| MOR for ANSYS | Model Reduction | Publications | Journal Papers |
| Eurosime course on MOR for ANSYS |
New book Fast Simulation of Electro-Thermal MEMS: Efficient Dynamic Compact Models. Book at Amazon or at Springer.
E. B. Rudnyi, J. G. Korvink,
Review: Automatic Model
Reduction for Transient Simulation of MEMS-based Devices.
Sensors Update v. 11, p. 3-33, 2002.
Final paper at Wiley.
The rapid development of MEMS-based devices requires 3D time-dependent simulations for coupled physical domains (thermal, mechanical, electrical, etc.). This in turn requires the solution of high-dimensional ordinary differential equations (ODEs) that result from space discretization of the device. However, instead of a "brute force" approach to integrate a large system of ODEs, one can use modern mathematical methods to reduce the system's dimension. The goal of the present paper is to review them from an engineering perspective. It is shown that in many cases important for practice the order of ODEs can be reduced by several orders of magnitude almost without sacrificing precision.
T. Bechtold, E. B. Rudnyi and J. G. Korvink,
Automatic Generation of
Compact Electro-Thermal Models for Semiconductor Devices.
IEICE Transactions on Electronics, 2003, v. E86C, N 3, pp. 459 - 465.
Final paper at IEICE.
A high power dissipation density in today's miniature electronic/mechanical systems makes on-chip thermal management very important. In order to achieve quick to evaluate, yet accurate electro-thermal models, needed for the thermal management of microsystems, a model order reduction is necessary. In this paper, we present an automatic, Krylov-subspace-based order reduction of a electro-thermal model, which we illustrate by a novel type of micropropulsion device. Numerical simulation results of the full finite element model and the reduced order model, that describes the transient electro-thermal behavior, are presented. A comparison between Krylov-subspace-based order reduction, order reduction using control theoretical approaches and commercially available reduced order modeling has been performed. A Single-Input-Single-Output setup for the Arnoldi reduction algorithm was proved to be sufficient to accurately represent the complete time-dependent temperature distribution of the device.
T. Bechtold, E. B. Rudnyi and J. G. Korvink,
Error indicators for fully automatic extraction of heat-transfer
macromodels for MEMS.
Journal of Micromechanics and Microengineering 2005, v. 15, N 3, pp. 430-440.
Paper at IOP.
In this paper, we present three heuristic error indicators for the iterative model order reduction of electro-thermal MEMS models via the Arnoldi algorithm. Such error indicators help a designer to choose an optimal order of the reduced model, required to achieve a desired accuracy, and hence allow a completely automatic extraction of heat-transfer macromodels for MEMS. We first suggest a convergence criterion between two successive reduced models of order r and r + 1. We further propose to use a solution of the Lyapunov equations for reduced-order systems in each iteration, and alternatively to employ sequential model order reduction, which is based on consecutively applying Arnoldi and control-theory methods.
J. S. Han, E. B. Rudnyi, J. G. Korvink.
Efficient optimization of transient dynamic problems in MEMS devices
using model order reduction.
Journal of Micromechanics and Microengineering 2005, v. 15, N 4, p. 822-832.
Paper at IOP.
One of the main obstacles to including transient dynamic effects into the performance functions of a structural optimization for microelectromechanical systems (MEMS) is the high computational cost of each time-dependent response simulation. This paper focuses on the application of model order reduction techniques to optimal design so as to reduce the transient analysis time for the optimization process. To do this, our open-source software mor4ansys performs model order reductions via the block Arnoldi algorithm directly to ANSYS finite element models. We adopt a micro accelerometer as an example to demonstrate the advantages of this approach. The harmonic and transient results of a reduced-order model of the accelerometer yield very good agreement with that from the original high-dimensional ANSYS model. The use of reduced-order models within the optimization iterations produces almost the same results as those without model order reduction, and speeds up the total computation by at least an order of magnitude.
T. Bechtold, E. B. Rudnyi, J. G. Korvink, M. Graf, A.
Hierlemann.
Connecting heat transfer macromodels for MEMS-array
structures.
Journal of Micromechanics and Microengineering 2005, v. 15, N 6, p.
1205-1214.
Paper at IOP.
Different methodologies to extract a dynamic compact thermal model of a microelectronic or MEMS device have been developed in recent years. They include strategies based on data fitting, a time-constant spectrum, modal analysis and finally formal model reduction. Researchers seek compact thermal multiport representation for system level simulation. However, thermal flux is not lumped by nature as electrical flow and, as a matter of fact, there appears to be very few works on how to couple dynamic compact thermal models with each other. In the present work, we take a finite element model of a MOS-transistor-based microhotplate array made in ANSYS as a case study. We consider two available techniques to make the model reduction. First, we employ the block Arnoldi algorithm that makes model reduction of the whole array at once. Second, we use the modified Guyan algorithm for a single hotplate and couple reduced models via substructuring. We compare both techniques with each other and discuss the possibility of combining the best parts of the two approaches.
T. Bechtold, E. B. Rudnyi, J. G. Korvink.
Dynamic electro-thermal simulation of microsystems: a review.
Journal of Micromechanics and Microengineering 2005, v. 15, N 11, p. R17-R31.
Paper at IOP.
An overview of electro-thermal modeling of microsystems is presented. We consider the most important coupling between thermal and electrical phenomena, and then focus on the industry's central concern, that of Joule heating. A description of different solution approaches for the heat transfer partial differential equation, which constitutes the central part of electro-thermal simulation, is given. We briefly review the analytical solutions and consider further the numerical approaches, which are based on spatial discretization of the thermal domain. Lastly, we describe the final level of approximation, the dynamic compact thermal modeling. We emphasize the formal model order reduction methods, because they directly follow the spatial discretization, and thus preserve the investment into the finite element modeling.
J. G. Korvink, E. B. Rudnyi, A. Greiner, and Z.
Liu.
MEMS and NEMS Simulation.
In MEMS: A Practical Guide to Design, Analysis, and Applications, ed. Jan G.
Korvink, Oliver Paul, William Andrew Publishing, Norwich, NY, 2005,
pp. 93-186. ISBN: 0815514972.
Book at Amazon.
Because MEMS and NEMS touch upon so many application areas, the ideal simulation tool must follow suite and provide a vast range of coupled multi-domain physical effects. In reality, no single tool caters for all the needs of the MEMS community, and hence MEMS designers carry the burden to find the appropriate tools and strategy for their task. Fortunately, many alternative routes exist to achieve a given goal, but some insight is needed to get the most out of the simulators, especially if the target is to use simulation to achieve a design advantage. In this chapter we take a closer look at what is out there, and at the key features of each of the simulation methods. We develop a simulation strategy to maximise the benefit from simulation, picking out a couple of key areas that are currently the focus of commercial applications. To round the chapter off, we illustrate the ideas with some concrete applications from our own work.
L. H. Feng, E. B. Rudnyi, J. G. Korvink.
Preserving the film coefficient as a parameter in the compact thermal
model for fast electro-thermal simulation.
IEEE Transactions on Computer-Aided Design of Integrated Circuits and
Systems, December, 2005, v. 24, N 12, p. 1838-1847.
Final paper at IEEE.
Compact thermal models are often used during joint electro-thermal simulation of MEMS and circuits. Formal model reduction allows us to generate compact thermal models automatically from high-dimensional finite element models. Unfortunately, it requires us to fix a film coefficient employed to describe the convection boundary conditions. As a result, compact models produced by model reduction do not comply with the requirements of being boundary condition independent. In the present paper, we suggest an approach of successive series expansion with respect to the film coefficient as well as to the frequency during model reduction, which allows us to overcome the problem and keep the film coefficient as a symbolic parameter in the reduced model. The approach is justified with a numerical example of electro-thermal simulation of a microthruster unit.
E. B. Rudnyi and J. G. Korvink.
Model Order Reduction for Large Scale Engineering Models Developed in
ANSYS.
Lecture Notes in Computer Science, v. 3732, pp. 349-356, 2006.
Title: Applied Parallel Computing. State of the Art in Scientific Computing: 7th International Conference, PARA 2004, Lyngby, Denmark, June 20-23, 2004. Revised Selected Papers.
Final paper at Springer.
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.
J. Lienemann, E. B. Rudnyi and J. G. Korvink.
MST MEMS model order reduction: Requirements and Benchmarks.
Linear Algebra and its Applications, v. 415, N 2-3, p. 469-498, 2006.
Final Paper at ScienceDirect.
The needs for model reduction in microsystem technology (MST) are described from an engineering perspective. Two representative MST model reduction bench- marks are presented in order to facilitate further development in this area. The first benchmark application is from the area of electro-thermal simulation, the second one considers an electrostatically actuated beam as found in radio frequency ap- plications. Model reduction is contrasted with compact modeling, which currently enjoys widespread use among engineers, and important challenges to be addressed are listed.
Dimension Reduction of Large-Scale Systems.
Benner, P., Mehrmann, V., Sorensen, D. (eds).
Lecture Notes in Computational Science and
Engineering (LNCSE). Springer-Verlag, Berlin/Heidelberg, Germany, v.
45, 2005,
Book at Springer.
L. Feng, D. Koziol, E. B. Rudnyi, and J. G. Korvink.
Parametric Model Reduction for Fast Simulation of Cyclic Voltammograms
.
Sensors Letters, v. 4, N 2, p. 165-173, 2006.
Final Paper at IngentaConnect.
Model order reduction is a well-established technique for fast simulation of large-scale models based on ordinary differential equations, especially those in the field of integrated circuits and micro-electro-mechanical systems. In this paper, we propose the use of parametric model reduction for fast simulation of a cyclic voltammogram. Instead of being considered as a time varying system, the model for a cyclic voltammogram is treated as a system with a parameter (applied voltage) which is to be preserved during model reduction. Because voltage is preserved in the symbolic form during model reduction, we can simulate the cyclic voltammogram with a reduced system and therefore invest much less time and memory as compared with direct simulation based on the original large-scale model. We present our approach for a case study based on scanning electrochemical microscopy.
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