Residual based sampling in POD model order reduction of drift-diffusion equations in parametrized electrical networks

被引：23

作者：

Hinze, Michael ^{[2
]}

Kunkel, Martin ^{[1
]}

机构：

[1] Univ Bundeswehr Munchen, Fak Luft & Raumfahrttech, D-85577 Neubiberg, Germany

[2] Univ Hamburg, Fachbereich Math, D-20146 Hamburg, Germany

来源：

ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK | 2012年 / 92卷 / 02期

关键词：

Model order reduction; reduced basis methods; parametrized dynamical systems; mixed finite element methods; drift-diffusion equations; integrated circuits; DISCRETIZATION;

D O I：

10.1002/zamm.201100004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：91 / 104

页数：14

共 25 条

[1] Discrete Empirical Interpolation in POD Model Order Reduction of Drift-Diffusion Equations in Electrical Networks
Hinze, Michael
Kunkel, Martin
SCIENTIFIC COMPUTING IN ELECTRICAL ENGINEERING (SCEE 2010), 2012, 16 : 423 - 431
[2] Model order reduction of parametrized nonlinear reaction-diffusion systems
Grepl, Martin A.
COMPUTERS & CHEMICAL ENGINEERING, 2012, 43 : 33 - 44
[3] AN EFFICIENT OUTPUT ERROR ESTIMATION FOR MODEL ORDER REDUCTION OF PARAMETRIZED EVOLUTION EQUATIONS
Zhang, Yongjin
Feng, Lihong
Li, Suzhou
Benner, Peter
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2015, 37 (06) : B910 - B936
[4] A physics-based strategy for choosing initial iterate for solving drift-diffusion equations
Jia, Xiaowei
An, Hengbin
Hu, Yi
Mo, Zeyao
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2023, 131 : 1 - 13
[5] A DIRECT APPROACH TO SOLVING THE DRIFT-DIFFUSION MODEL-EQUATIONS FOR USE IN CERTAIN MOSFET DEVICES
SARVAS, J
SPANIER, J
MATHEMATICAL AND COMPUTER MODELLING, 1995, 22 (08) : 17 - 31
[6] Dictionary-based Model Order Reduction via POD-DEIM with Support Vector Machine for the Parametrized Burgers' Equation
Sukuntee, Norapon
Chaturantabut, Saifon
THAI JOURNAL OF MATHEMATICS, 2022, : 38 - 52
[7] A Parametrized Model Order Reduction Method Based on Integral Equation for Array Structures
Ying, Xiaojie
Shao, Hanru
Hu, Jun
IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, 2024, 23 (04): : 1286 - 1290
[8] Implementation of Simplified Model Order Reduction Based on POD for Dynamic Simulation of Electric Motors
Okamoto, Kazuya
Sakamoto, Hiroki
Igarashi, Hajime
2019 22ND INTERNATIONAL CONFERENCE ON THE COMPUTATION OF ELECTROMAGNETIC FIELDS (COMPUMAG 2019), 2019,
[9] Driving bifurcating parametrized nonlinear PDEs by optimal control strategies: application to Navier-Stokes equations with model order reduction
PICHI, F. E. D. E. R. I. C. O.
STRAZZULLO, M. A. R. I. A.
BALLARIN, F. R. A. N. C. E. S. C. O.
ROZZA, G. I. A. N. L. U. I. G. I.
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS, 2022, 56 (04) : 1361 - 1400
[10] POD-based model order reduction with an adaptive snapshot selection for a discontinuous Galerkin approximation of the time-domain Maxwell's equations
Li, Kun
Huang, Ting-Zhu
Li, Liang
Lanteri, Stephane
JOURNAL OF COMPUTATIONAL PHYSICS, 2019, 396 : 106 - 128

← 1 2 3 →