Giuseppe Alì

Parabolic Differential-Algebraic Models in Electrical Network Design

In refined network analysis, a compact network model is combined with distributed models for semiconductor devices in a multidimensional approach. For linear RLC networks containing diodes as distributed devices, we construct a mathematical model that joins the differential-algebraic initial value problem for the electric circuit with parabolic-elliptic boundary value problems modeling the diodes. For this mixed initial boundary value problem of partial differential-algebraic equations a first existence and uniqueness result is given, and its asymptotic behavior is discussed.

INDEX-AWARE MODEL ORDER REDUCTION FOR LINEAR INDEX-2 DAES WITH CONSTANT COEFFICIENTS ∗

A model order reduction method for index-2 differential-algebraic equations (DAEs) is introduced, which is based on the intrinsic differential equations and on the remaining algebraic constraints. This extends the method introduced in a previous paper for index-1 DAEs. This procedure is implemented numerically and the results show numerical evidence of its robustness over the traditional methods.

The zero-electron-mass limit in the Euler–Poisson system for both well- and ill-prepared initial data

The Euler–Poisson system consists of the balance laws for electron density and current density coupled to the Poisson equation for the electrostatic potential. The limit of vanishing electron mass of this system with both well- and ill-prepared initial data on the whole space case is discussed in this paper. Although it has some relations to the incompressible limit of the Euler equations, i.e. the limit velocity satisfies the incompressible Euler equations with damping, things are more complicated due to the linear singular perturbation including the coupling with the Poisson equation. A careful analysis on the structure of the linear perturbation has been done so that we are able to show the convergence for well-prepared initial data and ill-prepared initial data where the convergence occurs away from time t = 0.

Index-aware model order reduction for differential-algebraic equations

We introduce a model order reduction (MOR) procedure for differential-algebraic equations, which is based on the intrinsic differential equation contained in the starting system and on the remaining algebraic constraints. The decoupling procedure in differential and algebraic part is based on the projector and matrix chain which leads to the definition of tractability index. The differential part can be reduced by using any MOR method, we use Krylov-based projection methods to illustrate our approach. The reduction on the differential part induces a reduction on the algebraic part. In this paper, we present the method for index-1 differential-algebraic equations. We implement numerically this procedure and show numerical evidence of its validity.

A hydrodynamical model for covalent semiconductors with a generalized energy dispersion relation

We present the first macroscopical model for charge transport in compound semiconductors to make use of analytic ellipsoidal approximations for the energy dispersion relationships in the neighbours of the lowest minima of the conduction bands. The model considers the main scattering mechanisms charges undergo in polar semiconductors, that is the acoustic, polar optical, intervalley non-polar optical phonon interactions and the ionized impurity scattering. Simulations are shown for the cases of bulk 4H and 6H-SiC.

Analysis of a PDE Thermal Element Model for Electrothermal Circuit Simulation

In this work we address the well-posedness of the steady-state and transient problems stemming from the coupling of a network of lumped electric elements and a PDE model of heat diffusion in the chip substrate. In particular we consider the thermal element model presented in [1] and we prove that it can be controlled by any combination of voltage sources (imposing the average current in a region of the chip) and current sources (imposing the Joule power per unit area produced in a region) connected to its temperature nodes. This result justifies the implementation of the element as a linear n-port conductance as carried out in [2].

A Convergent Iteration Scheme for Semiconductor/Circuit Coupled Problems

A dynamic iteration scheme is proposed for a coupled system of electric circuit and distributed semiconductor (pn-diode) model equations. The device is modelled by the drift-diffusion (DD) equations and the circuit by MNA-equations. The dynamic iteration scheme is investigated on the basis of discrete models and coupling via sources and compact models. The analytic divergence and analytic convergence results are verified numerically.

Existence and Uniqueness for an Elliptic PDAE Model of Integrated Circuits

In refined network analysis, a compact network model is coupled with distributed models for interconnects and semiconductor devices, linking differential-algebraic equations to partial differential equations, thus creating PDAEs. This paper deals with linear RLC networks containing one-dimensional diodes as distributed devices, modeled by the stationary drift-diffusion equations. For the resulting mixed initial boundary value problem we prove a uniqueness result for solutions close to equilibrium, i.e., with small initial data and electrical sources, based on a contraction argument.

Scientific computing in electrical engineering

Coupled Problems.- A Unified Approach for the Analysis of Networks Composed of Transmission Lines and Lumped Circuits.- Circuit Simulation for Nanoelectronics.- Hot-Phonon Effects on the Transport Propertiesof an Indium Phosphide n+?n?n+ Diode.- Modeling and Simulation for Thermal-Electric Coupling in an SOI-Circuit.- A Staggered ALE Approach for Coupled Electromechanical Systems.- Orthogonalisation in Krylov Subspace Methodsfor Model Order Reduction.- Algebraic Sparsefied Partial Equivalent Electric Circuit (ASPEEC).- Analytical and Numerical Techniques for Simulatinga 3D Rainwater Droplet in a Strong Electric Field.- 3-D FE Particle Based Model of Ion Transport Across Ionic Channels.- Coupled Calculation of Electromagnetic Fields and Mechanical Deformation.- Circuit Simulation.- Challenging Coupled Problems in TCAD.- On the Formulation and Lumped Equivalents Extraction Techniques for the Efficient Modeling of Long Interconnects.- Symbolic Methods in Industrial Analog Circuit Design.- Index Analysis of Multirate Partial Differential-Algebraic Systems in RF-Circuits.- Semidiscretisation Methods for Warped MPDAEs.- Qualitative Properties of Equilibria in MNA Models of Electrical Circuits.- State and Semistate Models of Lumped Circuits.- An Index Analysis from Coupled Circuit and Device Simulation.- Multirate Methods in Chip Design: Interface Treatment and Multi Domain Extension.- Digital Linear Control Theory for Automatic Stepsize Control.- A General Compound Multirate Method for Circuit Simulation Problems.- Stochastic Differential Algebraic Equations in Transient Noise Analysis.- Electromagnetism.- Finite Element Modelling of Electrical Machines and Actuators.- Adaptive FEM Solver for the Computation of Electromagnetic Eigenmodes in 3D Photonic Crystal Structures.- COLLGUN: a 3D FE Simulator for the Design of TWTs Electron Guns and Multistage Collectors.- A New Thin-Solenoid Model for Accurate 3-D Representation of Focusing Axisymmetric Magnetic Fields in TWTs.- Hybridised PTD/AWE for Modelling Wide-Band Electromagnetic Wave Scattering.- Transverse Electric Plane Wave Scattering by Two Infinitely Long Conducting Elliptic Cylinders: Iterative Solution.- Simulation of Microwave and Semiconductor Laser Structures Including PML: Computation of the Eigen Mode Problem, the Boundary Value Problem, and the Scattering Matrix.- Solving of an Electric Arc Motion in a Vacuum Interrupter.- Analysis of Eddy Currents in a Gradient Coil.- An Integration of Optimal Topology and Shape Design for Magnetostatics.- Numerical Computation of Magnetic Field and Inductivity of Power Reactor with Respect of Real Magnetic Properties of Iron Core.- Calculation of 3D Space-Charge Fields of Bunches of Charged Particles by Fast Summation.- Comparison of the A,V -formulation and Hiptmairs Smoother.- Iterative Solution of Field Problems with a Varying Physical Parameter.- General Mathematical and Computational Methods.- Time Integration Methods for Coupled Equations.- Two-Band Quantum Models for Semiconductors Arising from the Bloch Envelope Theory.- Mixed Finite Element Numerical Simulation of a 2D Silicon MOSFET with the Non-Parabolic MEP Energy-Transport Model.- Comparison of Different Methodologies for Parameter Extraction in Circuit Design.- Sound Synthesis and Chaotic Behaviour in Chuas Oscillator.- A Kinetic Type Extended Model for Polarizable and Magnetizable Fluids.- Quantum Corrected Drift-Diffusion Modeling and Simulation of Tunneling Effects in Nanoscale Semiconductor Devices.- Reverse Statistical Modeling for Analog Integrated Circuits.- Coupled EM & Circuit Simulation Flow for Integrated Spiral Inductor.- An Optimal Control approach for an Energy Transport Model in Semiconductor Design.- A Multigroup-WENO Solver for the Non-Stationary Boltzmann-Poisson System for Semiconductor Devices.- Deterministic Numerical Simulation of 1d Kinetic Descriptions of Bipolar Electron Devices.- A Hybrid Intelligent Computational Methodology for Semiconductor Device Equivalent Circuit Model Parameter Extraction.- A SPICE-Compatible Mobility Function for Excimer Laser Annealed LTPS TFT Analog Circuit Simulation.- Parallelization of WENO-Boltzmann Schemes for Kinetic Descriptions of 2D Semiconductor Devices.- Hole Mobility in Silicon Semiconductors.- Anisotropic Mesh Adaptivity Via a Dual-Based A Posteriori Error Estimation for Semiconductors.- Kinetic Relaxation Models for the Boltzmann Transport Equation for Silicon Semiconductors.- Exact Solutions for the Drift-Diffusion Model of Semiconductors via Lie Symmetry Analysis.- Different Extrapolation Strategies in Implicit Newmark-Beta Schemes for the Solution of Electromagnetic High-Frequency Problems.- Basic Research for Software Tools and Work in Progress.- Electromagnetic Characterization Flow of Leadless Packages for RF Applications.- Domain Decomposition Techniques and Coupled PDE/ODE Simulation of Semiconductor Devices.- Interconnection Modeling Challenges in System-in-Package (SiP) Design.- General Linear Methods for Nonlinear DAEs in Circuit Simulation.

Hyperbolic PDAEs for Semiconductor Devices Coupled with Circuits

We address the problem of coupling a system of network equations corresponding to an electric circuit with a detailed model for a device connected to the circuit. The device is modeled by an hydrodynamic model based on the maximum entropy principle, which results in a hyperbolic system of partial differential equations. We perform a numerical simulation with an oscillator coupled with an n-n-n channel.