Residual Based Sampling in POD Model Order Reduction of Drift-Diffusion Equations in Parametrized Electrical Networks

TL;DR

This paper applies proper orthogonal decomposition (POD) to reduce the complexity of drift-diffusion equations in parametrized electrical networks, enabling efficient surrogate modeling and adaptive model construction.

Contribution

It introduces a residual-based sampling approach for POD model reduction of high-dimensional drift-diffusion equations in electrical circuits, including adaptive techniques for parameter-dependent models.

Findings

POD effectively reduces model dimension while maintaining accuracy.

The adaptive approach extends model validity over parameter ranges.

Surrogate models accurately replicate diode behavior in complex circuits.

Abstract

We consider integrated circuits with semiconductors modeled by modified nodal analysis and drift-diffusion equations. The drift-diffusion equations are discretized in space using mixed finite element method. This discretization yields a high dimensional differential-algebraic equation. We show how proper orthogonal decomposition (POD) can be used to reduce the dimension of the model. We compare reduced and fine models and give numerical results for a basic network with one diode. Furthermore we discuss an adaptive approach to construct POD models which are valid over certain parameter ranges. Finally, numerical investigations for the reduction of a 4-diode rectifier network are presented, which clearly indicate that POD model reduction delivers surrogate models for the diodes involved, which depend on the position of the semiconductor in the network.