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Hierarchical matrices are an efficient framework for large-scale fully populated matrices arising, e.g., from the finite element discretization of solution operators of elliptic boundary value problems. In addition to storing such matrices, approximations of the usual matrix operations can be computed with logarithmic-linear complexity, which can be exploited to setup approximate preconditioners in an efficient and convenient way. Besides the algorithmic aspects of hierarchical matrices, the main aim of this book is to present their theoretical background. The book contains the existing approximation theory for elliptic problems including partial differential operators with nonsmooth coefficients. Furthermore, it presents in full detail the adaptive cross approximation method for the efficient treatment of integral operators with non-local kernel functions.The theory is supported by many numerical experiments from real applications.

Numerical analysis --- Computer. Automation --- informatica --- numerieke analyse --- differentiaalvergelijkingen --- wiskunde --- Partial differential equations --- Boundary value problems --- Differential equations, Elliptic --- Matrices --- 519.61 --- 519.63 --- 681.3*G14 --- 681.3 *G18 --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Algebra, Abstract --- Algebra, Universal --- Elliptic differential equations --- Elliptic partial differential equations --- Linear elliptic differential equations --- Differential equations, Linear --- Differential equations, Partial --- Boundary conditions (Differential equations) --- Differential equations --- Functions of complex variables --- Mathematical physics --- Initial value problems --- 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) --- 681.3*G14 Quadrature and numerical differentiation: adaptive quadrature; equal intervalintegration; error analysis; finite difference methods; gaussian quadrature; iterated methods; multiple quadrature --- Quadrature and numerical differentiation: adaptive quadrature; equal intervalintegration; error analysis; finite difference methods; gaussian quadrature; iterated methods; multiple quadrature --- 519.61 Numerical methods of algebra --- Numerical methods of algebra --- 519.63 Numerical methods for solution of partial differential equations --- Numerical methods for solution of partial differential equations

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This book collects the proceedings of the Parallel Computational Fluid Dynamics 2008 conference held in Lyon, France. Contributed papers by over 40 researchers representing the state of the art in parallel CFD and architecture from Asia, Europe, and North America examine major developments in (1) block-structured grid and boundary methods to simulate flows over moving bodies, (2) specific methods for optimization in Aerodynamics Design, (3) innovative parallel algorithms and numerical solvers, such as scalable algebraic multilevel preconditioners and the acceleration of iterative solutions, (4) software frameworks and component architectures for parallelism, (5) large scale computing and parallel efficiencies in the industrial context, (6) lattice Boltzmann and SPH methods, and (7) applications in the environment, biofluids, and nuclear engineering.

informatica --- Mathematical physics --- Fluid mechanics --- theoretische fysica --- Engineering sciences. Technology --- informaticaonderzoek --- ingenieurswetenschappen --- vloeistofstroming --- Computer science --- aerodynamica --- Computational fluid dynamics --- Parallel processing (Electronic computers) --- 519.63 --- 681.3*G18 --- CFD (Computational fluid dynamics) --- Fluid dynamics --- 519.63 Numerical methods for solution of partial differential equations --- Numerical methods for solution of partial differential equations --- 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 --- Computer simulation --- Data processing --- Engineering mathematics. --- Computer aided design. --- Computer science. --- Classical and Continuum Physics. --- Mathematical and Computational Engineering. --- Computer-Aided Engineering (CAD, CAE) and Design. --- Computational Science and Engineering. --- Fluid- and Aerodynamics. --- Theoretical, Mathematical and Computational Physics. --- Informatics --- Science --- CAD (Computer-aided design) --- Computer-assisted design --- Computer-aided engineering --- Design --- Engineering --- Engineering analysis --- Mathematical analysis --- Mathematics --- Continuum physics. --- Applied mathematics. --- Computer-aided engineering. --- Computer mathematics. --- Fluids. --- Mathematical physics. --- Physical mathematics --- Physics --- Hydraulics --- Mechanics --- Hydrostatics --- Permeability --- Computer mathematics --- Electronic data processing --- CAE --- Classical field theory --- Continuum physics --- Continuum mechanics