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.
Numerical simulation and modelling have been growing in importance and seeing steadily increasing practical application. The proliferation of applications and physical domains for which simulation technologies are now needed, compounded by generally increased complexity, has expanded the scope of numerical simulation and modelling within CAD and spurred new research directions. Numerical Simulation and Modelling of Electronic and Biochemical Systems provides an introduction to the fundamentals of numerical simulation, and to the basics of modelling electronic circuits and biochemical reactions. The emphasis is on capturing a minimal set of important concepts succinctly, but concretely enough that the reader will be left with an adequate foundation for further independent exploration. Starting from mathematical models of basic electronic elements, circuits are modelled as nonlinear differential-algebraic equation (DAE) systems. Two basic techniques - quiescent steady state and transient - for solving these differential equations systems are then developed. It is then shown how biochemical reactions can also be modelled deterministically as DAEs. Following this, frequency domain techniques for finding sinusoidal steady states of linear DAEs are developed, as are direct and adjoint techniques for computing parameter sensitivities and the effects of stationary random noise. For readers interested in a glimpse of topics beyond these basics, an introduction to nonlinear periodic steady state methods (harmonic balance and shooting) and the multitime partial differential equation formulation is provided. Also provided is an overview of model order reduction, an important topic of current research that has roots in numerical simulation algorithms. Finally, sample applications of nonlinear oscillator macromodels - in circuits (PLLs), biochemical reaction-diffusion systems and nanoelectronics - are presented.
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.
Model Order Reduction Techniqes focuses on model reduction problems with particular applications in electrical engineering. Starting with a clear outline of the technique and their wide methodological background, central topics are introduced including mathematical tools, physical processes, numerical computing experience, software developments and knowledge of system theory. Several model reduction algorithms are then discussed. The aim of this work is to give the reader an overview of reduced-order model design and an operative guide. Particular attention is given to providing basic concepts for building expert systems for model reducution.
This dissertation, "Analytical and Numerical Procedures for Fast Periodic Steady-state and Transient Analyses of Nonlinear Circuits" by Haotian, Liu, 劉昊天, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Effective and efficient simulation and verification techniques are always highly demanded in the electronic design automation (EDA) community. However, existing modeling and simulation approaches could no longer fulfill this growing demand due to the presence of large-scale distributed components and strongly nonlinear devices. In this thesis, two novel techniques are presented for fast simulation and verification of analog and radio-frequency (RF) circuits. Emphasis is placed on developing an analytical approach for periodic steady-state (PSS) analysis and an effective model order reduction (MOR) technique for nonlinear, especially highly nonlinear, systems arising in analog/RF circuit applications. The first approach, named autonomous Volterra (AV), achieves efficient PSS analysis of nonlinear circuits. With elegant analytic forms and availability of efficient solvers, AV constitutes a competitive steady-state algorithm besides the two mainstream PSS algorithms, namely, shooting Newton (SN) and harmonic balance (HB). Nonlinear systems are first captured in nonlinear differential algebraic equations (DAEs), followed by expansion into linear Volterra subsystems. A key step of steady-state analysis lies in modeling each Volterra subsystem with autonomous nonlinear inputs. The PSS solution of these subsystems then proceeds with a series of Sylvester equation solves, completely avoiding the guesses of initial condition and time stepping as in SN, as well as the uncertain length of Fourier series as in HB. Error control in AV is also straightforward by monitoring the norms of the Sylvester equation solutions. It is further demonstrated that AV is readily parallelizable with superior scalability towards large-scale problems. Besides PSS analysis, another important step in analog/RF design is transient as well as general time simulation. To this end, the second part of this thesis features a tensorbased nonlinear model order reduction (TNMOR) algorithm that allows efficient simulation of nonlinear circuits via the emerging techniques utilizing tensors, namely, a multidimensional generalization of matrices. Unlike existing nonlinear model order reduction (NMOR) methods, high-order nonlinearities are captured using tensors in TNMOR, followed by decomposition and reduction to a compact tensor-based reduced-order model (ROM). Consequently, TNMOR completely avoids the dense reduced-order system matrices, which in turn permits faster simulation and less memory requirement. Numerical experiments on transient and PSS analyses confirm the superior accuracy and efficiency of TNMOR, particularly in highly nonlinear scenarios. DOI: 10.5353/th_b5312316 Subjects: Radio circuits - Design and construction
The idea for this book originated during the workshop “Model order reduction, coupled problems and optimization” held at the Lorentz Center in Leiden from S- tember 19–23, 2005. During one of the discussion sessions, it became clear that a book describing the state of the art in model order reduction, starting from the very basics and containing an overview of all relevant techniques, would be of great use for students, young researchers starting in the ?eld, and experienced researchers. The observation that most of the theory on model order reduction is scattered over many good papers, making it dif?cult to ?nd a good starting point, was supported by most of the participants. Moreover, most of the speakers at the workshop were willing to contribute to the book that is now in front of you. The goal of this book, as de?ned during the discussion sessions at the workshop, is three-fold: ?rst, it should describe the basics of model order reduction. Second, both general and more specialized model order reduction techniques for linear and nonlinear systems should be covered, including the use of several related numerical techniques. Third, the use of model order reduction techniques in practical appli- tions and current research aspects should be discussed. We have organized the book according to these goals. In Part I, the rationale behind model order reduction is explained, and an overview of the most common methods is described.
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 three-volume handbook covers methods as well as applications. This third volume focuses on applications in engineering, biomedical engineering, computational physics and computer science.
Simulation based on mathematical models plays a major role in computer aided design of integrated circuits (ICs). Decreasing structure sizes, increasing packing densities and driving frequencies require the use of refined mathematical models, and to take into account secondary, parasitic effects. This leads to very high dimensional problems which nowadays require simulation times too large for the short time-to-market demands in industry. Modern Model Order Reduction (MOR) techniques present a way out of this dilemma in providing surrogate models which keep the main characteristics of the device while requiring a significantly lower simulation time than the full model. With Model Reduction for Circuit Simulation we survey the state of the art in the challenging research field of MOR for ICs, and also address its future research directions. Special emphasis is taken on aspects stemming from miniturisations to the nano scale. Contributions cover complexity reduction using e.g., balanced truncation, Krylov-techniques or POD approaches. For semiconductor applications a focus is on generalising current techniques to differential-algebraic equations, on including design parameters, on preserving stability, and on including nonlinearity by means of piecewise linearisations along solution trajectories (TPWL) and interpolation techniques for nonlinear parts. Furthermore the influence of interconnects and power grids on the physical properties of the device is considered, and also top-down system design approaches in which detailed block descriptions are combined with behavioral models. Further topics consider MOR and the combination of approaches from optimisation and statistics, and the inclusion of PDE models with emphasis on MOR for the resulting partial differential algebraic systems. The methods which currently are being developed have also relevance in other application areas such as mechanical multibody systems, and systems arising in chemistry and to biology. The current number of books in the area of MOR for ICs is very limited, so that this volume helps to fill a gap in providing the state of the art material, and to stimulate further research in this area of MOR. Model Reduction for Circuit Simulation also reflects and documents the vivid interaction between three active research projects in this area, namely the EU-Marie Curie Action ToK project O-MOORE-NICE (members in Belgium, The Netherlands and Germany), the EU-Marie Curie Action RTN-project COMSON (members in The Netherlands, Italy, Germany, and Romania), and the German federal project System reduction in nano-electronics (SyreNe).
This dissertation, "Nonlinear Circuits Modeling and Analysis by the Associated Transform of Volterra Transfer Functions" by Yang, Zhang, 張陽, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Model order reduction (MOR) is one of the general techniques in the fields of computeraided design (CAD) and electronic design automation (EDA) which accelerates the flow of electronic simulations and verifications. By MOR, the original circuit, which is described by a set of ordinary differential equations (ODEs), can be trimmed into a much smaller reduced-order model (ROM) in terms of the number of state variables, with approximately the same input-output (I/O) characteristics. Hence, simulations using this ROM will be much more efficient and effective than using the original system. In this thesis, a novel and fast approach of computing the projection matrices serving high-order Volterra transfer functions in the context of weakly and strongly nonlinear MOR is proposed. The innovation is to carry out an association of multivariate Laplace-domain variables in high-order multiple-input multiple-output (MIMO) transfer functions to generate univariate single-s transfer functions. In contrast to conventional projection-based nonlinear MOR which finds projection subspaces about every si in multivariate transfer functions, only that about a single s is required in the proposed approach. This translates into much more compact nonlinear ROMs without compromising accuracy. Different algorithms and their extensions are devised in this thesis. Extensive numerical examples are given to prove and verify the algorithms. DOI: 10.5353/th_b5194797 Subjects: Electronic circuits - Mathematical models
Progress in today's high-technology industries is strongly associated with the development of new mathematical tools. A typical illustration of this partnership is the mathematical modelling and numerical simulation of electric circuits and semiconductor devices. At the second Oberwolfach conference devoted to this important and timely field, scientists from around the world, mainly applied mathematicians and electrical engineers from industry and universities, presented their new results. Their contributions, forming the body of this work, cover electric circuit simulation, device simulation and process simulation. Discussions on experiences with standard software packages and improvements of such packages are included. In the semiconductor area special lectures were given on new modelling approaches, numerical techniques and existence and uniqueness results. In this connection, mention is made, for example, of mixed finite element methods, an extension of the Baliga-Patankar technique for a three dimensional simulation, and the connection between semiconductor equations and the Boltzmann equations.
