Numerical Approximation Methods

This book introduces the basic aspects of applied mathematics. It also covers such topics as information data manipulation, information coding, data approximation, data dimensionality reduction, data

A unique and comprehensive graduate text and reference on numerical methods for electromagnetic phenomena, from atomistic to continuum scales, in biology, optical-to-micro waves, photonics, nanoelectronics and plasmas. The state-of-the-art numerical methods described include: • Statistical fluctuation formulae for the dielectric constant • Particle-Mesh-Ewald, Fast-Multipole-Method and image-based reaction field method for long-range interactions • High-order singular/hypersingular (Nyström collocation/Galerkin) boundary and volume integral methods in layered media for Poisson–Boltzmann electrostatics, electromagnetic wave scattering and electron density waves in quantum dots • Absorbing and UPML boundary conditions • High-order hierarchical Nédélec edge elements • High-order discontinuous Galerkin (DG) and Yee finite difference time-domain methods • Finite element and plane wave frequency-domain methods for periodic structures • Generalized DG beam propagation method for optic

"This book is an introduction to numerical methods for students in engineering. It covers solution of equations, interpolation and data fitting, solution of differential equations, eigenvalue problems

Combining control theory and modeling, this textbook introduces and builds on methods for simulating and tackling concrete problems in a variety of applied sciences. Emphasizing "learning by doing," t

Physicists, chemical engineers, and other scientists set out the theory, numerical methods, and practice of computational gas-solids flows for advanced graduate students, researchers, and practitioner

This book consists of contributions given in honor of Wolfgang J.R. Hoefer. Space and time discretizing time domain methods for electromagnetic full-wave simulation have emerged as key numerical metho

This book provides insight into advanced numerical and experimental investigations of the microstructural aspects of strength and damage of metals and metal-based composites. In particular, atomistic

Stormy development of electronic computation techniques (computer systems and software), observed during the last decades, has made possible automation of data processing in many important human activ

The book provides a survey of numerical methods for acoustics, namely the finite element method (FEM) and the boundary element method (BEM). It is the first book summarizing FEM and BEM (and optimizat

Computational fluid dynamics (CFD) is concerned with the efficient numerical solution of the partial differential equations that describe fluid dynamics. CFD techniques are commonly used in the many a

The first time that such a complete systematic analysis of the mathematical and numerical techniques related to the orthogonal methods has been given. With the explosion of the wireless world, greate

Intersecting two large research areas--numerical analysis and applied probability/quering theory--this book is a self -contained introduction to the numerical solution of structured Markov chains, whi

An Introduction to C++ and Numerical Methods provides a brief yet comprehensive introduction to programming and numerical methods for students in engineering, chemistry, physics, and applied mathemati

What makes this book stand out from the competition is that it is more computational. Once done with both volumes, readers will have the tools to attack a wider variety of problems than those worked o

Many important phenomena in fluid motion are evident in vortex flow, i.e., flows in which vortical structures are significant in determining the whole flow. This book, which consists of lectures gi

Quasi-interpolation is one of the most useful and often applied methods for the approximation of functions and data in mathematics and applications. Its advantages are manifold: quasi-interpolants are able to approximate in any number of dimensions, they are efficient and relatively easy to formulate for scattered and meshed nodes and for any number of data. This book provides an introduction into the field for graduate students and researchers, outlining all the mathematical background and methods of implementation. The mathematical analysis of quasi-interpolation is given in three directions, namely on the basis (spline spaces, radial basis functions) from which the approximation is taken, on the form and computation of the quasi-interpolants (point evaluations, averages, least squares), and on the mathematical properties (existence, locality, convergence questions, precision). Learn which type of quasi-interpolation to use in different contexts and how to optimise its features to su

Differential Equations with Mathematica, Fifth Edition uses the fundamental concepts of the popular platform to solve (analytically, numerically, and/or graphically) differential equations of interest to students, instructors, and scientists. Mathematica's diversity makes it particularly well suited to performing calculations encountered when solving many ordinary and partial differential equations. In some cases, Mathematica's built-in functions can immediately solve a differential equation by providing an explicit, implicit, or numerical solution. In other cases, Mathematica can be used to perform the calculations encountered when solving a differential equation. Because one goal of elementary differential equations courses is to introduce students to basic methods and algorithms so that they gain proficiency in them, nearly every topic covered this book introduces basic commands, also including typical examples of their application. A study of differential equations relies on concep

David Sandwell developed this advanced textbook over a period of nearly 30 years for his graduate course at Scripps Institution of Oceanography. The book augments the classic textbook Geodynamics by Don Turcotte and Jerry Schubert, presenting more complex and foundational mathematical methods and approaches to geodynamics. The main new tool developed in the book is the multi-dimensional Fourier transform for solving linear partial differential equations. The book comprises nineteen chapters, including: the latest global data sets; quantitative plate tectonics; plate driving forces associated with lithospheric heat transfer and subduction; the physics of the earthquake cycle; postglacial rebound; and six chapters on gravity field development and interpretation. Each chapter has a set of student exercises that make use of the higher-level mathematical and numerical methods developed in the book. Solutions to the exercises are available online for course instructors, on request.

Based on course-tested material, this rigorous yet accessible graduate textbook covers both fundamental and advanced optimization theory and algorithms. It covers a wide range of numerical methods and topics, including both gradient-based and gradient-free algorithms, multidisciplinary design optimization, and uncertainty, with instruction on how to determine which algorithm should be used for a given application. It also provides an overview of models and how to prepare them for use with numerical optimization, including derivative computation. Over 400 high-quality visualizations and numerous examples facilitate understanding of the theory, and practical tips address common issues encountered in practical engineering design optimization and how to address them. Numerous end-of-chapter homework problems, progressing in difficulty, help put knowledge into practice. Accompanied online by a solutions manual for instructors and source code for problems, this is ideal for a one- or two-sem

This monograph is the first to present the theory of global attractors of Hamiltonian partial differential equations. A particular focus is placed on the results obtained in the last three decades, with chapters on the global attraction to stationary states, to solitons, and to stationary orbits. The text includes many physically relevant examples and will be of interest to graduate students and researchers in both mathematics and physics. The proofs involve novel applications of methods of harmonic analysis, including Tauberian theorems, Titchmarsh's convolution theorem, and the theory of quasimeasures. As well as the underlying theory, the authors discuss the results of numerical simulations and formulate open problems to prompt further research.

Many leading experts contribute to this follow-up to An Introduction to Reservoir Simulation using MATLAB/GNU Octave: User Guide for the MATLAB Reservoir Simulation Toolbox (MRST). It introduces more advanced functionality that has been recently added to the open-source MRST software. It is however a self-contained introduction to a variety of modern numerical methods for simulating multiphase flow in porous media, with applications to geothermal energy, chemical enhanced oil recovery (EOR), flow in fractured and unconventional reservoirs, and in the unsaturated zone. The reader will learn how to implement new models and algorithms in a robust, efficient manner. A large number of numerical examples are included, all fully equipped with code and data so that the reader can reproduce the results and use them as a starting point for their own work. Like the original textbook, this book will prove invaluable for researchers, professionals and advanced students using reservoir simulation me

A unique text integrating numerics, mathematics and applications to provide a hands-on approach to using optimization techniques, this mathematically accessible textbook emphasises conceptual understanding and importance of theorems rather than elaborate proofs. It allows students to develop fundamental optimization methods before delving into MATLAB®'s optimization toolbox, and to link MATLAB's results with the results from their own code. Following a practical approach, the text demonstrates several applications, from error-free analytic examples to truss (size) optimization, and 2D and 3D shape optimization, where numerical errors are inevitable. The principle of minimum potential energy is discussed to highlight the deep relationship between engineering and optimization. MATLAB code in every chapter illustrates key concepts and the text demonstrates the coupling between MATLAB and SOLIDWORKS® for design optimization. A wide variety of optimization problems are covered including con

Do you need to understand feedback? Perhaps you're a little rusty on theory basics? Dig in to this self-contained guide for an accessible and concise explanation of the fundamentals. Distills the relevant essence of linear system theory, calculus, differential equations, linear algebra, basic physics, numerical methods, and complex analysis, and links them back to an explanation of feedback theory. Provides a tight synthesis of analytical and conceptual understanding. Maintains a focus on common use cases. Whether you are a struggling undergraduate, a doctoral student preparing for your qualifying exams, or an industry practitioner, this easy-to-understand book invites you to relax, enjoy the material, and follow your curiosity.

Based on the author's forty years of teaching experience, this unique textbook covers both basic and advanced concepts of optimization theory and methods for process systems engineers. Topics covered include continuous, discrete and logic optimization (linear, nonlinear, mixed-integer and generalized disjunctive programming), optimization under uncertainty (stochastic programming and flexibility analysis), and decomposition techniques (Lagrangean and Benders decomposition). Assuming only a basic background in calculus and linear algebra, it enables easy understanding of mathematical reasoning, and numerous examples throughout illustrate key concepts and algorithms. End-of-chapter exercises involving theoretical derivations and small numerical problems, as well as in modeling systems like GAMS, enhance understanding and help put knowledge into practice. Accompanied by two appendices containing web links to modeling systems and models related to applications in PSE, this is an essential

Do you need to understand feedback? Perhaps you're a little rusty on theory basics? Dig in to this self-contained guide for an accessible and concise explanation of the fundamentals. Distills the relevant essence of linear system theory, calculus, differential equations, linear algebra, basic physics, numerical methods, and complex analysis, and links them back to an explanation of feedback theory. Provides a tight synthesis of analytical and conceptual understanding. Maintains a focus on common use cases. Whether you are a struggling undergraduate, a doctoral student preparing for your qualifying exams, or an industry practitioner, this easy-to-understand book invites you to relax, enjoy the material, and follow your curiosity.