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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

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This book provides insight in the mathematics of Galerkin finite element method as applied to parabolic equations. The approach is based on first discretizing in the spatial variables by Galerkin's method, using piecewise polynomial trial functions, and then applying some single step or multistep time stepping method. The concern is stability and error analysis of approximate solutions in various norms, and under various regularity assumptions on the exact solution. The book gives an excellent insight in the present ideas and methods of analysis. The second edition has been influenced by recent progress in application of semigroup theory to stability and error analysis, particulatly in maximum-norm. Two new chapters have also been added, dealing with problems in polygonal, particularly noncovex, spatial domains, and with time discretization based on using Laplace transformation and quadrature.

519.63 --- 681.3 *G18 --- Differential equations, Parabolic --- -Finite element method --- 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) --- 519.63 Numerical methods for solution of partial differential equations --- Numerical methods for solution of partial differential equations --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- Numerical analysis --- Isogeometric analysis --- Parabolic differential equations --- Parabolic partial differential equations --- Differential equations, Partial --- Numerical solutions --- Finite element method --- 517 --- 519.6 --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Computational mathematics. Numerical analysis. Computer programming --- 517 Analysis --- Analysis --- Finite element method. --- Numerical solutions. --- Galerkin methods. --- Partial differential equations --- Equations différentielles paraboliques --- Méthode des éléments finis --- Solutions numériques --- Numerical analysis. --- Global analysis (Mathematics). --- Numerical Analysis. --- Analysis. --- Theoretical, Mathematical and Computational Physics. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Mathematical analysis --- Mathematical analysis. --- Analysis (Mathematics). --- Mathematical physics. --- Physical mathematics --- Physics --- 517.1 Mathematical analysis --- Mathematics

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Fluid-structure interactions (FSI), that is interactions of some movable or deformable structure with an internal or surrounding fluid flow, are among the most important and, with respect to both modelling and computational issues, the most challenging multi-physics problems. The variety of FSI occurrences is abundant and ranges from tent-roofs to micropumps, from parachutes via airbags to blood flow in arteries. This volume of LNCSE contains a collection of papers presented at the International Workshop on FSI held in October 2005 in Hohenwart and organized by DFG's Research Unit 493 "FSI: Modelling, Simulation, and Optimization". The papers address partitioned and monolithic coupling approaches, methodical issues and applications, and discuss FSI from the mathematical, informatical, and engineering point of view.

Fluid-structure interaction --- 51-74 --- 519.63 --- 681.3 *G18 --- 681.3*I61 --- Structure-fluid interaction --- Fluid dynamics --- Structural dynamics --- 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*I61 Simulation theory: model classification; continuous simulation; discrete simulation (Simulation and modeling) --- Simulation theory: model classification; continuous simulation; discrete simulation (Simulation and modeling) --- 519.63 Numerical methods for solution of partial differential equations --- Numerical methods for solution of partial differential equations --- Mathematical models --- Mathematics in engineering science and technology --- Engineering. --- Construction --- Industrial arts --- Technology --- Hydraulic engineering. --- Computer science. --- Engineering mathematics. --- Cardiology. --- Engineering Fluid Dynamics. --- Computational Science and Engineering. --- Theoretical, Mathematical and Computational Physics. --- Mathematical and Computational Engineering. --- Heart --- Internal medicine --- Engineering --- Engineering analysis --- Mathematical analysis --- Informatics --- Science --- Engineering, Hydraulic --- Fluid mechanics --- Hydraulics --- Shore protection --- Diseases --- Mathematics --- Fluid mechanics. --- Computer mathematics. --- Mathematical physics. --- Applied mathematics. --- Physical mathematics --- Physics --- Computer mathematics --- Electronic data processing --- Hydromechanics --- Continuum mechanics