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Evolution equations --- Numerical solutions.

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Boundary element methods --- Boundary value problems --- Numerical solutions

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The behaviour of systems occurring in real life is often modelled by partial differential equations. This book investigates how a user or observer can influence the behaviour of such systems mathematically and computationally. A thorough mathematical analysis of controllability problems is combined with a detailed investigation of methods used to solve them numerically, these methods being validated by the results of numerical experiments. In Part I of the book the authors discuss the mathematics and numerics relating to the controllability of systems modelled by linear and non-linear diffusion equations; Part II is dedicated to the controllability of vibrating systems, typical ones being those modelled by linear wave equations; finally, Part III covers flow control for systems governed by the Navier-Stokes equations modelling incompressible viscous flow. The book is accessible to graduate students in applied and computational mathematics, engineering and physics; it will also be of use to more advanced practitioners.

Control theory --- Distributed parameter systems --- Differential equations, Partial --- Numerical solutions --- Control theory. --- Distributed parameter systems. --- Systems, Distributed parameter --- Engineering systems --- System analysis --- Numerical analysis --- Dynamics --- Machine theory --- Numerical solutions. --- Differential equations, Partial - Numerical solutions

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Differential equations --- Equations différentielles --- Data processing --- Mathematical models. --- Informatique --- 517.91 --- Mathematical models --- 515.350285 --- Models, Mathematical --- Simulation methods --- Numerical solutions&delete& --- Numerical solutions

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This monograph is the first to provide a comprehensive, self-contained and rigorous presentation of some of the most powerful preconditioning methods for solving finite element equations in a common block-matrix factorization framework. Topics covered include the classical incomplete block-factorization preconditioners and the most efficient methods such as the multigrid, algebraic multigrid, and domain decomposition. Additionally, the author discusses preconditioning of saddle-point, nonsymmetric and indefinite problems, as well as preconditioning of certain nonlinear and quadratic constrained minimization problems that typically arise in contact mechanics. The book presents analytical as well as algorithmic aspects. This text can serve as an indispensable reference for researchers, graduate students, and practitioners. It can also be used as a supplementary text for a topics course in preconditioning and/or multigrid methods at the graduate level.

Computer. Automation --- algebra --- informatica --- matrices --- differentiaalvergelijkingen --- wiskunde --- Algebra --- Partial differential equations --- EPUB-LIV-FT LIVMATHE LIVSTATI SPRINGER-B --- Differential equations, Linear --- Differential equations, Partial --- Finite element method --- Numerical solutions --- Computer science --- Differential equations, partial. --- Computational Mathematics and Numerical Analysis. --- Partial Differential Equations. --- Computer mathematics --- Electronic data processing --- Mathematics --- Mathematics. --- Computer mathematics. --- Partial differential equations. --- Finite element method. --- Numerical solutions. --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- Numerical analysis --- Isogeometric analysis --- Differential equations, Linear - Numerical solutions --- Differential equations, Partial - Numerical solutions