Evgenii B. Rudnyi

Efficient optimization of transient dynamic problems in MEMS devices using model order reduction

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.

Dynamic electro-thermal simulation of microsystems—a review

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 industrys 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.

Model order reduction for large scale engineering models developed in ANSYS

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.

Preserving the film coefficient as a parameter in the compact thermal model for fast electrothermal simulation

Compact thermal models are often used during joint electrothermal simulation of microelectromechanical systems (MEMS) and circuits. Formal model reduction allows generation of compact thermal models automatically from high-dimensional finite-element models. Unfortunately, it requires fixing 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, the authors suggest an approach of successive series expansion with respect to the film coefficient as well as to the frequency during model reduction that allows 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 electrothermal simulation of a microthruster unit.

Oberwolfach Benchmark Collection

A Web-site to store benchmarks for model reduction is described. The site structure, submission rules and the file format are presented.

Error indicators for fully automatic extraction of heat-transfer macromodels for MEMS

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.

Efficient extraction of thin-film thermal parameters from numerical models via parametric model order reduction

In this paper we present a novel highly efficient approach to determine material properties from measurement results. We apply our method to thermal properties of thin-film multilayers with three different materials, amorphous silicon, silicon nitride and silicon oxide. The individual material properties are identified by solving an optimization problem. For this purpose, we build a parameterized reduced-order model from a finite element (FE) model and fit it to the measurement results. The use of parameterized reduced-order models within the optimization iterations speeds up the transient solution time by several orders of magnitude, while retaining almost the same precision as the full-scale model.

Connecting heat transfer macromodels for array MEMS structures

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.

Computationally efficient and stable order reduction methods for a large-scale model of MEMS piezoelectric energy harvester

In this work, we present a computationally efficient model order reduction technique for a large-scale multiport model of piezoelectric energy harvester. This novel technique generates stable reduced order models. The method combines model reduction based on Krylov subspaces and a Schur complement transformation of the resulting system. We demonstrate an excellent match between the full-scale and the reduced order model during transient and harmonic simulation.

Automatic order reduction of thermo-electric models for MEMS: Arnoldi versus Guyan

In this paper we present an automatic order reduction of a linear thermo-electric model describing a novel type of micropropulsion device. Model order reduction is essential to achieve easily to evaluate, yet accurate macromodel of the device. We present numerical simulation results of the full finite element model and the different reduced order models that describe the transient thermo-electric behaviour of the device. The advantages of an Arnoldi-algorithm-based model order reduction over a commercially available reduced order modeling after Guyan are shown.