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This book introduces, in an accessible way, the basic elements of Numerical PDE-Constrained Optimization, from the derivation of optimality conditions to the design of solution algorithms. Numerical optimization methods in function-spaces and their application to PDE-constrained problems are carefully presented. The developed results are illustrated with several examples, including linear and nonlinear ones. In addition, MATLAB codes, for representative problems, are included. Furthermore, recent results in the emerging field of nonsmooth numerical PDE constrained optimization are also covered. The book provides an overview on the derivation of optimality conditions and on some solution algorithms for problems involving bound constraints, state-constraints, sparse cost functionals and variational inequality constraints.

Mathematics. --- Optimization. --- Partial Differential Equations. --- Numerical Analysis. --- Differential equations, partial. --- Numerical analysis. --- Mathematical optimization. --- Mathématiques --- Analyse numérique --- Optimisation mathématique --- Mathematical models. --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- 519.63 --- Numerical methods for solution of partial differential equations --- 519.63 Numerical methods for solution of partial differential equations --- Differential equations, Partial. --- Constrained optimization. --- Optimization, Constrained --- Partial differential equations --- Partial differential equations. --- Mathematical optimization --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis

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The Sixth Edition of this influential best-selling book delivers the most up-to-date and comprehensive text and reference yet on the basis of the finite element method (FEM) for all engineers and mathematicians. Since the appearance of the first edition 38 years ago, The Finite Element Method provides arguably the most authoritative introductory text to the method, covering the latest developments and approaches in this dynamic subject, and is amply supplemented by exercises, worked solutions and computer algorithms.The classic FEM text, written by the subject's leading authors

Finite element method. --- Engineering mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- Numerical analysis --- Isogeometric analysis --- Mathematics --- 519.63 --- 517.96 --- 517.96 Finite differences. Functional and integral equations --- Finite differences. Functional and integral equations --- 519.63 Numerical methods for solution of partial differential equations --- Numerical methods for solution of partial differential equations --- Mechanical properties of solids --- finite element method --- computer-aided engineering --- eindige elementen --- CAE (computer aided engineering)

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Computational Fluid Dynamics enables engineers to model and predict fluid flow in powerful, visually impressive ways and is one of the core engineering design tools, essential to the study and future work of many engineers. This textbook is designed to explcitly meet the needs engineering students taking a first course in CFD or computer-aided engineering. Fully course matched, with the most extensive and rigorous pedagogy and features of any book in the field, it is certain to be a key text. The only course text available specifically designed to give an applications-lead, commercial

Mathematical physics --- Fluid mechanics --- CFD (computational fluid dynamics) --- Fluid dynamics. --- Heat --- Turbulence. --- Transmission. --- Engineering --- General and Others --- Fluid dynamics --- Turbulence --- 519.63 --- 681.3 *G18 --- Flow, Turbulent --- Turbulent flow --- Heat transfer --- Thermal transfer --- Transmission of heat --- Energy transfer --- Dynamics --- 519.63 Numerical methods for solution of partial differential equations --- Numerical methods for solution of partial differential equations --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Transmission

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Stochastic numerical methods play an important role in large scale computations in the applied sciences. The first goal of this book is to give a mathematical description of classical direct simulation Monte Carlo (DSMC) procedures for rarefied gases, using the theory of Markov processes as a unifying framework. The second goal is a systematic treatment of an extension of DSMC, called stochastic weighted particle method. This method includes several new features, which are introduced for the purpose of variance reduction (rare event simulation). Rigorous convergence results as well as detailed numerical studies are presented.

Stochastic analysis. --- Transport theory. --- Boltzmann transport equation --- Transport phenomena --- Mathematical physics --- Particles (Nuclear physics) --- Radiation --- Statistical mechanics --- Analysis, Stochastic --- Mathematical analysis --- Stochastic processes --- Numerical analysis. --- Distribution (Probability theory. --- Differential equations, partial. --- Numerical Analysis. --- Probability Theory and Stochastic Processes. --- Theoretical, Mathematical and Computational Physics. --- Partial Differential Equations. --- Partial differential equations --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Stochastic analysis --- Transport theory --- 519.63 --- 681.3 *G18 --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 519.63 Numerical methods for solution of partial differential equations --- Numerical methods for solution of partial differential equations --- Probabilities. --- Mathematical physics. --- Partial differential equations. --- Physical mathematics --- Physics --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk

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The use of surface potentials to describe solutions of partial differential equations goes back to the middle of the 19th century. Numerical approximation procedures, known today as Boundary Element Methods (BEM), have been developed in the physics and engineering community since the 1950s. These methods turn out to be powerful tools for numerical studies of various physical phenomena which can be described mathematically by partial differential equations. The Fast Solution of Boundary Integral Equations provides a detailed description of fast boundary element methods which are based on rigorous mathematical analysis. In particular, a symmetric formulation of boundary integral equations is used, Galerkin discretisation is discussed, and the necessary related stability and error estimates are derived. For the practical use of boundary integral methods, efficient algorithms together with their implementation are needed. The authors therefore describe the Adaptive Cross Approximation Algorithm, starting from the basic ideas and proceeding to their practical realization. Numerous examples representing standard problems are given which underline both theoretical results and the practical relevance of boundary element methods in typical computations. The most prominent example is the potential equation (Laplace equation), which is used to model physical phenomena in electromagnetism, gravitation theory, and in perfect fluids. A further application leading to the Laplace equation is the model of steady state heat flow. One of the most popular applications of the BEM is the system of linear elastostatics, which can be considered in both bounded and unbounded domains. A simple model for a fluid flow, the Stokes system, can also be solved by the use of the BEM. The most important examples for the Helmholtz equation are the acoustic scattering and the sound radiation.

beeldverwerking --- analyse (wiskunde) --- Computer. Automation --- toegepaste wiskunde --- Mathematical physics --- Mathematics --- Engineering sciences. Technology --- differentiaalvergelijkingen --- ingenieurswetenschappen --- wiskunde --- Differential equations --- fysica --- Boundary element methods --- 519.63 --- BEM (Engineering analysis) --- BIE analysis --- BIE methods --- Boundary element analysis --- Boundary elements methods --- Boundary integral equation analysis --- Boundary integral equation methods --- Boundary integral methods --- Numerical analysis --- 519.63 Numerical methods for solution of partial differential equations --- Numerical methods for solution of partial differential equations --- Boundary element methods. --- Numerical analysis. --- Mathematical analysis --- Mathematics. --- Engineering mathematics. --- Computer vision. --- Differential Equations. --- Mathematics, general. --- Mathematical and Computational Engineering. --- Applications of Mathematics. --- Theoretical, Mathematical and Computational Physics. --- Image Processing and Computer Vision. --- Ordinary Differential Equations. --- 517.91 Differential equations --- Machine vision --- Vision, Computer --- Artificial intelligence --- Image processing --- Pattern recognition systems --- Engineering --- Engineering analysis --- Math --- Science --- Applied mathematics. --- Mathematical physics. --- Optical data processing. --- Differential equations. --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- Physical mathematics --- Physics --- Optical equipment