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519.6 --- Computational mathematics. Numerical analysis. Computer programming --- Numerical analysis. --- Computer interfaces. --- MATLAB. --- 519.6 Computational mathematics. Numerical analysis. Computer programming

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This volume is a collection of articles based on the plenary talks presented at the 2005 meeting in Santander of the Society for the Foundations of Computational Mathematics. The talks were given by some of the foremost world authorities in computational mathematics. The topics covered reflect the breadth of research within the area as well as the richness and fertility of interactions between seemingly unrelated branches of pure and applied mathematics. As a result this volume will be of interest to researchers in the field of computational mathematics and also to non-experts who wish to gain some insight into the state of the art in this active and significant field.

Numerical analysis --- 519.6 --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Computational mathematics. Numerical analysis. Computer programming --- Computational mathematics --- FoCM

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Covers the state of the art in automatic differentiation theory and practice. Intended for computational scientists and engineers, this book aims to provide insight into effective strategies for using automatic differentiation for design optimization, sensitivity analysis, and uncertainty quantification.

Differential calculus --- Differential-difference equations --- Data processing --- Difference-differential equations --- Difference equations --- Differential equations --- Functional equations --- Calculus, Differential --- Calculus --- 519.6 --- 681.3*I12 --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Computational mathematics. Numerical analysis. Computer programming --- 681.3*I12 Algorithms: algebraic algorithms; nonalgebraic algorithms; analysis of algorithms (Algebraic manipulation; computing methodologies) --- Algorithms: algebraic algorithms; nonalgebraic algorithms; analysis of algorithms (Algebraic manipulation; computing methodologies) --- Computer science. --- Software engineering. --- Global analysis (Mathematics). --- Computer engineering. --- Computer science --- Computational Science and Engineering. --- Software Engineering/Programming and Operating Systems. --- Analysis. --- Electrical Engineering. --- Computational Mathematics and Numerical Analysis. --- Mathematics of Computing. --- Mathematics. --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Computers --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Computer software engineering --- Engineering --- Informatics --- Science --- Mathematics --- Design and construction --- Computer mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Electrical engineering. --- Computer science—Mathematics. --- Electric engineering --- 517.1 Mathematical analysis --- Mathematical analysis

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Lattice Boltzmann models have a remarkable ability to simulate single- and multi-phase fluids and transport processes within them. A rich variety of behaviors, including higher Reynolds numbers flows, phase separation, evaporation, condensation, cavitation, buoyancy, and interactions with surfaces can readily be simulated. This book provides a basic introduction that emphasizes intuition and simplistic conceptualization of processes. It avoids the more difficult mathematics that underlies LB models. The model is viewed from a particle perspective where collisions, streaming, and particle-particle/particle-surface interactions constitute the entire conceptual framework. Beginners and those with more interest in model application than detailed mathematical foundations will find this a powerful "quick start" guide. Example simulations, exercises, and computer codes are included. Working code is provided on the Internet. .

hydrologie --- Pedology --- simulaties --- informatica --- vormgeving --- Fluid mechanics --- mechanica --- Artificial intelligence. Robotics. Simulation. Graphics --- vloeistoffen --- ingenieurswetenschappen --- Thermodynamics --- geologie --- bodemkunde --- bodembescherming --- Geology. Earth sciences --- thermodynamica --- Classical mechanics. Field theory --- Lattice gas --- Maxwell-Boltzmann distribution law. --- Transport theory --- Mathematical models. --- Gas, Lattice --- Crystal lattices --- Boltzmann distribution law --- Maxwell-Boltzmann density function --- Maxwell distribution --- Distribution (Probability theory) --- Kinetic theory of gases --- Maxwell-Boltzmann distribution law --- 519.6 --- 681.3*J2 --- 681.3*J2 Physical sciences and engineering (Computer applications) --- Physical sciences and engineering (Computer applications) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Computational mathematics. Numerical analysis. Computer programming --- Mathematical models --- Lattice gas. --- Multiphase flow --- Fluid dynamics --- Gaz réticulaires --- Maxwell-Boltzmann, Distribution de. --- Théorie du transport --- Écoulement polyphasique --- Dynamique des fluides --- Modèles mathématiques.

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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