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This monograph is based on research undertaken by the authors during the last ten years. The main part of the work deals with homogenization problems in elasticity as well as some mathematical problems related to composite and perforated elastic materials. This study of processes in strongly non-homogeneous media brings forth a large number of purely mathematical problems which are very important for applications. Although the methods suggested deal with stationary problems, some of them can be extended to non-stationary equations. With the exception of some well-known facts from functional an

Partial differential equations --- Numerical solutions of differential equations --- Mathematical physics --- Navier-Stokes equations. --- Navier-Stokes equations --- Navier-Stokes, Equations de --- ELSEVIER-B EPUB-LIV-FT --- Equations, Navier-Stokes --- Differential equations, Partial --- Fluid dynamics --- Viscous flow --- 519.6 --- 681.3 *G18 --- Fluides, Dynamique des --- 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) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Computational mathematics. Numerical analysis. Computer programming --- Equations de navier-stokes --- Traitement numerique

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Efficient numerical solution of realistic and, therefore, complex equation systems occupies many researchers in many disciplines. For various reasons, but mainly in order to approximate reality, a very large number of unknowns are needed. Using classical techniques, the solution of such a system of equations would take too long, and so sometimes MultiLevel techniques are used to accelerate convergence. Over the last one and a half decades, the authors have studied the problem of Elastohydrodynamic Lubrication, governed by a complex integro-differential equation. Their work has resulted in a very efficient and stable solver. In this book they describe the different intermediate problems analyzed and solved, and how those ingredients finally come together in the EHL solver. A number of these intermediate problems, such as Hydrodynamic Lubrication and Dry Contact, are useful in their own right. In the Appendix the full codes of the Poisson problem, the Hydrodynamic Lubrication problem, the dry contact solver and the EHL solver are given. These codes are all written in 'C' language, based on the 'ANSI-C' version.

Lubrication and lubricants. --- Lubrifiants --- Lubrication and lubricants --- 519.6 --- 681.3 *G18 --- Grease --- Lubricants --- Tribology --- Bearings (Machinery) --- Lubrication systems --- Oils and fats --- 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) --- Mechanical Engineering - General --- Mechanical Engineering --- Engineering & Applied Sciences --- 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 --- Tribology. --- Friction --- Surfaces (Technology) --- Lubrification

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This latest volume in the Wavelets Analysis and Its Applications Series provides significant and up-to-date insights into recent developments in the field of wavelet constructions in connection with partial differential equations. Specialists in numerical applications and engineers in a variety of fields will find Multiscale Wavelet for Partial Differential Equations to be a valuable resource.Key Features* Covers important areas of computational mechanics such as elasticity and computational fluid dynamics* Includes a clear study of turbulence modeling* Contains rece

Numerical solutions of differential equations --- Differential equations, Partial --- Wavelets (Mathematics) --- 517.518.8 --- 681.3 *G18 --- 517.518.8 Approximation of functions by polynomials and their generalizations --- Approximation of functions by polynomials and their generalizations --- Wavelet analysis --- Harmonic analysis --- 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) --- Numerical analysis --- Numerical solutions --- Numerical solutions.

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Uniquely, this book presents a coherent, concise and unified way of combining elements from two distinct "worlds," functional analysis (FA) and partial differential equations (PDEs), and is intended for students who have a good background in real analysis. This text presents a smooth transition from FA to PDEs by analyzing in great detail the simple case of one-dimensional PDEs (i.e., ODEs), a more manageable approach for the beginner. Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Moreover, the wealth of exercises and additional material presented, leads the reader to the frontier of research. The first part of the text deals with abstract results in FA and operator theory. The second part is concerned with the study of spaces of functions (of one or more real variables) having specific differentiability properties, e.g., the celebrated Sobolev spaces, which lie at the heart of the modern theory of PDEs. The Sobolev spaces occur in a wide range of questions, both in pure and applied mathematics, appearing in linear and nonlinear PDEs which arise, for example, in differential geometry, harmonic analysis, engineering, mechanics, physics etc. and belong in the toolbox of any graduate student studying analysis. This book has its roots in a celebrated course taught by the author for many years and is a completely revised, updated, and expanded English edition of die important Analyse Fonctionnelle (1983). Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English version is a welcome addition to this list.

Differential equations, Partial. --- Functional analysis. --- Sobolev spaces. --- Sobolev spaces --- Sobolev, Espaces de --- 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) --- Spaces, Sobolev --- Mathematics. --- Difference equations. --- Functional equations. --- Partial differential equations. --- Functional Analysis. --- Partial Differential Equations. --- Difference and Functional Equations. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Partial differential equations --- Equations, Functional --- Functional analysis --- Calculus of differences --- Differences, Calculus of --- Equations, Difference --- Math --- Science --- Differential equations, Partial --- 517.95 --- 517.98 --- 681.3*G18 --- Function spaces --- 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) --- 517.95 Partial differential equations --- 517.98 Functional analysis and operator theory --- Functional analysis and operator theory --- Analytical spaces --- 681.3 *G18 --- Analyse fonctionnelle --- Equations aux dérivées partielles --- EPUB-LIV-FT LIVMATHE LIVSTATI SPRINGER-B --- Differential equations, partial. --- Analyse fonctionnelle. --- Équations aux dérivées partielles. --- Sobolev, Espaces de.

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There exist a wide range of applications where a significant fraction of the momentum and energy present in a physical problem is carried by the transport of particles. Depending on the specific application, the particles involved may be photons, neutrons, neutrinos, or charged particles. Regardless of which phenomena is being described, at the heart of each application is the fact that a Boltzmann like transport equation has to be solved. The complexity, and hence expense, involved in solving the transport problem can be understood by realizing that the general solution to the 3D Boltzmann transport equation is in fact really seven dimensional: 3 spatial coordinates, 2 angles, 1 time, and 1 for speed or energy. Low-order approximations to the transport equation are frequently used due in part to physical justification but many in cases, simply because a solution to the full transport problem is too computationally expensive. An example is the diffusion equation, which effectively drops the two angles in phase space by assuming that a linear representation in angle is adequate. Another approximation is the grey approximation, which drops the energy variable by averaging over it. If the grey approximation is applied to the diffusion equation, the expense of solving what amounts to the simplest possible description of transport is roughly equal to the cost of implicit computational fluid dynamics. It is clear therefore, that for those application areas needing some form of transport, fast, accurate and robust transport algorithms can lead to an increase in overall code performance and a decrease in time to solution.

Neutron transport theory --- Photon transport theory --- Radiative transfer --- Transport theory --- Research. --- Boltzmann transport equation --- Transport phenomena --- Mathematical physics --- Particles (Nuclear physics) --- Radiation --- Statistical mechanics --- Transfer, Radiative --- Astrophysics --- Geophysics --- Heat --- Multigroup diffusion (Neutron transport) --- Neutron diffusion theory --- Nuclear fission --- Nuclear fusion --- Nuclear reactors --- Radiation and absorption --- 517.95 --- 519.63 --- 681.3 *G18 --- 519.63 Numerical methods for solution of partial differential equations --- Numerical methods for solution of partial differential equations --- 517.95 Partial differential equations --- Partial differential equations --- 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) --- Research --- Computer science. --- Computational Science and Engineering. --- Theoretical, Mathematical and Computational Physics. --- Astrophysics and Astroparticles. --- Informatics --- Science --- Computer mathematics. --- Mathematical physics. --- Astrophysics. --- Astronomical physics --- Astronomy --- Cosmic physics --- Physics --- Physical mathematics --- Computer mathematics --- Electronic data processing --- Mathematics