Contents Part I Introduction The COMSON Project Part II Partial Differential Algebraic Equations PDAE Modeling and Discretization

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1 Contents Part I Introduction 1 The COMSON Project... 3 Michael Günther and Uwe Feldmann 1.1 Trends in Microelectronics Scope of the COMSON Project Methodology The Demonstrator Platform E-Learning Modelling, Simulation and Optimisation Partial Differential Algebraic Equations Dynamic Iteration Model Order Reduction Optimisation References Part II Partial Differential Algebraic Equations 2 PDAE Modeling and Discretization Giuseppe Alì, Massimiliano Culpo, Roland Pulch, Vittorio Romano, and Sebastian Schöps 2.1 Introduction on Modeling and PDAEs Mathematical Modeling in Nanoelectronics Classification of PDAE Models Modeling, Analysis and Discretization of Coupled Problems Refined Modeling of Networks with Devices Electro-Thermal Effects at the System Level Multiphysics Modeling via Maxwell s Equations Thermal and Quantum Effects in Semiconductors References ix

2 x Contents 3 Simulation of Coupled PDAEs: Dynamic Iteration and Multirate Simulation Giuseppe Alì, Andreas Bartel, Michael Günther, Vittorio Romano, and Sebastian Schöps 3.1 Aim and Outline Theory of Dynamic Iteration Schemes for Coupled DAEs Description of Coupled Systems Iteration Schemes for Coupled DAE Systems Convergence and Stability Applications in Electrical Engineering Refined Network Models Electro-Thermal Coupling Coupled System of Electric Networks and Maxwell s Magnetoquasistatic Equations and Their Properties Coupled Numerical Simulations of the Thermal Effects in Silicon Devices The Numerical Method Numerical Simulation of the Crystal Lattice Heating in MOSFETs Coupled Circuit-Device Simulation References Part III Model Order Reduction 4 Model Order Reduction: Methods, Concepts and Properties Athanasios C. Antoulas, Roxana Ionutiu, Nelson Martins, E. Jan W. ter Maten, Kasra Mohaghegh, Roland Pulch, Joost Rommes, Maryam Saadvandi, and Michael Striebel 4.1 Circuit Simulation and Model Order Reduction Input-Output Systems in Circuit Simulation The Need for Model Order Reduction MOR Methods Projection Based MOR Truncation Based MOR Other Approaches Examples Summary Eigenvalue Methods and Model Order Reduction Transfer Functions, Dominant Poles and Modal Equivalents Specialized Eigensolution Methods Generalizations to Other Eigenvalue Problems Improving Krylov Models by Using Dominant Poles

3 Contents xi Numerical Examples Concluding Remarks Passivity Preserving Model Order Reduction Model Reduction via Projection Matrices Passive Systems Spectral Zeros and Generalized Eigenvalue Problem Passivity Preserving Model Reduction Model Reduction by Projection Model Reduction by Projection Numerical Results Conclusion Passivity Preserving Model Reduction Using the Dominant Spectral Zero Method Background on MOR MOR by Spectral Zero Interpolation The Dominant Spectral Zero Method Numerical Results Concluding Remarks Appendix: SADPA for Computing Dominant Spectral Zeros A Framework for Synthesis of Reduced Order Models Problem Formulation Foster Synthesis of Rational Transfer Functions Structure Preservation and Synthesis by Unstamping Numerical Examples Conclusions and Outlook References Parameterized Model Order Reduction Gabriela Ciuprina, Jorge Fernández Villena, Daniel Ioan, Zoran Ilievski, Sebastian Kula, E. Jan W. ter Maten, Kasra Mohaghegh, Roland Pulch, Wil H.A. Schilders, L. Miguel Silveira, Alexandra Ştefănescu, and Michael Striebel 5.1 Parametric Model Order Reduction Representation of Parametric Systems Reduction of Parametric Systems Practical Consideration and Structure Preservation Examples Conclusions Robust Procedures for Parametric Model Order Reduction of High Speed Interconnects Field Problem Formulation: 3D PDE Models Numeric Discretization and State Space Models Transmission Lines: 2D + 1D Models Numeric Extraction of Line Parameters

4 xii Contents Variability Analysis of Line Parameters Parametric Models Based on Taylor Series Parametric Circuit Synthesis Case Study Conclusions Model Order Reduction and Sensitivity Analysis Recap MNA and Time Integration of Circuit Equations Sensitivity Analysis Model Order Reduction (with POD) The BRAM Algorithm Sensitivity by Uncertainty Quantification MOR for Singularly Perturbed Systems Model Order Reduction and "-Embedding Test Example and Numerical Results Conclusions References Advanced Topics in Model Order Reduction Davit Harutyunyan, Roxana Ionutiu, E. Jan W. ter Maten, Joost Rommes, Wil H.A. Schilders, and Michael Striebel 6.1 Model Order Reduction of Nonlinear Network Problems Linear Versus Nonlinear Model Order Reduction Some Nonlinear MOR Techniques TPWL and POD Other Approaches Numerical Experiments Model Order Reduction for Multi-terminal Circuits Reduction of R Networks Reduction of RC Networks Numerical Results Concluding Remarks Simulation of Mutually Coupled Oscillators Using Nonlinear Phase Macromodels and Model Order Reduction Techniques Phase Noise Analysis of Oscillator LC Oscillator Mutual Inductive Coupling Resistive and Capacitive Coupling Small Parameter Variation Model for Oscillators Oscillator Coupling with Balun Oscillator Coupling to a Transmission Line Model Order Reduction Numerical Experiments Conclusion References

5 Contents xiii Part IV Optimization 7 Optimization Methods and Applications to Microelectronics CAD Salvatore Rinaudo, Valeria Cinnera Martino, Franco Fiorante, Giovanni Stracquadanio, and Giuseppe Nicosia 7.1 Motivation The Optimization Problem Parameter Extraction for Compact Circuit Models Automatic Physical Layout Optimization of Discrete Power MOSFETs for Reducing the Effects of Current Density Modeling Approach The Optimization Algorithm The Optimization Flow Simulation Results Conclusion References Part V COMSON Methodology 8 COMSON Demonstrator Platform Georg Denk, Tamara Bechtold, Massimiliano Culpo, Carlo de Falco, and Alexander Rusakov 8.1 Introduction Design of the Demonstrator Platform Modules Tutorial on Working with the Demonstrator Platform with Emphasis on MOR Overview and Structure of MOR Modules MOR Case Studies A Step by Step Model Reduction Tutorial Coupled Simulation (MOR + Circuit Simulation) The Demonstrator Platform as a Development Tool for Research Class C Benchmark: n-channel Power MOS-FET Implementation and Development Procedure Simulation Set-Up and Results on the Class C Benchmark References

6 xiv Contents 9 elearning in Industrial Mathematics with Applications to Nanoelectronics Giuseppe Alì, Eleonora Bilotta, Lorella Gabriele, Pietro Pantano, José Sepúlveda, Rocco Servidio, and Alexander Vasenev 9.1 Introduction An Overview on elearning An Historic Perspective elearning in Microelectronics Industry An Integrated Platform for Advanced Training in Microelectronics User Needs Analysis Platform Development The Components of the CoMSON Platform The Information System The CoMSON elearning Platform Graphical User Interfaces User Interfaces in the elearning Platform A Graphical Tool to Visualize Scientific Data in the Simulation Platform Interfacing the Components of the CoMSON Platform elearning Contents Creation: Methods and Strategies General Methods and Strategies for the Development of an elearning Course Some Examples of Course Implementation Practical Strategies for elearning Contents Creation Blended Learning First Empirical Study Second Empirical Study Platform Evaluation: Test and Revision Conclusions and Future Perspectives References Index

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