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These are the proceedings of the 26th International Conference on Domain Decomposition Methods in Science and Engineering, which was hosted by the Chinese University of Hong Kong and held online in December 2020. Domain decomposition methods are iterative methods for solving the often very large systems of equations that arise when engineering problems are discretized, frequently using finite elements or other modern techniques. These methods are specifically designed to make effective use of massively parallel, high-performance computing systems. The book presents both theoretical and computational advances in this domain, reflecting the state of art in 2020.

Mathematics—Data processing. --- Computational Mathematics and Numerical Analysis. --- Descomposició (Matemàtica) --- Processament de dades --- Equacions en derivades parcials --- EDPs --- Equació diferencial en derivades parcials --- Equacions diferencials en derivades parcials --- Equacions diferencials parcials --- Equacions diferencials --- Dispersió (Matemàtica) --- Equació d'ona --- Equació de Dirac --- Equació de Fokker-Planck --- Equació de Schrödinger --- Equacions de Navier-Stokes --- Equacions de Hamilton-Jacobi --- Equacions de Maxwell --- Equacions de Monge-Ampère --- Equacions de Von Kármán --- Equacions diferencials el·líptiques --- Equacions diferencials hiperbòliques --- Equacions diferencials parabòliques --- Equacions diferencials parcials estocàstiques --- Funcions harmòniques --- Laplacià --- Problema de Cauchy --- Problema de Neumann --- Teoria espectral (Matemàtica) --- Processament de dades electròniques --- Processament automàtic de dades --- Processament electrònic de dades --- Processament integrat de dades --- Sistematització de dades (Ordinadors) --- Tractament de dades --- Tractament electrònic de dades --- Tractament integrat de dades --- Automatització --- Informàtica --- Complexitat computacional --- Curació de dades --- Depuració (Informàtica) --- Estructures de dades (Informàtica) --- Gestió de bases de dades --- Informàtica mòbil --- Informàtica recreativa --- Intel·ligència artificial --- Sistemes en línia --- Temps real (Informàtica) --- Tractament del llenguatge natural (Informàtica) --- Processament òptic de dades --- Protecció de dades --- Transmissió de dades --- Tolerància als errors (Informàtica) --- Matemàtica --- Probabilitats --- Decomposition method --- Differential equations, Partial --- Method, Decomposition --- Operations research --- Programming (Mathematics) --- System analysis

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This book develops the basic mathematical theory of the finite element  method, the most widely used technique for engineering design and analysis.

The third edition contains four new sections: the BDDC domain decomposition preconditioner, convergence analysis of an adaptive algorithm, interior penalty methods and Poincara'e-Friedrichs inequalities for piecewise W1\_p functions. New exercises have also been added throughout.

The initial chapter provides an introducton to the entire subject, developed in the one-dimensional case. Four subsequent chapters develop the basic theory in the multidimensional case, and a fifth chapter presents basic applications of this theory. Subsequent chapters provide an introduction to:

 - multigrid methods and domain decomposition methods

 - mixed methods with applications to elasticity and fluid mechanics

 - iterated penalty and augmented Lagrangian methods

 - variational "crimes" including nonconforming and isoparametric  methods, numerical integration and interior penalty methods

 - error estimates in the maximum norm with applications to nonlinear problems

 - error estimators, adaptive meshes and convergence analysis of an adaptive algorithm

- Banach-space operator-interpolation techniques

The book has proved useful to mathematicians as well as engineers and  physical scientists. It can be used for a course that provides an  introduction to basic functional analysis, approximation theory and  numerical analysis, while building upon and applying basic techniques of real variable theory. It can also be used for courses that emphasize physical applications or algorithmic efficiency.


Numerical solutions of differential equations --- Functional analysis --- finite element method --- computer-aided engineering --- CAE (computer aided engineering) --- Boundary conditions (Differential equations) --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic 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) --- Boundary value problems --- Finite element method --- 519.6 --- 681.3 *G18 --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Computational mathematics. Numerical analysis. Computer programming --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- Numerical analysis --- Isogeometric analysis --- Numerical solutions --- Mathematics --- eindige elementen --- Numerical solutions. --- Mathematics. --- Computer mathematics. --- Computational intelligence. --- Mechanics. --- Mechanics, Applied. --- Functional analysis. --- Computational Mathematics and Numerical Analysis. --- Computational Intelligence. --- Theoretical and Applied Mechanics. --- Functional Analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Computer mathematics --- Electronic data processing --- Boundary value problems - numerical solutions --- Finite element method - mathematics

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These are the proceedings of the 24th International Conference on Domain Decomposition Methods in Science and Engineering, which was held in Svalbard, Norway in February 2017. Domain decomposition methods are iterative methods for solving the often very large systems of equations that arise when engineering problems are discretized, frequently using finite elements or other modern techniques. These methods are specifically designed to make effective use of massively parallel, high-performance computing systems. The book presents both theoretical and computational advances in this domain, reflecting the state of art in 2017.

Decomposition method --- Computer science --- Differential equations, partial. --- Computer science. --- Computer simulation. --- Computer aided design. --- Computational Mathematics and Numerical Analysis. --- Partial Differential Equations. --- Computer Engineering. --- Mathematics of Computing. --- Simulation and Modeling. --- Computer-Aided Engineering (CAD, CAE) and Design. --- Mathematics. --- CAD (Computer-aided design) --- Computer-assisted design --- Computer-aided engineering --- Design --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Electromechanical analogies --- Mathematical models --- Simulation methods --- Model-integrated computing --- Informatics --- Science --- Partial differential equations --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Mathematics --- Computer mathematics. --- Partial differential equations. --- Computer engineering. --- Computer science—Mathematics. --- Computer-aided engineering. --- CAE --- Engineering --- Computers --- Data processing --- Design and construction