Showing papers on "Model order reduction published in 2004"

Model Order Reduction Techniques with Applications in Finite Element Analysis

Abstract: Despite the continued rapid advance in computing speed and memory the increase in the complexity of models used by engineers persists in outpacing them. Even where there is access to the latest hardware, simulations are often extremely computationally intensive and time-consuming when full-blown models are under consideration. The need to reduce the computational cost involved when dealing with high-order/many-degree-of-freedom models can be offset by adroit computation. In this light, model-reduction methods have become a major goal of simulation and modeling research. Model reduction can also ameliorate problems in the correlation of widely used finite-element analyses and test analysis models produced by excessive system complexity. Model Order Reduction Techniques explains and compares such methods focusing mainly on recent work in dynamic condensation techniques: - Compares the effectiveness of static, exact, dynamic, SEREP and iterative-dynamic condensation techniques in producing valid reduced-order models; - Shows how frequency shifting and the number of degrees of freedom affect the desirability and accuracy of using dynamic condensation; - Answers the challenges involved in dealing with undamped and non-classically damped models; - Requires little more than first-engineering-degree mathematics and highlights important points with instructive examples. Academics working in research on structural dynamics, MEMS, vibration, finite elements and other computational methods in mechanical, aerospace and structural engineering will find Model Order Reduction Techniques of great interest while it is also an excellent resource for researchers working on commercial finite-element-related software such as ANSYS and Nastran.

Model order reduction for large scale engineering models developed in ANSYS

Abstract: We present the software mor4ansys that allows engineers to employ modern model reduction techniques to finite element models developed in ANSYS. We focus on how one extracts the required information from ANSYS and performs model reduction in a C++ implementation that is not dependent on a particular sparse solver. We discuss the computational cost with examples related to structural mechanics and thermal finite element models.

Model-order reduction of finite-element approximations of passive electromagnetic devices including lumped electrical-circuit models

Abstract: A methodology is presented for the development of reduced-order macromodels for multiport passive electromagnetic devices that include embedded lumped elements. The proposed methodology utilizes a discrete state-space model for the electromagnetic device, generated through the application of the finite-element method for the spatial discretization of Maxwell's curl equations. The incorporation of lumped resistors, inductors, and capacitors is effected through the direct stamping of the state-space voltage-current relationship for these elements in the matrices of the generated state-space form of the discrete model. The conditions necessary for the discrete model to be passive are discussed. The subsequent reduction of the discrete state-space model is effected through the application of a Krylov-subspace-based model-order reduction scheme that guarantees the passivity of the generated multiport macromodel, provided that the original state-space model is passive. The proposed methodology is demonstrated and validated through its application for the generation of reduced-order macromodels for a coaxial cable circuit and a microstrip directional coupler circuit.

Model order reduction techniques for linear systems with large numbers of terminals

Abstract: This paper addresses the well known difficulty of applying model order reduction (MOR) to linear circuits with a large number of input-output terminals. Traditional MOR techniques substitute the original large but sparse matrices used in the mathematical modeling of linear circuits by models that approximate the behavior of the circuit at its terminals, and use significantly smaller matrices. Unfortunately these small MOR matrices become dense as the number of terminals increases, thus canceling the benefits of size reduction. The paper introduces a model reduction technique suitable for circuits with numerous terminals. The technique exploits the correlation that almost always exists between circuit responses at different terminals. The correlation is rendered explicit through an SVD-based algorithm and the result is a substantial sparsification of the MOR matrices. The proposed sparsification technique is applicable to a large class of problems encountered in the analysis and design of interconnect in VLSI circuits. Relevant examples are used to analyze and validate the method.

Efficient simulation of nonuniform transmission lines using integrated congruence transform

Abstract: This paper presents a new algorithm based on integrated congruence transform for efficient simulation of nonuniform transmission lines. The proposed algorithm introduces the concept of model-order reduction (MOR) via implicit usage of the Hilbert-space moments in distributed networks. The key idea in the proposed algorithm is the development of an orthogonalization procedure that does not require the explicit computation of the Hilbert-space moments in order to find their spanning orthogonal basis. The proposed orthogonalization procedure can thus be used to compute an orthogonal basis for any set of elements that are related through a differential operator in a generalized Hilbert space, without the need to have these elements in an explicit form. The proposed algorithm also addresses the problem of MOR of nonuniform transmission lines, through defining a weighted inner product and norm mappings over the Hilbert space of the moments. Numerical examples demonstrate more accurate numerical approximation capabilities over using the moments explicitly.

A new methodology for the transient analysis of lossy and dispersive multiconductor transmission lines

Abstract: This paper presents a new technique for the transient analysis of multiconductor transmission lines (MTLs). The proposed model is derived from the analytical characterization of half-T ladder networks (HTLNs), which approximate the MTLs. Using closed-form polynomials (named D'Amico-Faccio-Ferri (DFF) and DFFz), poles and residues of the two-port representation of MTLs are extracted analytically, thus leading to a time-domain macromodel, which can be incorporated in a circuit simulator. Furthermore, the knowledge of poles allows one to develop an efficient model order reduction technique by selecting only the dominant poles of the system within a fixed bandwidth. Stability and passivity properties of the proposed model are intrinsically enforced as a consequence of stability and passivity of HTLNs and rational approximation procedure.

Extraction of heat-transfer macromodels for MEMS devices

Abstract: In this paper, a model order reduction technique for MEMS heat-transfer system-level modeling is presented. A 3D heat-transfer solver, which is appropriate for MEMS thermal analysis, is implemented using the finite-difference method (FDM). The numerical models generated by the FDM solver can be reduced into low-order macromodels by an Arnoldi-based technique. This order reduction operation has been implemented as an automatic process. Because the macromodels are generated from the finite-element or the finite-difference (FEM/FDM) approximation of the original solid models, they preserve the original characteristics for most operation conditions. Also, since the orders of the macromodels are much less than those of their original FEM/FDM models, the computational costs are significantly reduced by about two to four orders of magnitude. This performance improvement thus makes the macromodels compatible for system-level or circuit simulations, which is essential for overall performance prediction. We also demonstrate that the macromodel results are in good agreement with the experimental results. The macromodels are also converted into the circuit component modules written by the hardware description language, and are inserted into a circuit simulator for system-level simulations with other circuit components.

MEMS Compact Modeling Meets Model Order Reduction: Examples of the Application of Arnoldi Methods to Microsystem Devices

Abstract: Modeling and simulation of the behavior of a system consisting of many single devices is an essential requirement for the reduction of design cycles in the development of microsystem applications. Analytic solutions for the describing partial differential equations of each component are only available for simple geometries. For complex geometries, either approximations or numerical methods can be used. However, the numerical treatment of the PDEs of thousands of interconnected single devices with each exhibiting a complex behavior is almost impossible without reduction of the order of unknowns to a lower-dimensional system. We present a fully automatic method to generate a compact model of second-order linear systems based on the Arnoldi process, and provide an example of successfull model order reduction to a gyroscope.

Exploiting input information in a model reduction algorithm for massively coupled parasitic networks

Abstract: In this paper we present a model reduction algorithm that circumvents some of the issues encountered for parasitic networks with large numbers of input/output "ports". Our approach is based on the premise that for such networks, there are typically strong dependencies between the input waveforms at different network "ports". We present an approximate truncated balanced realizations procedure that, by exploiting such correlation information, produces much more compact models compared to standard algorithms such as PRIMA.

Analytical multipoint moment matching reduction of distributed thermal networks

Abstract: In this paper, the multipoint moment matching method for model order reduction of discretized linear thermal networks is extended to distributed linear thermal networks. As a result, from the analytical canonical forms of distributed linear thermal networks, reduced thermal networks are derived analytically. This direct construction of the reduced network, from the exact analytical solutions, avoids the inevitable inaccuracies inherent in conventional surface and volume meshing. It allows nearly exact reduced thermal network construction by domain decomposition for arbitrarily complicated structures.

Generating compact, guaranteed passive reduced-order models of 3-D RLC interconnects

Abstract: As very large scale integration (VLSI) circuit speeds and density continue to increase, the need to accurately model the effects of three-dimensional (3-D) interconnects has become essential for reliable chip and system design and verification. Since such models are commonly used inside standard circuit simulators for time or frequency domain computations, it is imperative that they be kept compact without compromising accuracy, and also retain relevant physical properties of the original system, such as passivity. In this paper, we describe an approach to generate accurate, compact, and guaranteed passive models of RLC interconnects and packaging structures. The procedure is based on a partial element equivalent circuit (PEEC)-like approach to modeling the impedance of interconnect structures accounting for both the charge accumulation on the surface of conductors and the current traveling in their interior. The resulting formulation, based on nodal or mixed nodal and mesh analysis, enables the application of existing model order reduction techniques. Compactness and passivity of the model are then ensured with a two-step reduction procedure where Krylov-subspace moment-matching methods are followed by a recently proposed, nearly optimal, passive truncated balanced realization-like algorithm. The proposed approach was used for extracting passive models for several industrial examples, whose accuracy was validated both in the frequency domain as well as against measured time-domain data.

Multilevel model order reduction

Abstract: We present a multilevel Model Order Reduction scheme for enhancing numerical analysis of electromagnetic fields by means of grid based techniques. The scheme allows one to create nested macromodels and combine macromodels with the Fast Frequency Sweep. The implementation of the method is illustrated on the Finite Difference Frequency Domain technique and efficient nodal order reduction algorithm (ENOR) but the concept can easily be applied also for other mesh based methods and other order reduction schemes.

Recent Advances in Finite Integration Technique for High Frequency Applications

Abstract: We review some recent extensions of the Finite Integration Technique (FIT), which is known to be a generalization of the Finite Difference Time Domain (FDTD) method. Some shortcomings of the standard formulation are discussed which limit the applicability or at least the efficiency of the time domain variant of FIT. The novel developments which are proposed in this paper cover both the basic geometrical modeling in space and time and advanced methods to solve the algebraic problems in time and frequency domain. A numerical application is presented to demonstrate the performance of the algorithms in the high frequency regime.

An efficient nonlinear circuit simulation technique

Abstract: This paper proposes a novel method for the analysis and simulation of integrated circuits (ICs) with the potential to greatly shorten the IC design cycle. The circuits are assumed to be subjected to input signals that have widely separated rates of variation, e.g., in communication systems, an RF carrier modulated by a low-frequency information signal. The proposed technique involves two stages. Initially, a particular order result for the circuit response is obtained using a multiresolution collocation scheme involving cubic spline wavelet decomposition. A more accurate solution is then obtained by adding another layer to the wavelet series approximation. However, the novel technique presented here enables the reuse of results acquired in the first stage to obtain the second-stage result. Therefore, vast gains in efficiency are obtained. Furthermore, a nonlinear model-order reduction technique can readily be used in both stages making the calculations even more efficient. Results will highlight the efficacy of the proposed approach

Full-wave analysis in SPICE via model-order reduction

Abstract: Full-wave analysis is traditionally performed in the frequency domain, or in the time domain using specialized simulators (e.g., finite difference time domain). We describe here an approach that allows us to generate full-wave models for SPICE simulation. The advantage of this approach is that it allows us to easily consider the effects of arbitrary terminations. A frequency-domain finite-element method or method-of-moments solver is used to determine the frequency response of a three-dimensional structure, and then a SPICE model is constructed, which matches this frequency response across a specified frequency band. Some examples are presented to demonstrate the efficacy of the technique.

Using frequency response coherent structures for model-order reduction in microwave applications

Abstract: An effective practical technique for model-order reduction of large-scale linear time-invariant problems in microwave applications is presented. The reduction is performed as the Galerkin projection onto a subspace of frequency response coherent structures that contain the spectrum of the system multiinput impulse response. The subspace basis is created by the proper orthogonal decomposition of the system transfer characteristics sampled at discrete frequency points. A reduced-order modeling of an integrated planar spiral transformer is used for practical verification and comparison to the standard moment matching subspace approach.

Model order reduction of 3D electro-thermal model for a novel micromachined hotplate gas sensor

Abstract: In this paper we present an automatic, Arnoldi-based model order reduction of a 3D electro-thermal model for a novel sensor device. Model order reduction is essential for achieving a quickly evaluable, yet still accurate, macromodel of the device, needed for system-level simulation. We present below numerical simulation results of the full-scale finite element model and the compact-reduced order model, and show how the nonlinearities in the input function can be treated even with the linear reduction algorithm.

Passive reduction algorithm for RLC interconnect circuits with embedded state-space systems (PRESS)

Abstract: With the increasing operating frequencies and functionality in modern designs, the resulting size of circuit equations of high-frequency interconnect and microwave subnetworks are becoming large. Model-order reduction-based algorithms were recently suggested to handle the solution complexity of such circuits. The major objectives in state-of-the-art model-reduction algorithms are: 1) achieving accurate and compact models; 2) numerically stable and efficient generation of models; and 3) preservation of system properties such as passivity. Algorithms such as PRIMA generate guaranteed passive reduced-order models for large interconnect circuits described by RLC type of circuits. However, with the diverse technologies and complex geometries, it is becoming prevalent to describe some of the embedded linear modules in terms of state-space equations. In this paper, we show how to extend the scope of PRIMA-type first-level reduction algorithms for simultaneous reduction of combined circuits containing both RLC interconnects and embedded modules described by general passive state-space equations, while preserving the passivity of the resulting reduced-order model. Necessary formulation, proof of macromodel passivity, and validation examples are given.

Passivity-preserving model reduction via a computationally efficient project-and-balance scheme

Abstract: This paper presents an efficient t o-stage project-and-balance scheme for passivity-preserving model order reduction. Orthogonal dominant eigenspace projection is implemented by integrating the Smith method and Krylov subspace iteration. It is followed by stochastic balanced truncation herein a novel method, based on the complete separation of stable and unstable invariant subspaces of a Hamiltonian matrix, is used for solving two dual algebraic Riccati equations at the cost of essentially one. A fast-converging quadruple-shift bulge-chasing SR algorithm is also introduced for this purpose. Numerical examples confirm the quality of the reduced-order models over those from conventional schemes.

Model-order reduction of linear and weakly nonlinear time-varying RF and microwave circuits

Abstract: Model-order reduction techniques of RF and microwave linear and weakly nonlinear time-varying circuits are presented. The reduced models capture the memory and linear or weakly nonlinear input-output behavior of the circuit, as well as the matching conditions at the model ports. The reported techniques serve to reduce models of a number of RF and microwave functions such as lumped or distributed linear circuits, small-signal amplifiers, mixers, modulators, etc. The reduced models can be implemented in any simulator using standard library components and can be employed both in frequency and time-domain simulations, demonstrating good agreement and significant reduction of simulation time with respect to the simulation of the complete circuit. The model-order reduction techniques are illustrated through different examples.

A trajectory piecewise-linear approach to model order reduction for nonlinear stationary magnetic devices

Abstract: In power electronics and electric machinery, finite-element based time-domain modeling has been used frequently. Generally, the time-domain modeling of magnetic devices is completed by solving a high order system at each time step. Fortunately, the full order state-space models can be reduced methodically without additional assumption. The method for reducing the order of magnetically linear system is presented in previous work. However, in the analysis of magnetic devices the problems are usually nonlinear due to the presence of ferromagnetic materials. In this paper, a nonlinear model of the magnetic devices is presented and reduced by using a trajectory piecewise-linear approach.

Sliding mode control for singularly perturbed system

Abstract: When dealing with large scale systems, the dimension and ill condition of the state matrix motivate the use of model order reduction methods. Singular perturbation theory is found to be a good approach to obtain a reduced order model. This article presents the use of a single sliding mode controller designed for the slow component of singular perturbed system. The stability analysis is investigated using the Lyapunov approach. We provide sufficient condition for asymptotic stability of the full order singular perturbed system.

On the application of model-order reduction in the fast and reliable optimization of microwave filters and diplexers

Abstract: This paper discusses the application of model-order reduction in the optimization of microwave devices. It focuses on the direct optimization of the scattering matrix poles and zeros, yielding an advanced reliability and universality at a computational cost that is comparable to a surrogate model optimization. The scattering matrix poles and zeros are computed from a state-space model that is obtained from a finite-integration discretization and then optimized to match a set of target poles and zeros.

Parametric reduced order modeling for interconnect analysis

Abstract: VLSI circuit models are subject to parameter variations due to temperature, geometry, process, and operating conditions. Parameter model order reduction is motivated by such practical problems. The purpose is to obtain a parametric reduced order model so that repeated reduction can be avoided. In this paper we propose two techniques: a nominal projection technique and an interpolation technique. The nominal projection technique is effective for small parameter perturbation by using a robust projection. The interpolation technique takes the advantage of simple matrix structure resulting from the PVL algorithm. A new moment matching concept in the discrete-time domain is also introduced, which is intended for a better performance in waveform matching and stability. Interconnect examples are used to test the effectiveness of the proposed methods.

Nonlinear Model Order Reduction and Control of Particle Size Distribution in a Semibatch Vinyl Acetate/Butyl Acrylate Emulsion Copolymerization Reactor

Abstract: This paper addresses the control of the full particle size distribution (PSD) in a semibatch emulsion copolymerization reactor. The numerical approximation of a fundamental population balance model results in a high order system to accurately describe the distribution of particle size; therefore, model order reduction is required. Pseudo random input signals are input to the mechanistic model to generate a data set which covers the reachable region of the system, on the basis of which the transformation matrices are calculated by principal component analysis (PCA). A linear time varying model with reduced order obtained from the transformation matrices is augmented in the prediction equation of linear model predictive control. The performance of the controller is evaluated to drive the particle size distribution at the final time of the batch to the desired distribution in the presence of disturbances.

Orthogonalisation in Krylov subspace methods for model order reduction

Abstract: The modelling of the EM behaviour of electronic structures nowadays involves a broad frequency range and coupling of analog and digital behaviour. Much research and increasing computational resources enabled the designers in the past decades to simulate complicated and large structures. One of the approaches to make this modelling feasible is Model Order Reduction. In this approach one tries to capture the essential features of a large model, into a smaller, a more easy to handle model. A wide range of different techniques has been proposed and investigated in the last few decades. Especially Krylov-subspace methods have proved themselves to be very suitable for this area of application (eg. [2], [4], [6] and [8]). Many of these methods guarantee preservation of passivity, which makes them even more interesting. However, implementing the methods straightforwardly is not enough to make them applicable for real-life applications. In order to make the methods accurate, efficient and suitable for large systems, extra attention and mathematical knowledge is needed. In this paper we will focus on the orthogonalisation of the Krylov space, which is seen to be of importance. Special attention is paid to the orthogonalisation of a Block Krylov space. Also some directions to cheaply avoid parts of the redundancy in the Krylov space methods are pointed out in this paper.

A fast Newton/Smith algorithm for solving algebraic Riccati equations and its application in model order reduction

Abstract: A very fast Smith-method-based Newton algorithm is introduced for the solution of large-scale continuous-time algebraic Riccati equations (CAREs). When the CARE contains low-rank matrices, as is common in the modeling of physical systems, the proposed algorithm, called the Newton/Smith CARE or NSCARE algorithm, offers significant computational savings over conventional CARE solvers. The effectiveness of the algorithm is demonstrated in the context of VLSI model order reduction, wherein stochastic balanced truncation (SBT) is used to reduce large-scale passive circuits. It is shown that the NSCARE algorithm exhibits guaranteed quadratic convergence under mild assumptions. Moreover, two large-sized matrix factorizations and one large-scale singular value decomposition (SVD), necessary for SBT, can be omitted by utilizing the Smith method output in each Newton iteration, thereby significantly speeding up the model reduction process.