Parametric modeling and model order reduction for (electro-)thermal analysis of nanoelectronic structures

Lihong Feng,Peter Meuris,Peter Benner,Yao Yue,Nicodemus Banagaaya,Wim Schoenmaker

doi:10.1186/s13362-016-0030-8

Abstract

In this work, we discuss the parametric modeling for the (electro)-thermal analysis of components of nanoelectronic structures and automatic model order reduction of the consequent parametric models. Given the system matrices at different values of the parameters, we introduce a simple method of extracting system matrices which are independent of the parameters, so that parametric models of a class of linear parametric problems can be constructed. Then the reduced-order models of the large-scale parametric models are automatically obtained using a posteriori output error bounds for the reduced-order models. Simulations of both thermal and electro-thermal systems confirm the validity of the proposed methods.

Highlights

Parameter variations have become essential in the design of micro- and nano-electronic (-mechanical) systems as well as of coupled electro-thermal problems, since in many analyses such as optimization and uncertainty quantification, modeling and simulation at many values of the parameters are unavoidable
We propose to use an a posteriori output error bound [ ] to construct the ROM automatically, i.e., the algorithm can build a reduced-order model satisfying a prescribed error tolerance without further specification of algorithmic parameters, e.g., interpolation points and the order of the ROM, which can be automatically determined by the algorithm in an adaptive manner
By using the error bound to access the reliability of the reduced-order model, we develop an automatic procedure for constructing the ROM

Summary

Introduction

Parameter variations have become essential in the design of micro- and nano-electronic (-mechanical) systems as well as of coupled electro-thermal problems, since in many analyses such as optimization and uncertainty quantification, modeling and simulation at many values of the parameters are unavoidable. We propose to use parametric model order reduction (PMOR) to compute a reduced-order model (ROM) that is of a much lower dimension, and accurate for all values of the parameters within a specified range.

Results

Conclusion