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Algebra, Abstract. --- Difference equations --- Singular perturbations (Mathematics). --- Numerical solutions.

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Differential equations, Partial --- Finite element method --- Numerical solutions

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A thorough and rigorous analysis of electromagnetic fields in cavities This book offers a comprehensive analysis of electromagnetic fields in cavities of general shapes and properties. Part One covers classical deterministic methods to conclude resonant frequencies, modal fields, and cavity losses; quality factor; mode bandwidth; and the excitation of cavity fields from arbitrary current distributions for metal-wall cavities of simple shape. Part Two covers modern statistical methods to analyze electrically large cavities of complex shapes and properties. Electr

537.8 --- 537.8 Electromagnetism. Electromagnetic field. Electrodynamics. Maxwell theory --- Electromagnetism. Electromagnetic field. Electrodynamics. Maxwell theory --- Electromagnetic fields --- Maxwell equations --- Numerical analysis --- Fields, Electromagnetic --- Magnetic fields --- Electric fields --- Numerical solutions --- Electromagnetic fields. --- Numerical solutions.

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Numerical analysis presents different faces to the world. For mathematicians it is a bona fide mathematical theory with an applicable flavour. For scientists and engineers it is a practical, applied subject, part of the standard repertoire of modelling techniques. For computer scientists it is a theory on the interplay of computer architecture and algorithms for real-number calculations. The tension between these standpoints is the driving force of this book, which presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The exposition maintains a balance between theoretical, algorithmic and applied aspects. This second edition has been extensively updated, and includes new chapters on emerging subject areas: geometric numerical integration, spectral methods and conjugate gradients. Other topics covered include multistep and Runge-Kutta methods; finite difference and finite elements techniques for the Poisson equation; and a variety of algorithms to solve large, sparse algebraic systems.

517.91 --- 519.62 --- 681.3*G18 --- 519.62 Numerical methods for solution of ordinary differential equations --- Numerical methods for solution of ordinary differential equations --- Numerical solutions&delete& --- Numerical solutions --- Partitial differential equations: domain decomposition methods; elliptic equations; finite difference methods; finite element methods; finite volume methods; hyperbolic equations; inverse problems; iterative solution techniques; methods of lines; multigrid and multilevel methods; parabolic equations; special methods --- Differential equations --- 517.91 Differential equations --- Numerical solutions. --- numerisk analyse --- differensialligninger

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In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics.

Mathematics. --- Mathematics, general. --- Analysis. --- Numerical Analysis. --- Mathematical Modeling and Industrial Mathematics. --- Applications of Mathematics. --- Computational Mathematics and Numerical Analysis. --- Global analysis (Mathematics). --- Computer science --- Numerical analysis. --- Mathématiques --- Analyse globale (Mathématiques) --- Informatique --- Analyse numérique --- Differential equations, Partial --- Numerical analysis --- Numerical solutions --- Numerical solutions. --- Differential equations, Partial -- Numerical solutions. --- Electronic books. -- local. --- Mathematics --- Mathematical Theory --- Calculus --- Physical Sciences & Mathematics --- Mathematical analysis. --- Analysis (Mathematics). --- Applied mathematics. --- Engineering mathematics. --- Computer mathematics. --- Mathematical models. --- Mathematical analysis --- Models, Mathematical --- Simulation methods --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Engineering --- Engineering analysis --- 517.1 Mathematical analysis --- Math --- Science --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Differential equations, Partial - Numerical solutions