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Über dieses Buch

This collection of selected papers presented at the 12th International Conference on Scientific Computing in Electrical Engineering, SCEE 2018, held in Taormina, Sicily, Italy, in September 2018, showcases the state of the art in SCEE.

The aim of the SCEE 2018 conference was to bring together scientists from academia and industry, mathematicians, electrical engineers, computer scientists, and physicists, and to promote intensive discussions on industrially relevant mathematical problems, with an emphasis on the modeling and numerical simulation of electronic circuits and of electromagnetic fields.

This extensive reference work is divided into five parts: Computational Electromagnetics, Device Modeling and Simulation, Circuit Simulation, Mathematical and Computational Methods, Model Order Reduction. Each part starts with a general introduction, followed by the respective contributions.

The book will appeal to mathematicians and electrical engineers. Further, it introduces algorithm and program developers to recent advances in the other fields, while industry experts will be introduced to new programming tools and mathematical methods.

Inhaltsverzeichnis

Frontmatter

Computational Electromagnetics

Frontmatter

Surface Charging Formulations for Engineering Applications: Validation by Experiments and Transient Models

Abstract
Electrostatic BEM (Boundary Element Method) formulations are presented for the calculation of dielectric surface charging, including saturation and restrike phenomena. The simulation results turn out to be in agreement with surface potential measurements in a simple rod-barrier-plane configuration, where lightning impulses initiate streamers and charge accumulation on the barrier. The usefulness of the given BEM-formulation is additionally supported by transient charging simulations in the framework of an electric carrier drift model.
Andreas Blaszczyk, Thomas Christen, Hans Kristian Meyer, Michael Schueller

A Mass-Lumped Mixed Finite Element Method for Maxwell’s Equations

Abstract
A novel mass-lumping strategy for a mixed finite element approximation of Maxwell’s equations is proposed which on structured orthogonal grids coincides with the spatial discretization of the Yee scheme. The proposed method, however, generalizes naturally to unstructured grids and anisotropic materials and thus yields a natural variational extension of the Yee scheme for these situations.
Herbert Egger, Bogdan Radu

Adaptive Mesh Refinement Adaptive mesh refinement for Rotating Electrical Machines Rotating electrical machines Taking into Account Boundary Approximation Errors

Abstract
In this work we present an error estimator for a class of second order quasilinear elliptic problems in 2D. The computational domain consists of two parts—called rotor and stator in the framework of electrical motors—separated by a curvilinear interface. For the coupling of the rotor and the stator on the interface we use a Nitsche technique as described in Hollaus et al. (Nitsche-type mortaring for Maxwell’s equations, In: Progress in electromagnetics research symposium proceedings, Cambridge, pp 397–402, 5–8 July 2010). The residual error estimator is constructed similarly to the approach used in Houston et al. (IMA J Numer Anal 28:245–273, 2008) with adaptations due to the coupling strategy. The error estimator takes into account the polygonal approximation of the stator and the rotor using ideas from hierarchical error estimates.
Armin Fohler, Walter Zulehner

Isogeometric Simulation and Shape Optimization with Applications to Electrical Machines

Abstract
Future e-mobility calls for efficient electrical machines. For different areas of operation, these machines have to satisfy certain desired properties that often depend on their design. Here we investigate the use of multipatch Isogeometric Analysis (IgA) for the simulation and shape optimization of the electrical machines. In order to get fast simulation and optimization results, we use non-overlapping domain decomposition (DD) methods to solve the large systems of algebraic equations arising from the IgA discretization of underlying partial differential equations. The DD is naturally related to the multipatch representation of the computational domain, and provides the framework for the parallelization of the DD solvers.
Peter Gangl, Ulrich Langer, Angelos Mantzaflaris, Rainer Schneckenleitner

Techniques for Modeling Fiber Laser Amplifiers

Abstract
Numerical techniques for simulation of electromagnetic wave propagation within fiber amplifiers are discussed. Since a full-featured simulation using the Maxwell system on a realistic fiber is beyond reach, simplified models using Coupled Mode Theory (CMT) form the state of the art. This work presents a novel concept of an equivalent short fiber, namely an artificial fiber which imitates a longer fiber in essential characteristics. A CMT simulation on an equivalent short fiber requires only a fraction of the computational resources needed to simulate the full length fiber.
Jay Gopalakrishnan, Tathagata Goswami, Jacob Grosek

A Thermal Extension of Tellinen’s Scalar Hysteresis Model Tellinen’s Scalar Hysteresis Model

Abstract
There exist different models which approximate the phenomenon of magnetic hysteresis. Only some of them inherently consider the thermal dependency of hysteresis or have been extended with that respect. In this paper, Tellinen’s scalar magnetic hysteresis model is reviewed and illustrated. Thereby, special focus is laid upon the physical motivation. Afterwards, the underlying concept is adapted and extended w.r.t. thermal behavior. In the end, a temperature dependent scalar magnetic hysteresis model is deduced and investigated.
Jan Kühn, Andreas Bartel, Piotr Putek

Computational Characterization of a Composite Ceramic Block for a Millimeter Wave Heat Exchanger

Abstract
Electromagnetic and electromagnetic-thermal coupled problems are solved by the finite-difference time-domain technique for an AlN:Mo composite ceramic block backed by a thin metal plate and irradiated by a high-power W-band plane wave. Computation is based on experimental data on temperature-dependent complex permittivity, specific heat, and thermal conductivity. Non-uniformity of patterns of dissipated power and temperature is quantified via standard-deviation-based metrics. A 10×10×10±2 mm block of the composite with concentration of Mo from 0.25 to 4% is considered as irradiated by the plane wave with power density on the block’s front surface from 0.3 to 1.0 W/mm2 at 95 GHz. It is shown that the block can be heated up to 1000 oC highly uniformly for 50–110 s. The composite producing maximum total dissipated power is found to have Mo content about 3%.
Petra Kumi, Jonathan S. Venne, Vadim V. Yakovlev, Martin S. Hilario, Brad W. Hoff, Ian M. Rittersdorf

Device Modeling and Simulation

Frontmatter

Modeling Mechanochemistry in Li-ion Batteries

Abstract
Mechanochemistry in Li-ion batteries involve interaction of ions migrating in a cell with mechanical stresses as well as electromagnetic fields. We aim at modeling this multiphysics in a battery cell by involving thermomechanics with the corresponding balance equations of mass, momentum, energy and electromagnetism with the aid of the Maxwell equations. Before applying specific assumptions relevant for Li-ion batteries, we address developing a complete theory by using continuum mechanics and thermodynamics.
Bilen Emek Abali

Automatic Extraction of Transport Model Parameters of an Organic Semiconductor Organic semiconductor Material

Abstract
In Africa et al. (Sci Rep 7(1):3803, 2017) a step-by-step procedure was presented that enables to determine the density of states width, the carrier mobility and the injection barrier height of an OTFT! structure by fitting data from simple measurements to suitable numerical simulations. At each step of the procedure only one parameter value is determined, thus highly simplifying the fitting procedure and enhancing its robustness. In this study we apply such procedure to p-type organic polymers. A very satisfactory fitting of experimental measurements is obtained, and physically meaningful values for the aforementioned parameters are extracted thus further confirming the soundness of the parameter extraction method.
Pasquale Claudio Africa, Dario A. Natali, Mario Caironi, Carlo de Falco

On a Bloch-Type Model with Electron–Phonon Interactions: Modeling and Numerical Simulations

Abstract
In this work, we discuss how to take into account electron–phonon interactions in a Bloch type model for the description of quantum dots. The model consists in coupling an equation on the density matrix with a set of equations on quantities called phonon-assisted densities, one for each phonon mode. After a description of the model, we discuss how to discretize efficiently this non-linear coupling in view of numerical simulations.
Brigitte Bidégaray-Fesquet, Clément Jourdana, Kole Keita

Charge and Phonon Transport in Suspended Monolayer Graphene

Abstract
Thermal effects are playing a crucial role for the design of electron nanoscale devices. The present contribution deals with charge and phonon transport under an applied external electric field in a suspended monolayer of graphene. A major question is represented by the phonon-phonon collision operator involving in general a three particle scattering mechanism. To model the phonon-phonon interactions a relaxation time approximation is employed. This requires the introduction of a local equilibrium phonon temperature whose definition is still a matter of debate for a general non equilibrium situation. Here, two different approaches are presented and discussed.
Marco Coco, Giovanni Mascali, Vittorio Romano

Monte Carlo Simulation Monte Carlo simulation of Electron-Electron Interactions in Bulk Silicon

Abstract
We have developed a novel Monte Carlo (MC) algorithm to study carrier transport in semiconductors in the presence of electron-electron scattering (EES). It is well known that the Boltzmann scattering operator for EES is nonlinear in the single-particle distribution function. Numerical solution methods of the resulting nonlinear Boltzmann equation are usually based on more or less severe approximations. In terms of the pair distribution function, however, the scattering operator is linear. We formulate a kinetic equation for the pair distribution function and related MC algorithms for its numerical solution. Assuming a spatially homogeneous system we derived a two-particle MC algorithm for the stationary problem and an ensemble MC algorithm for the transient problem. Both algorithms were implemented and tested for bulk silicon. As a transient problem we analyzed the mixing of a hot and a cold carrier ensemble. The energy of the hot ensemble relaxes faster with EES switched on. The cold ensemble is temporarily heated by the energy transferred from the hot ensemble. Switching on the electric field rapidly is known to result in an velocity overshoot. We observe that EES enhances the overshoot. The stationary algorithm was used to calculate the energy distribution functions at different field strengths.
Guillermo Indalecio, Hans Kosina

Semi-classical and Quantum Hydrodynamic Modeling of Electron Transport in Graphene

Abstract
The present work aims at formulating hydrodynamic models for a proper description of charge transport in graphene, which is extremely important for growing technological development in CAD tools. The analysis is carried out in two different steps. Initially a semi-classical hydrodynamic model is developed starting from the moment system associated with Boltzmann equation and obtaining the closure relations with the Maximum Entropy Principle. At this level quantum effects are neglected. In the second step the model previously developed is extended to include quantum effects by incorporating the first order quantum corrections. To asses the validity of this model numerical simulations are under current investigation.
Liliana Luca, Vittorio Romano

Quantum Model for the Transport of Nearly Localized Particles

Abstract
A quantum model based on the Gaussian-Hermite expansion of the wave function of a system of n particles is proposed. The dynamics is described by trajectories in a configuration space. Our method is designed to provide some corrections to the classical motion of nearly localized particles. As an application of our model we describe the motion of a nearly localized particle in a 2D confining structure.
Omar Morandi

Wigner Monte Carlo Simulation of a Double Potential Barrier

Abstract
The Wigner transport equation can be solved stochastically by Monte Carlo simulations, based on the generation and annihilation of particles. This creation mechanism has been recently understood in terms of the Markov jump process, producing new stochastic algorithms. One of this has been used to investigate the quantum transport through a double potential barrier.
Orazio Muscato

Simulation of Graphene Field Effect Transistors

Abstract
Field effects transistors, where the active region is constituted by a single layer of graphene, are simulated and the characteristic curves are shown. The current–voltage curves present a behaviour different from that of devices made of classical semiconductors, like Si or GaAs, because of the zero gap in monolayer graphene. The current is no longer a monotone function of the gate voltage but there exists an inversion gate voltage corresponding to which the type of majority carriers changes. Usually the considered devices are investigated by adopting reduced one dimensional models with some averaging procedure. Here a full two-dimensional simulation is presented. The model is based on a system of drift-diffusion equations for electrons and holes. The numerical method is based on the Scharfettel and Gummel scheme. A special treatment of the Poisson equation is adopted for taking into account the charge in the graphene sheet. The characteristic curves for fixed gate voltages and for fixed source-drain voltages have been obtained.
Giovanni Nastasi, Vittorio Romano

Circuit Simulation

Frontmatter

LinzFrame: A Modular Mixed-Level Simulator with Emphasis on Radio Frequency Circuits

Abstract
Purpose: LinzFrame is a circuit and device simulator with emphasis on radio frequency circuits (RF) applications. Slowly changing amplitudes are modulated by a carrier signal at a very high center frequency. These waveforms are referred to as multi-tone signals. RF devices are often distributed elements, i.e. their behavior cannot be adequately represented by terminal voltages and currents.
Design/Methodology: Besides SPICE-like analysis features LinzFrame offers several techniques dedicated to RF circuits. Among them are the multi-tone Harmonic Balance (HB), periodic steady state shooting method, a toolbox for autonomous circuits (oscillators), and multi-rate envelope methods. Besides transient analysis based on the BDF formulas, a toolbox for a spline-wavelet approximation has been developed. This technique combines the advantages of variable time step techniques (such as BDF) with a compact representation of signals by a set of basis functions (such as HB). In contrary to HB a spline-wavelet representation of signals with variable refinements allows for a representation of signals with sharp slew rates without the unwanted Gibbs phenomenon.
In recent time, the simulator has been extended to a circuit-device mixed-level simulator by coupling the circuit simulator to a TCAD simulator. This feature enables the co-simulation of device and circuit levels, where the critical devices are simulated and optimized in full 3D, such as distributed elements.
Originality/Value: LinzFrame enables the holistic (strong) coupling of a circuit and a device simulator, enabling either modeling of the circuit/device as lumped (concentrated) model or as a full 3D model, depending on the needed accuracy. Moreover it circumvents the prohibitive run-time of conventional transient analysis by several multi-rate techniques dedicated to RF circuits/devices.
Kai Bittner, Hans Georg Brachtendorf, Wim Schoenmaker

Fast Transient Simulation of RC Circuits with Dense Capacitive Coupling

Abstract
The main motivation of this work is lying in the acceleration of transient simulation of Analog Mixed Signal circuits. In the electronics industry, smaller and faster electronic devices are always demanded. Full device-parasitic transient simulations of realistic circuits are time consuming or even infeasible due to a huge number of electrical components and unavoidable parasitics. In this paper, we introduce a novel technique to address the problem with the presence of parasitic capacitances. The SelectC technique activates/inactivates coupling capacitances during the transient simulation, therefore, giving faster transient simulation time.
N. T. K. Dang, J. M. L. Maubach, J. Rommes, P. Bolcato, W. H. A. Schilders

Predictor/Corrector Newton-Raphson (PCNR): A Simple, Flexible, Scalable, Modular, and Consistent Replacement for Limiting in Circuit Simulation

Abstract
Modern circuit simulators predominantly use Newton-Raphson (NR) iteration to solve circuit equations. To improve NR convergence, circuit simulators use a practice called “limiting”. This ensures that sensitive circuit quantities (such as diode voltages) do not change too much between successive NR iterations. However, in most simulators, the implementation of limiting tends to be inflexible, non-modular, inconsistent, and confusing. We therefore propose Predictor/Corrector Newton-Raphson (PCNR), a replacement for limiting that overcomes these disadvantages while incurring modest computational overhead. The key ideas behind PCNR are, (1) to add each limited circuit quantity as an extra unknown to the circuit’s Modified Nodal Analysis (MNA) system of equations, (2) to split each NR iteration into a “prediction” phase followed by a “correction” phase, and (3) to mitigate the computational cost of the extra unknowns by eliminating them from all Ax = b solves using a Schur complement based technique.
Karthik V. Aadithya, Eric R. Keiter, Ting Mei

Mathematical and Computational Methods

Frontmatter

GCA- Matrix Compression for Electrostatic Simulations

Abstract
We consider a compression method for boundary element matrices arising in the context of the computation of electrostatic fields. Green cross approximation combines an analytic approximation of the kernel function based on Green’s representation formula and quadrature with an algebraic cross approximation scheme in order to obtain both the robustness of analytic methods and the efficiency of algebraic ones. One particularly attractive property of the new method is that it is well-suited for acceleration via general-purpose graphics processors (GPUs).
Steffen Börm, Sven Christophersen

On Symmetry Reductions of a Third-Order Partial Differential Equation

Abstract
This work is devoted to perform symmetry reductions of a third-order partial differential equation belonging to a wide class which models many real-world phenomena. In particular, many third-order partial differential equations of this class appear in different macroscopic models for semiconductors, which consider quantum effects, for instance, quantum hydrodynamic models; or models for the transmission of electrical lines, among others. The symmetry group of the considered equation has been determined. We prove that this group constitutes a three-dimensional solvable Lie group which allows us to reduce the equation to a first-order nonlinear ODE. Furthermore, a solution of the equation is determined by quadrature in a particular case.
M. S. Bruzón, R. de la Rosa, M. L. Gandarias, R. Tracinà

An Unbiased Hybrid Importance Sampling Monte Carlo Approach for Yield Estimation in Electronic Circuit Design

Abstract
The yield of an Integrated Circuit (IC) is commonly expressed as the fraction (in %) of working chips overall manufactured chips and often interpreted as the failure probability of its analog blocks. We consider the Importance Sampling Monte Carlo (ISMC) as a reference method for estimating failure probabilities. For situations where only a limited number of simulations is allowed, ISMC remains unattractive. In such cases, we propose an unbiased hybrid Monte Carlo approach that provides a fast estimation of the probability. Hereby we use a combination of a surrogate model, ISMC technique and the stratified sampling.
Anuj Kumar Tyagi, Xavier Jonsson, Theo Beelen, W. H. A. Schilders

Shape Optimization of a PM Synchronous Machine Under Probabilistic Constraints

Abstract
This paper proposes a robust and reliability-based shape optimization method to find the optimal design of a permanent magnet (PM) synchronous machine. Specifically, design of rotor poles and stator teeth is subjected to the shape optimization under manufacturing tolerances/imperfections and probabilistic constraints. In a forward problem, certain parameters are assumed to be random. This affects also a shape optimization problem, which is formulated in terms of a tracking-type robust cost functional. The latter is equipped with probabilistic constraints in order to attain a new, desired, robust design. The topological gradient is evaluated using the Topological Asymptotic Expansion Method, to which we apply a Stochastic Collocation Method. In the end, to illustrate our approach, we provide the optimization results for a 2D model of the PM machine.
Piotr Putek, Andreas Bartel, E.  Jan W. ter Maten, Michael Günther

Topology Shape and Parametric Design Optimization of Hall Effect Thrusters

Abstract
In magnetics, topology optimization (TO) is a tool helping to find a suitable ferromagnetic material space distribution in order to meet magnetic specifications. TO is a tool that becomes very interesting when the designer looks for new and original structures. Herein, TO is used to design a Hall-effect thruster. But, the topological solutions are often not feasible. In order to remedy to this, shape optimization (SO) and parametric optimization (PO) are carried out on the topological solution. SO and PO take account of the manufacturing constraints as well as the non linearity of the ferromagnetic materials.
Rtimi Youness, Maxime Bonnet, Frédéric Messine, Carole Hénaux

Model Order Reduction

Frontmatter

Quasi-Schur Transformation for the Stable Compact Modeling of Piezoelectric Energy Harvester Devices

Abstract
The ‘Schur after MOR’ method has proved successful in obtaining stable reduced piezoelectric device models. Even though the method is already used in industry, the stability preservation of ‘Schur after MOR’ is still mathematically unproven. In this work, we show that the involved quasi-Schur transformation indeed does efficiently re-stabilize the aforementioned reduced piezoelectric energy harvester models. The transformation is only quasi-Schur as the unstable reduced systems require eigenspace projection and approximation to become Schur-transformable. During the transformation, the negative eigenvalues are eliminated from the reduced stiffness matrix and the system is stabilized. Further, we compare ‘Schur after MOR’ to another recently presented stabilization method: ‘MOR after Implicit Schur’. We show that the computational effort is significantly reduced.
Siyang Hu, Chengdong Yuan, Tamara Bechtold

Stability Preservation in Model Order Reduction of Linear Dynamical Systems

Abstract
We examine projection-based model order reduction of Galerkin-type for linear dynamical systems. In the case of ordinary differential equations, a transformation of the original system guarantees that any reduced system inherits asymptotic stability. The transformation matrix satisfies a high-dimensional Lyapunov equation. We use a frequency domain approach, where the solution of the Lyapunov equation represents a matrix-valued integral. Consequently, quadrature methods yield approximations in numerical computations. In the case of differential-algebraic equations, the stabilization technique is applicable via a regularization. We present numerical results for a test example.
Roland Pulch

Backmatter

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