Model reduction via quasistatic approximations

Model Reduction via the

In Part II of this paper we present some elementary examples of distributed parameter system model reduction using the techniques described in Part I. In particular, we focus on using the Karhunen-Loeve expansion and Galerkin's method to formulated reduced order models for a heat diiusion system and temperature eld dynamics in a Rapid Thermal Chemical Vapor Deposition reactor. Simulation result...

3.3 CONDITIONS FOR FIELDS TO BE QUASISTATIC An appreciation for the quasistatic approximations will come with a consideration

An appreciation for the quasistatic approximations will come with a consideration of many case studies. Justification of one or the other of the approximations hinges on using the quasistatic fields to estimate the “error” fields, which are then hopefully found to be small compared to the original quasistatic fields. In developing any mathematical “theory” for the description of some part of th...

Weighted Model Reduction Via Interpolation

Weighted model reduction problems appear in many important applications such as controller reduction. The most common approach to this problem is the weighted balanced truncation method. Interpolatory approaches to weighted model reduction have been mostly limited to simply choosing interpolation points in the regions where the weights are dominant. In this paper, we extend the (unweighted) tan...

Model reduction via convex optimization

Roughly speaking, an “optimization problem” is the task of finding an element x = xo of a given set X for which the value Φ(x) of a given function Φ : X 7→ R is minimal. Alternatively, the objective could be to find an element xγ ∈ X such that Φ(xγh) < γ, where γ ∈ R is a given threshold, or to give evidence to non-existence of such xγ does not exist. Among the most familiar optimization proble...

Model reduction via moments matching