quasi-Monte Carlo methods. The reader will be provided with information on latest developments in these very active areas. The book is an excellent reference for theoreticians and practitioners interested in solving high-dimensional computational problems arising, in particular, in finance and statistics.

The book comprises an assembly of benchmarks and examples for porous media mechanics collected over the last twenty years. Analysis of thermo-hydro-mechanical-chemical (THMC) processes is essential to many applications in environmental engineering, such as geological waste deposition, geothermal energy utilisation, carbon capture and storage, water resources management, hydrology, even climate chance. In order to assess the feasibility as well as the safety of geotechnical applications, process-based modelling is the only tool to put numbers, i.e. to quantify future scenarios. This charges a huge responsibility concerning the reliability of computational tools. Benchmarking is an appropriate methodology to verify the quality of modelling tools based on best practices. Moreover, benchmarking and code comparison foster community efforts. The benchmark book is part of the OpenGeoSys initiative - an open source project to share knowledge and experience in environmental analysis and scientific computation.

Thirty years ago mathematical, as opposed to applied numerical, computation was difficult to perform and so relatively little used. Three threads changed that: the emergence of the personal computer; the discovery of fiber-optics and the consequent development of the modern internet; and the building of the Three "M's" Maple, Mathematica and Matlab. We intend to persuade that Mathematica and other similar tools are worth knowing, assuming only that one wishes to be a mathematician, a mathematics educator, a computer scientist, an engineer or scientist, or anyone else who wishes/needs to use mathematics better. We also hope to explain how to become an "experimental mathematician" while learning to be better at proving things. To accomplish this our material is divided into three main chapters followed by a postscript. These cover elementary number theory, calculus of one and several variables, introductory linear algebra, and visualization and interactive geometric computation.

This book presents four mathematical essays which explore the foundations of mathematics and related topics ranging from philosophy and logic to modern computer mathematics. While connected to the historical evolution of these concepts, the essays place strong emphasis on developments still to come. The book originated in a 2002 symposium celebrating the work of Bruno Buchberger, Professor of Computer Mathematics at Johannes Kepler University, Linz, Austria, on the occasion of his 60th birthday. Among many other accomplishments, Professor Buchberger in 1985 was the founding editor of the Journal of Symbolic Computation; the founder of the Research Institute for Symbolic Computation (RISC) and its chairman from 1987-2000; the founder in 1990 of the Softwarepark Hagenberg, Austria, and since then its director. More than a decade in the making, Mathematics, Computer Science and Logic - A Never Ending Story includes essays by leading authorities, on such topics as mathematical foundations from the perspective of computer verification; a symbolic-computational philosophy and methodology for mathematics; the role of logic and algebra in software engineering; and new directions in the foundations of mathematics. These inspiring essays invite general, mathematically interested readers to share state-of-the-art ideas which advance the never ending story of mathematics, computer science and logic. Mathematics, Computer Science and Logic - A Never Ending Story is edited by Professor Peter Paule, Bruno Buchberger's successor as director of the Research Institute for Symbolic Computation.

This volume presents selected contributions by top researchers in the field of operations research, originating from the XVI Congress of APDIO. It provides interesting findings and applications of operations research methods and techniques in a wide variety of problems. The contributions address complex real-world problems, including inventory management with lateral transshipments, sectors and routes in solid-waste collection and production planning for perishable food products. It also discusses the latest techniques, making the volume a valuable tool for researchers, students and practitioners who wish to learn about current trends. Of particular interest are the applications of nonlinear and mixed-integer programming, data envelopment analysis, clustering techniques, hybrid heuristics, supply chain management and lot sizing, as well as job scheduling problems. This biennial conference, organized by APDIO, the Portuguese Association of Operational Research, held in Braganca, Portugal, in June 2013, presented a perfect opportunity to discuss the latest development in this field and to narrow the gap between academic researchers and practitioners.

Computational Electromagnetics.- to Part I.- Challenges and Approaches in EMC Modeling of Wireless Consumer Devices.- A New Adaptive Approach to Modeling Measured Multi-Port Scattering Parameters.- Parametric Models of Transmission Lines Based on First Order Sensitivities.- Domain Partitioning Based Parametric Models for Passive On-Chip Components.- A Novel Graphical Based Tool for Extraction of Magnetic Reluctances Between On-Chip Current Loops.- A Robust Technique for Modelling Nonlinear Lumped Elements Spanning Multiple Cells in FDTD.- Computation of Eigenmodes in Periodic Structures with Dispersive Materials.- Region-Oriented BEM Formulation for Numerical Computations of Electric Fields.- Surface Integrated Field Equations Method to Solve 3D Electromagnetic Problems.- Reduced Basis Method for Electromagnetic Field Computations.- Using Nudg++ to Solve Poisson's Equation on Unstructured Grids.- Magnetic Force Calculations Applied to Magnetic Force Microscopy.- Relativistic High Order Particle Treatment for Electromagnetic Particle-In-Cell Simulations.- A Statistical Characterization of Resonant Electromagnetic Interactions with Thin Wires: Variance and Kurtosis Analysis.- Circuit Simulation.- to Part II.- Wavelets in Circuit Simulation.- On Local Handling of Inner Equations in Compact Models.- Hybrid Analysis of Nonlinear Time-Varying Circuits Providing DAEs with Index at Most One.- Transient Analysis of Nonlinear Circuits Based on Waves.- Simultaneous Step-Size and Path Control for Efficient Transient Noise Analysis.- Nonlinear Distortion in Differential Circuits with Single-Ended and Balanced Drive.- Evaluation of Oscillator Phase and Frequency Transfer Functions.- Polynomial Chaos for the Computation of Failure Probabilities in Periodic Problems.- Quasiperiodic Steady-State Analysis of Electronic Circuits by a Spline Basis.- Accurate Simulation of the Devil's Staircase of an Injection-Locked Frequency Divider.- ANN/DNN-Based Behavioral Modeling of RF/Microwave Components and Circuits.- Surrogate Modeling of Low Noise Amplifiers Based on Transistor Level Simulations.- Computational Statistics Approach to Capacitance Sensitivity Analysis and Gate Delay Time Minimization of TFT-LCDs.- Lookup-Table Based Settling Error Modeling in SIMULINK.- Speed-Up Techniques for Time-Domain System Simulations.- Coupled Problems.- to Part III.- Heating of Semiconductor Devices in Electric Circuits.- Analysis of a PDE Thermal Element Model for Electrothermal Circuit Simulation.- Automatic Thermal Network Extraction and Multiscale Electro-Thermal Simulation.- Simulations of an Electron-Phonon Hydrodynamical Model Based on the Maximum Entropy Principle.- Consistent Initialization for Coupled Circuit-Device Simulation.- Hyperbolic PDAEs for Semiconductor Devices Coupled with Circuits.- Large-Scale Atomistic Circuit-Device Coupled Simulation of Discrete-Dopant-Induced Characteristic Fluctuation in Nano-CMOS Digital Circuits.- Evaluation of Electromagnetic Coupling Between Microelectronic Device Structures Using Computational Electrodynamics.- Evaluation of Domain Decomposition Approach for Compact Simulation of On-Chip Coupled Problems.- DAE-Index and Convergence Analysis of Lumped Electric Circuits Refined by 3-D Magnetoquasistatic Conductor Models.- Mathematical and Computational Methods.- to Part IV.- Numerical Time Integration in Quasistatic Computational Electromagnetics.- A Novel Staggered Finite Volume Time Domain Method.- EM Scattering Calculations Using Potentials.- New Trends in the Preconditioning of Integral Equations of Electromagnetism.- Simulation of Large Interconnect Structures Using ILU-Type Preconditioner.- High-Order Discontinuous Galerkin Methods for Computational Electromagnetics and Uncertainty Quantification.- Efficient Simulation of Large-scale Dynamical Systems Using Tensor Decompositions.- Robust FETI Solvers for Multiscale Elliptic PDEs.- Nonlinear Models for Silicon Semiconductors.- Multiobjective Optimization Appl

The European Conferences on Numerical Mathematics and Advanced Applications (ENUMATH) are a series of conferences held every two years to provide a forum for discussion of new trends in numerical mathematics and challenging scientific and industrial applications at the highest level of international expertise. ENUMATH 2011 was hosted by the University of Leicester (UK) from the 5th to 9th September 2011. This proceedings volume contains more than 90 papers by speakers of the conference and gives an overview of recent developments in scientific computing, numerical analysis, and practical use of modern numerical techniques and algorithms in various applications. New results on finite element methods, multiscale methods, numerical linear algebra, and finite difference schemes are presented. A range of applications include computational problems from fluid dynamics, materials, image processing, and molecular dynamics.