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519.63 --- 519.63 Numerical methods for solution of partial differential equations --- Numerical methods for solution of partial differential equations --- Multigrid methods (Numerical analysis) --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Multigrid methods (Numerical analysis). --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 681.3 *G18 --- Numerical analysis --- Numerical solutions of differential equations

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This up-to-date book gives an account of the present state of the art of numerical methods employed in computational fluid dynamics. The underlying numerical principles are treated in some detail, using elementary methods. The author gives many pointers to the current literature, facilitating further study. (Source : Copac)

Numerical solutions of differential equations --- Artificial intelligence. Robotics. Simulation. Graphics --- Fluid mechanics --- Fluid dynamics --- Data processing. --- 532.5 --- -519.6 --- 681.3 *G10 --- 681.3 *G18 --- 681.3*J2 --- 519.63 --- Dynamics --- Liquid motion. Hydrodynamics --- Data processing --- Computational mathematics. Numerical analysis. Computer programming --- Computerwetenschap--?*G10 --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Physical sciences and engineering (Computer applications) --- Numerical methods for solution of partial differential equations --- Computational fluid dynamics. --- 519.63 Numerical methods for solution of partial differential equations --- 681.3*J2 Physical sciences and engineering (Computer applications) --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 532.5 Liquid motion. Hydrodynamics --- 519.6 --- CFD (Computational fluid dynamics) --- Computer simulation --- Fluid dynamics - Data processing.

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Domain decomposition methods provide powerful and flexible tools for the numerical approximation of partial differential equations arising in the modeling of many interesting applications in science and engineering. This book deals with discretization techniques on non-matching triangulations and iterative solvers with particular emphasis on mortar finite elements, Schwarz methods and multigrid techniques. New results on non-standard situations as mortar methods based on dual basis functions and vector field discretizations are analyzed and illustrated by numerical results. The role of trace theorems, harmonic extensions, dual norms and weak interface conditions is emphasized. Although the original idea was used successfully more than a hundred years ago, these methods are relatively new for the numerical approximation. The possibilites of high performance computations and the interest in large- scale problems have led to an increased research activity.

Numerical solutions of differential equations --- Decomposition method. --- Differential equations --- Numerical solutions. --- Decomposition method --- -519.6 --- 519.63 --- 681.3 *G18 --- Equations, Differential --- Bessel functions --- Calculus --- Method, Decomposition --- Operations research --- Programming (Mathematics) --- System analysis --- Numerical solutions --- Computational mathematics. Numerical analysis. Computer programming --- Numerical methods for solution of partial differential equations --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- 681.3 *G18 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 --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 517.91 Differential equations --- Discretization (Mathematics) --- 519.6 --- 517.91 --- Numerical analysis. --- Mathematical analysis. --- Analysis (Mathematics). --- Computer mathematics. --- Computer science—Mathematics. --- Computational intelligence. --- Numerical Analysis. --- Analysis. --- Computational Science and Engineering. --- Math Applications in Computer Science. --- Computational Intelligence. --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Computer mathematics --- Electronic data processing --- Mathematics --- 517.1 Mathematical analysis --- Mathematical analysis --- Numerical solutions&delete&

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This book is devoted to the study of the acoustic wave equation and of the Maxwell system, the two most common wave equations encountered in physics or in engineering. The main goal is to present a detailed analysis of their mathematical and physical properties. Wave equations are time dependent. However, use of the Fourier trans­ form reduces their study to that of harmonic systems: the harmonic Helmholtz equation, in the case of the acoustic equation, or the har­ monic Maxwell system. This book concentrates on the study of these harmonic problems, which are a first step toward the study of more general time-dependent problems. In each case, we give a mathematical setting that allows us to prove existence and uniqueness theorems. We have systematically chosen the use of variational formulations related to considerations of physical energy. We study the integral representations of the solutions. These representa­ tions yield several integral equations. We analyze their essential properties. We introduce variational formulations for these integral equations, which are the basis of most numerical approximations. Different parts of this book were taught for at least ten years by the author at the post-graduate level at Ecole Poly technique and the University of Paris 6, to students in applied mathematics. The actual presentation has been tested on them. I wish to thank them for their active and constructive participation, which has been extremely useful, and I apologize for forcing them to learn some geometry of surfaces.

517.9 --- Maxwell equations --- -Wave equations --- -519.6 --- 681.3 *G18 --- 681.3*G17 --- 537.8 --- 534 --- Equations, Maxwell --- Differential equations, Partial --- Electromagnetic theory --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Numerical solutions --- Computational mathematics. Numerical analysis. Computer programming --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- Electromagnetism. Electromagnetic field. Electrodynamics. Maxwell theory --- Vibrations. Acoustics --- Wave equations --- Numerical solutions. --- 534 Vibrations. Acoustics --- 537.8 Electromagnetism. Electromagnetic field. Electrodynamics. Maxwell theory --- 681.3*G17 Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Wave equation --- 519.6 --- Numerical analysis --- Mathematical analysis. --- Analysis (Mathematics). --- Optics. --- Electrodynamics. --- Acoustics. --- Computational intelligence. --- Electrical engineering. --- Analysis. --- Classical Electrodynamics. --- Computational Intelligence. --- Electrical Engineering. --- Electric engineering --- Engineering --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Dynamics --- Physics --- Light --- 517.1 Mathematical analysis --- Mathematical analysis