Sparse Model Order Reduction for Electro-Thermal Problems with Many Inputs

Recently, the block-diagonal structured model order reduction method for electro-thermal coupled problems with many inputs (BDSM-ET) was proposed in Banagaaya et al. (Model order reduction for nanoelectronics coupled problems with many inputs. In: Proceedings 2016 design, automation & test in Europe conference & exhibition, DATE 2016, Dresden, March 14–16, pp 313–318, 2016). After splitting the electro-thermal (ET) coupled problems into electrical and thermal subsystems, the BDSM-ET method reduces both subsystems separately, using Gaussian elimination and the block-diagonal structured MOR (BDSM) method, respectively. However, the reduced electrical subsystem has dense matrices and the nonlinear part of the reduced-order thermal subsystem is computationally expensive. We propose a modified BDSM-ET method which leads to sparser reduced-order models (ROMs) for both the electrical and thermal subsystems. Simulation of a very large-scale model with up to one million state variables shows that the proposed method achieves significant speed-up as compared with the BDSM-ET method.