Interconnection of Subsystem Reduced-Order Models in the Electrothermal Analysis of Large Systems

Abstract

Abstract-Heat conduction in an electronic device is commonly modeled as a discretized thermal system (eg, finite element or finite difference models) that typically uses large matrices for solving complex problems. The large size of electronic-system heat transfer models can be reduced using model reduction methods and the resulting reduced-order models can yield accurate results with far less computational costs. Electronic devices are typically composed of components, like chips, printed circuit boards, and heat sinks that are coupled together. There are two ways of creating reduced-order models for devices that have many coupled components. The first way is to create a single reduced-order model of the entire device. The second way is to interconnect reduced-order models of the components that constitute the device. The second choice (which we call the "reduce then interconnect" approach) allows the heat transfer specialist to perform quick simulations of different architectures of the device by using a library of reduced-order models of the different components that make up the device. However, interconnecting reduced-order models in a straightforward manner can result in unstable behavior. The purpose of this paper is two-fold: creating reduced-order models of the components using a Krylov subspace algorithm and interconnecting the reducedorder models in a stable manner using concepts from control theory. In this paper we explain the logic behind the "reduce then interconnect" approach, formulate a control-theoretic method for it, and finally exhibit the whole process numerically, by applying it to an example heat conduction problem.

Boundary-condition-independent reduced-order modeling of 3D objects by the POD-Galerkin methodology

“…There are many types of reduced-order models that are possible [1][2][3][4][5]. Reduced-order models have been developed using statistical techniques [6][7][8][9][10]. Reduced-order models for the finite-volume method of heat transfer analysis have been developed by Astrid [11].…”

Stability analysis and model order reduction of coupled systems

“…There exist various model reduction methods for dynamical systems; see [5,6] and references therein. However, model order reduction of coupled systems as well as stability and accuracy issues related to the coupling of the reducedorder subsystems received only little attention [7,8].…”

“…The first question that will be addressed in this paper is the stability theory for coupled systems. Based on work [10], we will propose sufficient conditions for the closed-loop descriptor system (6), (7) to be asymptotically stable.…”

“…Our approach is based on the approximation of the subsystems (1) by reduced-order models and coupling these models through the same interconnection relations. Such a structure-preserving model reduction approach has been previously considered in [8,7,11]. The reduced-order subsystems can be computed by the projection of (1) onto the appropriate subspaces determined either by the diagonal blocks of the controllability and observability Gramians of the closed-loop system (6) (see [8]) or by Krylov subspace methods applied to (6) (see [8,11]).…”

“…The reduced-order subsystems can be computed by the projection of (1) onto the appropriate subspaces determined either by the diagonal blocks of the controllability and observability Gramians of the closed-loop system (6) (see [8]) or by Krylov subspace methods applied to (6) (see [8,11]). The disadvantages of these techniques are that we need to work with very large matrices as in (7), and no stability and accuracy results are known.…”