Scientific Computing in Electrical Engineering

We compare different model reduction methods applied to the dynamical system of a coupled transmission line: balanced truncation (BT), truncation by balancing one gramian (or PMTBR - poor man's truncated balanced reduction), positive real balanced truncation (PRBT) and its Hamiltonian implementation (PRBT-Ham), PRIMA, spectral zero method (SZM) and its Hamiltonian implementation (SZM-Ham), and finally, optimal

ℌ

2

. Their performance is analyzed in terms of several criteria such as: preservation of controllability, observability, stability and passivity, relative

ℌ

2

and

ℌ

∞

norms, and the computational cost involved.

This paper deals with the transient simulation of large, nonlinear magnetoquasistatic field models which are monolithically coupled to electric circuits. Solid- and stranded-conductor models embedded in the field model are connected to the external circuit. In order to guarantee the numerical efficiency of the field-circuit coupled formulation, conductor models coupling the circuit to the field at a reference crosssection, have to be preferred over conductor models that couple the whole conductor volume to the circuit. The circuit is formulated in terms of both voltage drops and currents in order to avoid fill-in in the field matrix parts. For time stepping, an error-controlled, adaptive singly diagonally Runge-Kutta method is applied. A dense output solution is used to detect and localise switching events in the circuit. The actual time step is restricted to the time instant of switching at which consistent initial conditions are determined before restarting the time integration. The transient field-circuit coupling is applied to the models of a capacitor motor and a three-phase transformer.

The number of physical effects that have to be taken into account to accurately model and design current and future micro- and nano-electronics devices is continuously increasing. At the same time, the importance of the coupling among them is increasing as well. An accurate simulation of such effects with strong interactions is often non-trivial and in many cases a satisfactory solution is not yet available. Two challenging problems are presented in more detail: the first one refers to the thermomechanical problem of silicon oxidation, the second is the electrical coupling which occurs in strained silicon substrate.

Atmospheric aerosols exhibit a high degree of variability in their properties and their spatial and temporal distribution. Laser remote sensing is now-days used to provide systematic monitoring of the temporal evolution of the aerosol in order to understand the radiative, physical, chemical and dynamic processes in the atmosphere. In this paper, we present a new method for solving the inverse problem in LIDAR sounding based on a hybrid regularization procedure.

In this communication we present the CoMSON Demonstrator Platform (DP), a software tool designed to help researchers in testing and validating models and algorithms for coupled simulation of nanoelectronic circuits and devices. The structure of the DP is presented with an explanation of the motivations behind the critical design choices. A multilevel simulation of a CMOS AND gate using two different coupling algorithms is provided as an application example. The example is intended to demonstrate the suitability of the DP as a flexible prototyping environment and its ability to cope with real life industrial problems. In the numerical simulations both the semi-classical Drift-Diffusion model (DD) and a Quantum Corrected DD model (QCDD) are employed and their predictions are compared.

The paper presents an investigation of the magnetic field influence within low voltage switching process in vacuum, in the case of strong currents interrupting. The axial, transverse and radial magnetic field action upon the vacuum electric arc behavior is analyzed on a mono-phase model. The conclusions obtained by modeling the electromagnetic field in the vacuum quenching chamber are compared with the experimental results. The experimental set-up can reproduce the real switching conditions of the power vacuum circuit-breaker. The goal of the study is the improvement of the circuit-breaker switching capabilities.

Next-generation nano-scale RF-IC designs have an unprecedented complexity and performance that will inevitably lead to costly re-spins and loss of market opportunities. In order to cope with this, the aim of the European Framework 6 CHAMELEON RF project is to develop methodologies and prototype tools for a comprehensive and highly accurate analysis of complete functional IC blocks. These blocks will operate at RF frequencies of up to 60 GHz. In this paper an overview of the CHAMELEON RF project will be given and the first results achieved in the CHAMELEON RF project will be presented.

The paper reports the use of Finite Element (FE) simulation and experiments meant to explore the operation conditions of the PieZoelectric wafer Transducer (PZT). Piezoelectrics is the coupling of structural and electric fields and may be solved using the multi-physics approach. Accordingly, three different multiphysics models were developed to investigate a plane strain problem. The first one includes two PZTs mounted on an aluminium plate and is used to model both the emission and reception signals. The next two ones are developed to separately model the emission and detection processes, in order to decrease the computational effort. The wave displacements are generated by a PZT-like actuator and the output voltage is obtained at a PZT receiver both by a multi-physics approach. The analysis considered the transducer lengths, the effects of the finite pulse width, the pulse dispersion and the detailed interaction between the piezoelectric element and the transmitting medium. The transmitted and received signals for so-called A0 and S0 modes have maxima close to the frequencies predicted in other works. A series of sensitivity curves relating the generation and receiving of Lamb waves were also determined and plotted as a function of the pulse center frequency and of the PZT lengths.

In a load-commutated synchronous motor, the torque is driven by the currents in the stator windings, and these currents depend on the rotor position. Since the stator phases are star-connected, the static torque generated by two stator phases connected in series and powered with a constant current offers sufficient information to design a suitable current control strategy. The synchronous machine studied has a reverse type of construction. The switching sequence for the current inverter is correlated with the rotor position by magnetostatic simulation in FLUX2D, using the maximization of static torque as optimization criteria. This study also covers a computational method for determining the operating parameters of a synchronous machine using simulation of the Standstill Frequency Response Test (SSFR).

This paper presents a possibility of modelling the electromagnetic field, by taking into account the symmetry of the domains. The domain discretisation and implicitly the finite volume shape will be derived from the type of the symmetry. Thus, a reduction of the problem size, as well as a guaranteed symmetry of the solution, and a better approximation of the borders and of the discontinuity surfaces are achieved.

The design of microwave and millimeter wave devices requires more and more accurate synthesis procedures to satisfy the increasingly stringent specifications of modern communication systems [1]. Most of the available synthesis techniques are based on models that do not conveniently describe the physical behavior of circuits. The goal of the present paper is to calculate the scattering matrix for the case of single and cascaded strip gratings.

The strip gratings allow a complete transmission of certain frequencies and a complete reflection at other frequencies and, then, exists a simple type of frequency selective surface [2]. A wide variety of filter characteristics can be obtained by cascading multiple layers of frequencies-selective surfaces. In this paper, a new method for scattered matrix analysis is presented. This method is based on Floquet harmonics analysis.

This paper summarizes the recent circuit-simulation activities [Roo04]–[Sil06] at Helsinki University of Technology (TKK), Circuit Theory Laboratory (CTL). This paper is mostly based on the results of the national projects Advanced Radio Frequency SImulation and Modeling (ARFSIM 2002–2003) [Roo04], MOdeling and Simulation for Advanced Integrated Circuits and Systems (MOSAICS 2004–2005), and Accurate Models Aim for Zero Errors (AMAZE 2006–2008). All these projects have been funded by the National Technology Agency of Finland, Nokia Corporation, and AWR–APLAC Corporation; the annual volume at TKK CTL has been 4.0–5.5 man years. In these projects, APLAC circuit simulation and design tool [A06] has been used as a common platform for the circuit analysis and modeling methods developed.

With roots dating back to many years ago and applications in a wide variety of areas, model order reduction has emerged in the last few decades as a crucial step in the simulation, control, and optimization of complex physical systems. Reducing the order or dimension of models of such systems, is paramount to enabling their simulation and verification. While much progress has been achieved in the last few years regarding the robustness, efficiency and applicability of these techniques, certain problems of relevance still pose difficulties or renewed challenges that are not satisfactorily solved with the existing approaches. Furthermore, new applications for which dimension reduction is crucial, are becoming increasingly relevant, raising new issues in the quest for increased performance.

We extend the positive real balancing procedure for passive linear systems to the nonlinear systems case. We show that, just like in the linear case, model reduction based on this technique preserves passivity.

The modeling of RF/microwave components for computer-aided design is facing new challenges because of increasing operation frequencies, circuit complexity, integration density, and decreasing time to market. Recently, it has been shown that Artificial Neural Networks (ANNs) offer solutions to urgent modeling problems encountered with conventional numerical methods (e.g., 3-D EM simulation) and empirical models. Fast and accurate models based on ANNs have been created for a wide range of components [ZG00k], [PAR01].

In this paper we extend the Trajectory Piecewise Linear (TPWL) model order reduction (MOR) method for nonlinear differential algebraic equations (DAE). The TPWL method is based on combining several linear reduced models at different time points, which are created along a typical trajectory, to approximate the full nonlinear model. We discuss how to select the linearization tuples for linearization and the choice of linear MOR method. Then we study how to combine the local linearized reduced systems to create a global TPWL model. Finally, we show a numerical result.

In this paper we compare the numerical results obtained by different model order reduction software tools, in order to test their scalability for relevant problems of the microelectronic-industry. MOR for ANSYS is implemented in C++ and ROMWorkbench is a MATLAB code.We further compare two Arnoldi-based reduction algorithms, which seems to be the most promising for microsystem design applications. The chosen benchmarks are large scale linear ODE systems, which arise from the finite element discretisation of electro-thermal MEMS models.

Sensitivity analysis is an important tool that can be used to assess and improve the design and accuracy of a model describing an electronic circuit. Given a model description in the form of a set of differential-algebraic equations it is possible to observe how a circuit's output reacts to varying input parameters, which are introduced at the requirements stage of design. In this paper we consider the adjoint method more closely. This method is efficient when the number of parameters is large.We extend the transient sensitivity work of Petzold et al., in particular we take into account the parameter dependency of the dynamic term.We also compare the complexity of the direct and adjoint sensitivity and derive some error estimates. Finally we sketch out how Model Order Reduction techniques could be used to improve the efficiency of adjoint sensitivity analysis.

In this paper we will discuss certain aspects of the transient simulation of electrical circuits. It is a well known problem that DAEs in circuit simulation may possess a higher index (e.g. 2) and thus exhibit undesirable numerical behaviour. While methods for the reduction of the higher index exist, they are usually algebraic in nature. The large size of the systems in VLSI circuit simulation prohibits the use of algebraic methods for index reduction. We will present a topological approach to index reduction that changes certain elements of the circuit netlist to obtain a circuit DAE with usually improved numerical behaviour with respect to workload or accuracy.

Characterization of microstrip discontinuities is an important task in computer aided design (CAD) of microstrip circuits. Many methods for modeling the discontinuities have been developed, such as integral equation [1],[2] spectral domain approach [3], finite difference time domain [4], and finite element method [5].

The paper presents a method for generating filter transfer functions optimized in respect to a wide range of behavioral and implementation criteria. The optimization engine is the SQP algorithm, with the main parameters provided by a genetic algorithm tailored to this application.

The paper presents basic principles of the thermal networks method. Modeling of network elements has been shown for convection and radiation. A concept of hierarchical thermal network models for complex geometries has been explained. A formulation of a mass transfer model and a new iterative method of coupling ventilation and thermal networks have been introduced. The last section includes an example of the thermal network computation and a comparison with test results.

In most applications large integrated circuits comprise subcircuits of different functionality causing heterogeneous transient behaviour. Multirate methods exploit local latency by using different stepsizes according to the subcircuits' activity levels at each time point. Following the idea of mixed multirate for ordinary differential equations a hierarchical ROWbased multirate method that can deal with an arbitrary number of subcircuits is developed.

The (nonlinear) transient analysis of electrical circuit models plays an important role in circuit design. Multirate time integration can be able to achieve the same accuracy for much lower costs. An essential assumption is the existence of a good partition of the circuit in a slow and fast part. This paper describes how this can be done automatically.

A multidimensional model yields an alternative strategy for the numerical simulation of frequency-modulated signals. Thus the differential algebraic equations (DAEs), which describe an electric circuit, change into warped multirate partial differential algebraic equations (MPDAEs). Houben [6] introduced an approach for solving efficiently initial-boundary value problems of such MPDAE systems. Thereby, envelope-modulated solutions of the DAEs are reproduced. In this paper, the technique is analysed for obtaining quasiperiodic solutions of the DAEs. The crucial question is if biperiodic solutions of the MPDAEs are generated automatically by Houben's approach provided that the initial values of a biperiodic solution are applied.

The paper presents a historical review and the current state-of-the-art of the Finite Integration Technique (FIT), method which has been successfully used for almost 30 years for the solution of electromagnetic field problems. The presented applications are in the range of high-end RF and microwave technologies.

The paper describes the application of the Newton method in conjunction with the Finite Integration Technique. Even on orthogonal grid pairs, the material matrices become nondiagonal and lead to higher algorithmic complexity. A uni-directional version of these matrices provides a computationally inexpensive alternative. The paper compares and discusses the two algorithms' order of convergence and their computational complexity.

Two armatures of a linear actuator are discretized by the Finite Integration Technique at two independent three-dimensional Cartesian grids. The fixed and the moving armature are coupled at a sliding surface, situated in the middle of the air-gap. The moving armature is displaced in

x

-direction, on a plane parallel to the coupling plane and the generated forces are calculated. The mobile armature is made from laminated iron, in which the eddy current losses are negligible, but the fixed armature is made from massive iron in which the eddy currents have a significant influence. A coupled transient simulation is carried out, considering both the magnetic and the mechanic behavior of the actuator.

An efficient methodology to extract reduced order models for electromagnetic devices is presented. To solve field-circuits coupled problems, the electromagnetic field equations are discretized by the dual Finite Integration Technique (dFIT), a numerical method which allows the accuracy control of the extracted parameters. Several techniques are used to accelerate the extraction process, such as minimal virtual boundary, minimal mesh and minimal frequency samples set. The frequency characteristic of the device is then approximated by a rational function of appropriate degree in order to extract the reduced order model and its SPICE equivalent circuit. The behavior of the synthesized model extracted with proposed algorithm, in the case of passive on-chip devices placed on silicon substrate shows good agreement with respect to the measurements.

One of the major goals in designing of the integrated EMI filters is to improve their highfrequency characteristics. To achieve this, special technologies need to be developed, including the mechanisms for suppression of the equivalent parallel capacitance (EPC) and of the equivalent series inductance (ESL), in spite of increasing the high-frequency losses. In this light, the main goal of the paper is to develop and analyse the effectiveness of several EPCreducing technologies. The study is performed using the numerical analysis software Maxwell Q2D Extractor that is able to give at the end of the numerical analysis process the values of the lumped per-unit-length capacitance or inductance of the geometrical structure proposed. There are calculated the EPC of the four single winding structures and of the coupled windings.

The buffered block forward backward method is described and applied to the problem of scattering from dielectric cylinders. Numerical results suggest that the method converges in the case of scattering from bodies closed at infinity while it produces divergent results in the case of scattering from closed bodies.

The electrodynamic simulation of 3D high-voltage technical devices can be performed under the electro-quasistatic assumption. In order to avoid large spatial discretization domains, a Finite-Element-Method (FEM) is coupled to a Boundary-Element-Method (BEM) which implicitly asserts the electrophysical asymptotic attenuation condition. A symmetric FEM-BEM coupled formulation in time domain is presented. Numerical results are shown for the simulation of a three dimensional high-voltage application.

The paper analyzes the influence of the computational errors on the accuracy of magnetic material modelling with scalar Preisach model. The numerical tests on magnetic recording media allow the correct choosing of numerical algorithms for model parameter identification.

We first show the idea behind a space-mapping iteration technique for the effi- cient solution of optimization problems. Then we show how space-mapping optimization can be understood in the framework of defect correction. We observe a difference between the solution of the optimization problem and the computed space-mapping solutions. We repair this discrepancy by exploiting the correspondence with defect correction iteration and we construct the manifold-mapping algorithm, which is as efficient as the space-mapping algorithm but converges to the accurate solution.

Resistive, capacitive and inductive parasitic coupling effects are very important in integrated circuit technology development and must be taken into account in the global circuit analysis and design. These values are seldom possible to be computed analytically because often we deal with complex multi-route layout geometries. Optimizing the placement of the routes inside the integrated design, in accordance with imposed constraints, one may lead to the decrease of the coupling effects.

This work concerns the multiobjective optimization of an monolithic ESBT_ device aimed to get a characterization of the best design. The optimization will select the epitaxial specifications (thickness, doping concentration) which minimize the energy dissipation, maximize the current flow and keep a breakdown voltage of 1000V. Since these goals are in conflict with each other the best solution must be characterized with respect to all trade-offs. The search was carried out with an extension of the DIRECT algorithm to the multiobjective case.

This papers deals with the optimal design of semiconductor devices, based on the adjoint method and the Energy Transport model. A partially decoupled adjoint system is obtained by considering the electrostatic potential as the new design variable and by interpreting the Poisson equation as a state equation for the doping profile. This leads to an efficient iterative optimization algorithm based on a variant of the Gummel iteration.

In this paper we present a hierarchy of extended hydrodynamical models for electron transport in Silicon, which differ from each other for the number of scalar and vector moments of the electron distribution function used as state variables. The closure of the moment equations is achieved by means of the Maximum Entropy Principle. The main scattering mechanisms between electrons and phonons are taken into account. An application to the case of bulk Silicon is presented.

A typical problem in engineering is to find a numerical solution to a partial differential equation (or a coupled set thereof), given a number of boundary conditions, and the usual approach of solving the problem starts by discretizing the domain into elementary volumes. In this paper, we focus on mesh generation suitable for the solution of field problems in arbitrary VLSI structures. We assume that the problem cannot be easily reduced to a lower dimensionality by exploiting symmetry or regularity, so that the problem-domain is intrinsically threedimensional. Also, we assume that the selected numerical technique (e.g., the finite element method) requires a three-dimensional discretization (as opposed to a surface-discretization). Surveys on mesh generation are given in [2] and [5]. The mesh generator described in this paper is based on techniques from the Delaunay-based mesh generation literature. The main benefit of these techniques is that the quality of the resulting meshes can be

guaranteed

, and, equally important, that the meshes are still small enough to be

practically useful

. An additional advantage is that computation of the mesh is efficient in practice. In general, mesh computation is much faster than solving the subsequent numerical problems. An example mesh generated by our implementation is shown in Figure 1.

In nonlinear electromagnetic field computations, one is not only faced with large jumps of material coefficients across material interfaces but also with high variation in these coefficients even inside homogeneous materials due to the nonlinearity. The radiation condition can conveniently be taken into account by a coupled boundary integral and domain integral variational formulation. The coupled finite and boundary element discretization leads to large-scale nonlinear algebraic systems. In this paper we propose special inexact Newton methods where the Jacobi systems arising in every step of the Newton method are solved by a special preconditioned finite and boundary element tearing and interconnecting solver. The numerical experiments show that the preconditioner proposed in the paper can handle large jumps in the coefficients across the material interfaces as well as high variation in these coef- ficients on the subdomains. Furthermore, the convergence does not deteriorate if many inner subdomains touch the unbounded exterior subdomain.

In this paper, a numerical algorithm solving large sparse linear systems that arise in electromagnetic field computation will be presented. It is based on hierarchical partitioning of the matrix and uses block-wise low-rank approximation in combination with element dropping in order to construct a preconditioner for iterative solution. Within the BE-FE coupling, this approximate factorisation is applied as preconditioner for the FE system. The treatment of multiply connected domains will also be described. The efficiency of the presented solver will be shown by means of an electromagnetic valve.

We investigate the solution of linear systems that appear when model reduction via system balancing is applied in circuit simulation and design. We show how the properties and structure of the coefficient matrices allow the development and use of efficient parallel algorithms for the solution of the corresponding linear systems. Experimental results are reported on an Intel SMP multiprocessor.

We present a method for converting 1-D Maxwell equation into a linear system using the Multivariable Output Error State Space (MOESP) method, a subspace system identification method. To show the efficiency of the method, we first apply it to a set of ordinary differantial equations. Input and output from the equation set are computed by numerical methods and the obtained data is used for building the required matrices. An appropriate Single Input Single Output (SISO) linear system is estimated by MOESP algorithm for the equation at hand. The goal of the research is to build a low order linear state space system model for the Maxwell equation. On the other hand the order estimation for the system can be used in other way. For example, with this estimation one can determine an appropriate order for the physical system, for which one of the well-known model order reduction techniques can be used to obtain a reduced order model.

Stochastic differential algebraic equations (SDAEs) arise as a mathematical model for electrical network equations that are influenced by additional sources of Gaussian white noise. In this paper we discuss adaptive linear multi-step methods for the numerical integration of SDAEs, in particular stochastic analogues of the trapezoidal rule and the two-step backward differentiation formula, together with a new step-size control strategy. Test results illustrate the performance of the presented methods.

Grid technologies offer powerful computing resources for all domains, but the highly heterogeneous and dynamic nature of the Grids needs adaptable, scalable and extensible scheduling systems. In this paper we describe a dynamic, centralized scheduling mechanism based on Master-Worker paradigm for efficient execution of a set of loosely coupled tasks in a Grid environment. This mechanism offers high programmability features, adaptability and reliability towards processor failure. Experiments are presented that demonstrate the effectiveness of our approach.