Designing complex integrated circuits relies heavily on mathematical methods and calls for suitable simulation and optimization tools. The current design approach involves simulations and optimizations in different physical domains (device, circuit, thermal, electromagnetic) and in a range of electrical engineering disciplines (logic, timing, power, crosstalk, signal integrity, system functionality). COMSON was a Marie Curie Research Training Network created to meet these new scientific and training challenges by (a) developing new descriptive models that take these mutual dependencies into account, (b) combining these models with existing circuit descriptions in new simulation strategies and (c) developing new optimization techniques that will accommodate new designs. The book presents the main project results in the fields of PDAE modeling and simulation, model order reduction techniques and optimization, based on merging the know-how of three major European semiconductor companies with the combined expertise of university groups specialized in developing suitable mathematical models, numerical schemes and e-learning facilities. In addition, a common Demonstrator Platform for testing mathematical methods and approaches was created to assess whether they are capable of addressing the industry’s problems, and to educate young researchers by providing hands-on experience with state-of-the-art problems.

This book shows how modern Applied Mathematics influences everyday life. It features contributors from universities, research institutions and industry, who combine research and review papers to present a survey of current research. More than 20 contributions are divided into scales: nano, micro, macro, space and real life. In addition, coverage includes engaging and informative case studies as well as complex graphics and illustrations, many of them in color.

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.

Today's most commonly used circuit models increasingly tend to lose their validity in circuit simulation due to rapid technological developments, miniaturization and increased complexity of integrated circuits. The starting point of this thesis was to tackle these challenges by refining the critical parts of the circuit by combining circuit simulation directly with distributed device models. The approach set out in this thesis couples partial differential equations for electromagnetic devices - modeled by Maxwell's equations -, to differential-algebraic equations, which describe basic circuit elements including memristors and the circuit's topology. First, Maxwell's equations are spatially discretized and a potential formulation is derived, the coupled system is then formulated as a differential-algebraic equation with a properly stated leading term and analyzed. Topological and modeling conditions are presented to guarantee the tractability index of these differential-algebraic equations to be no greater than two. Finally, local solvability, perturbation results and an algorithm to calculate consistent initializations are derived for a general class of differential-algebraic equations with a properly stated leading term having tractability index-2.

Proceedings from the 14th European Conference for Mathematics in Industry held in Madrid present innovative numerical and mathematical techniques. Topics include the latest applications in aerospace, information and communications, materials, energy and environment, imaging, biology and biotechnology, life sciences, and finance. In addition, the conference also delved into education in industrial mathematics and web learning.

This contributed volume convenes a rich selection of works with a focus on innovative mathematical methods with applications in real-world, industrial problems. Studies included in this book are all motivated by a relevant industrial challenge, and demonstrate that mathematics for industry can be extremely rewarding, leading to new mathematical methods and sometimes even to entirely new fields within mathematics. The book is organized into two parts: Computational Sciences and Engineering, and Data Analysis and Finance. In every chapter, readers will find a brief description of why such work fits into this volume; an explanation on which industrial challenges have been instrumental for their inspiration; and which methods have been developed as a result. All these contribute to a greater unity of the text, benefiting not only practitioners and professionals seeking information on novel techniques but also graduate students in applied mathematics, engineering, and related fields.

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This first volume focuses on real-time control theory, data assimilation, real-time visualization, high-dimensional state spaces and interaction of different reduction techniques.

Increasing complexity combined with decreasing geometrical sizes in electric circuit design lead to high dimensional dynamical models to be considered by EDA tools. Model order reduction (MOR) has become a popular strategy to decrease the problem's size while preserving its crucial properties. MOR shall achieve accurate statements on a circuit's behavior within an affordable amount of computational time. Just recently, MOR techniques are designed to consider the differential algebraic nature of the underlying models. We present an approach based on an e-embedding, i.e., a strategy applied in the construction of numerical integration schemes for differential algebraic equations (DAEs). The system of DAEs is transformed into an artificial system of ordinary differential equations (ODEs), since MOR schemes for ODEs can be applied now. We construct, analyze and test different strategies with respect to the usage of the parameter e that transforms the DAEs into ODEs. Moreover, accurate mathematical models for MOS-devices introduce highly nonlinear equations. As the packing density of devices is growing in circuit design, huge nonlinear systems appear in practice. It follows an increasing demand for reduced order modeling of nonlinear problems. In the thesis, we also review the status of existing techniques for nonlinear MOR by investigating the performance of the schemes applied in circuit simulation.

This book is a collection of 65 selected papers presented at the 7th International Conference on Scientific Computing in Electrical Engineering (SCEE), held in Espoo, Finland, in 2008. The aim of the SCEE 2008 conference was to bring together scientists from academia and industry, e.g. mathematicians, electrical engineers, computer scientists, and physicists, with the goal of intensive discussions on industrially relevant mathematical problems, with an emphasis on modeling and numerical simulation of electronic circuits and devices, electromagnetic fields, and coupled problems.This extensive reference work is divided into five parts: 1. Computational electromagnetics, 2. Circuit simulation, 3. Coupled problems, 4. Mathematical and computational methods, and 5. Model-order reduction. Each part starts with an general introduction followed by the actual papers.

This volume is the fifth in a series of proceedings which started in 1999. The contributions include the latest results on the theory of wave propagation, extended thermodynamics, and the stability of the solutions to partial differential equations. Sample Chapter(s). Chapter 1: Reciprocal Transformations and Integrable Hamiltonian Hydrodynamic Type Systems (334 KB). Contents: Quantitative Estimates for the Large Time Behavior of a Reaction-Diffusion Equation with Rational Reaction Term (M Bisi et al.); Linearized Euler''s Variational Equations in Lagrangian Coordinates (G Boillat & Y J Peng); Restabilizing Forcing for a Diffusive Prey-Predator Model (B Buonomo & S Rionero); Fluid Dynamical Features of the Weak KAM Theory (F Cardin); Ricci Flow Deformation of Cosmological Initial Data Sets (M Carfora & T Buchert); Fuchsian Partial Differential Equations (Y Choquet-Bruhat); Analytic Structure of the Four-Wave Mixing Model in Photoreactive Material (R Conte & S Bugaychuk); A Note about Waves in Dissipative and Dispersive Solids (M Destrade & G Saccomandi); Exponential and Algebraic Relaxation in Kinetic Models for Wealth Distribution (B Dring et al.); Solitary Waves in Dispersive Materials (J Engelbrecht et al.); A GinzburgOCoLandau Model for the Ice-Water and Liquid-Vapor Phase Transitions (M Fabrizio); Stability Considerations for Reaction-Diffusion Systems (J N Flavin); A Mechanical Model for Liquid Nanolayers (H Gouin); A Particle Method for a Lotka-Volterra System with Nonlinear Cross and Self-Diffusion (M Groppi & M Sammartino); Transport Properties of Chemically Reacting Gas Mixtures (G M Kremer); Navier-Stokes in Aperture Domains: Existence with Bounded Flux and Qualitative Properties (P Maremonti); On Two-Pulse Interaction in a Class of Model Elastic Materials (A Mentrelli et al.); On a Particle-Size Segregation Equation (C Mineo & M Torrisi); Problems of Stability and Waves in Biological Systems (G Mulone); Multiple Cold and Hot Second Sound Shocks in HE II (A Muracchini & L Seccia); Differential Equations and Lie Symmetries (F Oliveri et al.); Bifurcation Analysis of Equilibria in Competitive Logistic Networks with Adaptation (A Raimondi & C Tebaldi); Poiseuille Flow of a Fluid Overlying a Porous Media (B Straughan); Analysis of Heat Conduction Phenomena in a One-Dimensional Hard-Point Gas by Extended Thermodynamics (S Tanigushi et al.); On Waves in Weakly Nonlinear Poroelastic Materials Modeling Impacts of Meteorites (K Wilmanski et al.); and other papers. Readership: Researchers in mathematics, physics, chemistry and engineering."