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System analysis --- Computational complexity --- Coupled problems (Complex systems) --- Systems engineering --- Computational complexity. --- System analysis. --- Systems engineering. --- Engineering systems --- System engineering --- Coupled field problems (Complex systems) --- Problems, Coupled (Complex systems) --- Complexity, Computational --- Network theory --- Systems analysis --- Design and construction --- Engineering --- Industrial engineering --- Dynamics --- Electronic data processing --- Machine theory --- System theory --- Mathematical optimization --- Network analysis --- Network science --- Operations Research

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Designs in nanoelectronics often lead to challenging simulation problems and include strong feedback couplings. Industry demands provisions for variability in order to guarantee quality and yield. It also requires the incorporation of higher abstraction levels to allow for system simulation in order to shorten the design cycles, while at the same time preserving accuracy. The methods developed here promote a methodology for circuit-and-system-level modelling and simulation based on best practice rules, which are used to deal with coupled electromagnetic field-circuit-heat problems, as well as coupled electro-thermal-stress problems that emerge in nanoelectronic designs. This book covers: (1) advanced monolithic/multirate/co-simulation techniques, which are combined with envelope/wavelet approaches to create efficient and robust simulation techniques for strongly coupled systems that exploit the different dynamics of sub-systems within multiphysics problems, and which allow designers to predict reliability and ageing; (2) new generalized techniques in Uncertainty Quantification (UQ) for coupled problems to include a variability capability such that robust design and optimization, worst case analysis, and yield estimation with tiny failure probabilities are possible (including large deviations like 6-sigma); (3) enhanced sparse, parametric Model Order Reduction techniques with a posteriori error estimation for coupled problems and for UQ to reduce the complexity of the sub-systems while ensuring that the operational and coupling parameters can still be varied and that the reduced models offer higher abstraction levels that can be efficiently simulated. All the new algorithms produced were implemented, transferred and tested by the EDA vendor MAGWEL. Validation was conducted on industrial designs provided by end-users from the semiconductor industry, who shared their feedback, contributed to the measurements, and supplied both material data and process data. In closing, a thorough comparison to measurements on real devices was made in order to demonstrate the algorithms’ industrial applicability.

Mathematical models. --- Mathematical optimization. --- Mathematical Modeling and Industrial Mathematics. --- Continuous Optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Models, Mathematical --- Coupled problems (Complex systems) --- Nanoelectronics --- Mathematics. --- Nanoscale electronics --- Nanoscale molecular electronics --- Electronics --- Nanotechnology --- Coupled field problems (Complex systems) --- Problems, Coupled (Complex systems) --- Dynamics

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519.61 --- Coupled problems (Complex systems) --- -Engineering mathematics --- -Numerical analysis --- -Transients (Dynamics) --- -Transient phenomena --- Transient responses --- Dynamics --- Oscillations --- Vibration --- Mathematical analysis --- Engineering --- Engineering analysis --- Coupled field problems (Complex systems) --- Problems, Coupled (Complex systems) --- System analysis --- Numerical methods of algebra --- Numerical solutions --- -Congresses --- Congresses --- Mathematical models --- Mathematics --- -Numerical methods of algebra --- 519.61 Numerical methods of algebra --- -519.61 Numerical methods of algebra --- Transient phenomena --- Engineering mathematics --- Numerical analysis --- Transients (Dynamics) --- Numerical solutions&delete& --- Mathematical models&delete& --- Fluid mechanics. --- Soil mechanics. --- Viscoelasticity.

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Contains contributions originating from the 'Conference on Optimal Control of Coupled Systems of Partial Differential Equations', held at the 'Mathematisches Forschungsinstitut Oberwolfach' in March 2008. This work covers a range of topics such as controllability, optimality systems, model-reduction techniques, and fluid-structure interactions.

Control theory -- Congresses. --- Coupled problems (Complex systems) -- Congresses. --- Differential equations, Partial -- Congresses. --- Mathematical optimization -- Congresses. --- Control theory --- Differential equations, Partial --- Coupled problems (Complex systems) --- Mathematical optimization --- Mathematics --- Civil & Environmental Engineering --- Operations Research --- Calculus --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Coupled field problems (Complex systems) --- Problems, Coupled (Complex systems) --- Mathematics. --- Partial differential equations. --- Partial Differential Equations. --- Dynamics --- System analysis --- Differential equations, partial. --- Partial differential equations --- Control theory - Congresses --- Differential equations, Partial - Congresses --- Coupled problems (Complex systems) - Congresses --- Mathematical optimization - Congresses

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High technology industries are in desperate need for adequate tools to assess the validity of simulations produced by ever faster computers for perennial unstable problems. In order to meet these industrial expectations, applied mathematicians are facing a formidable challenge summarized by these words - nonlinearity and coupling. This book is unique as it proposes truly original solutions: (1) Using hypercomputation in quadratic algebras, as opposed to the traditional use of linear vector spaces in the 20th century; (2) complementing the classical linear logic by the complex logic which

Social sciences --- Qualitative research --- Qualitative analysis (Research) --- Qualitative methods (Research) --- Research --- Data processing. --- Coupled problems (Complex systems) --- Mathematical optimization --- Nonlinear theories --- 519.61 --- 681.3*G4 --- Nonlinear problems --- Nonlinearity (Mathematics) --- Calculus --- Mathematical analysis --- Mathematical physics --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- 681.3*G4 Mathematical software: algorithm analysis; certification and testing; efficiency; portability; reliability and robustness; verification --- Mathematical software: algorithm analysis; certification and testing; efficiency; portability; reliability and robustness; verification --- 519.61 Numerical methods of algebra --- Numerical methods of algebra --- Coupled field problems (Complex systems) --- Problems, Coupled (Complex systems) --- Dynamics