Effective Physics Simulations based on Model Reduction and Domain Decomposition

Abstract

This investigation implements domain decomposition in proper orthogonal decomposition (POD) to construct an effective multi-block methodology for physics simulations of engineering and scientific problems. To develop such a methodology, the structure of interest is first partitioned into smaller blocks, and solution data of each block are collected from detailed numerical simulation (DNS) accounting for parametric variations in the block. The collected data that represent the block are used to generate (or train) a set of basis functions (or POD modes) that are therefore tailored to the characteristics of the block accounting for its parametric variations. With the well-trained modes, the approach significantly reduces the degree of freedom (DoF) needed to reach an accurate solution. To construct a model for a larger domain, the trained POD blocks are then glued together using the discontinuous Galerkin method to enforce thermal continuity at the block interfaces. The multiblock concept further minimizes the computational effort in the training process and allows the POD methodology to offer efficient simulation models for large-scale structure with a high resolution, which may be crucial for many engineering and scientific applications.The multi-block POD methodology has been applied to physics simulations in two distinct areas, including a prediction of the dynamic thermal distribution in a 2-block 3D semiconductor structure and simulation of a 3-block 1D quantum-well structure whose electron wave functions are governed by the Schrödinger equation. It has been illustrated that the POD methodology in both applications is able to offer very good agreement with the DNS results using just 3 or 4 POD modes in the 3D and 1D problems.