Residual Based Sampling in POD Model Order Reduction of Drift-Diffusion Equations in Parametrized Electrical Networks
For engineers simulating integrated circuits with semiconductors, this provides a model reduction technique that captures parameter-dependent behavior, though the results are preliminary and limited to simple networks.
This work applies proper orthogonal decomposition (POD) to reduce the dimensionality of drift-diffusion equations in parametrized electrical networks, demonstrating that POD yields surrogate models for diodes that depend on their network position. Numerical results for a 4-diode rectifier show the method's effectiveness.
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.