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These lectures concentrate on (nonlinear) stochastic partial differential equations (SPDE) of evolutionary type. All kinds of dynamics with stochastic influence in nature or man-made complex systems can be modelled by such equations. To keep the technicalities minimal we confine ourselves to the case where the noise term is given by a stochastic integral w.r.t. a cylindrical Wiener process.But all results can be easily generalized to SPDE with more general noises such as, for instance, stochastic integral w.r.t. a continuous local martingale. There are basically three approaches to analyze SPDE: the "martingale measure approach", the "mild solution approach" and the "variational approach". The purpose of these notes is to give a concise and as self-contained as possible an introduction to the "variational approach". A large part of necessary background material, such as definitions and results from the theory of Hilbert spaces, are included in appendices.

Stochastic differential equations. --- Equations différentielles stochastiques --- Electronic books. -- local. --- Stochastic analysis. --- Stochastic differential equations --- Mathematical Statistics --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- 519.63 --- 681.3*G18 --- Numerical methods for solution of partial differential equations --- 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 --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Analysis, Stochastic --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Partial differential equations. --- Probabilities. --- Analysis. --- Partial Differential Equations. --- Probability Theory and Stochastic Processes. --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Partial differential equations --- 517.1 Mathematical analysis --- Mathematical analysis --- Math --- Science --- Differential equations --- Fokker-Planck equation --- 681.3 *G18 --- Stochastic processes --- Global analysis (Mathematics). --- Differential equations, partial. --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic

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Differential equations, Partial --- Finite differences. --- Finite element method. --- Numerical analysis. --- Numerical solutions. --- Finite differences --- Finite element method --- Numerical analysis --- 517.95 --- 519.63 --- 681.3 *G18 --- Mathematical analysis --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- Isogeometric analysis --- Differences, Finite --- Finite difference 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 --- 517.95 Partial differential equations --- Partial differential equations --- Numerical solutions --- Equations aux derivees partielles --- Methodes numeriques

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Grid computing has become a topic of significant interest in the scientific community as a means of enabling application developers to aggregate resources scattered around the globe for solving large-scale scientific problems. This monograph addresses four critical software development aspects for the engineering and execution of applications on parallel and Grid architectures. A new directive-based language called ZEN is proposed for compact specification of wide value ranges of interest for arbitrary application parameters, including problem or machine sizes, array or loop distributions, software libraries, interconnection networks, or target execution machines. Based on the ZEN language, a novel experiment management tool called ZENTURIO is developed for automatic experiment management of large-scale performance and parameter studies on parallel and Grid architectures. This tool has been validated with respect to functionality and usefulness on several real-world parallel applications from various domains, including theoretical chemistry, photonics, finances, and numerical mathematics. Depending on the ZENTURIO experiment management architecture a generic optimization framework is built up that integrates general-purpose meta-heuristics for solving NP-complete performance and parameter optimization problems in an exponential search space specified using the ZEN experiment specification language. Finally a timely approach is proposed for modeling and executing scientific workflows in dynamic and heterogeneous Grid environments, introducing an abstract formal model for hierarchical representation of complex directed graph-based workflows. Thus this monograph contributes to various research areas related to integrated tool development for efficient engineering and high performance execution of scientific applications in Grid environments.

Computational grids (Computer systems) --- Grilles informatiques --- Computational grids (Computer systems). --- Computer systems. --- Electronic books. -- local. --- Electrical & Computer Engineering --- Engineering & Applied Sciences --- Computer Science --- Telecommunications --- Information Technology --- Computer Science (Hardware & Networks) --- 681.3*D29 --- 681.3*G18 --- 681.3*K6 --- Grid computing --- Grids, Computational (Computer systems) --- Computer systems --- Cyberinfrastructure --- Management: copyrights; cost estimation; life cycle; productivity; programming teams; software configuration management; software quality assurance; SQA (Software engineering)--See also {681.3*K63}; {681.3*K64} --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Management of computing and information systems: economics --- 681.3*K6 Management of computing and information systems: economics --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 681.3*D29 Management: copyrights; cost estimation; life cycle; productivity; programming teams; software configuration management; software quality assurance; SQA (Software engineering)--See also {681.3*K63}; {681.3*K64} --- ADP systems (Computer systems) --- Computing systems --- Systems, Computer --- Computer science. --- Computer communication systems. --- Software engineering. --- Operating systems (Computers). --- Computers. --- Computer logic. --- Computer Science. --- Theory of Computation. --- Computer Science, general. --- Computer Communication Networks. --- Operating Systems. --- Software Engineering. --- Logics and Meanings of Programs. --- Computer science logic --- Logic, Symbolic and mathematical --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Cybernetics --- Machine theory --- Calculators --- Cyberspace --- Computer operating systems --- Computers --- Disk operating systems --- Systems software --- Computer software engineering --- Engineering --- Communication systems, Computer --- Computer communication systems --- Data networks, Computer --- ECNs (Electronic communication networks) --- Electronic communication networks --- Networks, Computer --- Teleprocessing networks --- Data transmission systems --- Digital communications --- Electronic systems --- Information networks --- Telecommunication --- Electronic data processing --- Network computers --- Informatics --- Science --- Operating systems --- Distributed processing --- 681.3 *G18 --- Information theory. --- Logic design. --- Design, Logic --- Design of logic systems --- Digital electronics --- Electronic circuit design --- Logic circuits --- Switching theory --- Communication theory --- Communication