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Title: A comparison of iterative methods for a model coupled system of elliptic equations

Abstract

Many interesting areas of current industry work deal with non-linear coupled systems of partial differential equations. We examine iterative methods for the solution of a model two-dimensional coupled system based on a linearized form of the two carrier drift-diffusion equations from semiconductor modeling. Discretizing this model system yields a large non-symmetric indefinite sparse matrix. To solve the model system various point and block methods, including the hybrid iterative method Alternate Block Factorization (ABF), are applied. We also employ GMRES with various preconditioners, including block and point incomplete LU (ILU) factorizations. The performance of these methods is compared. It is seen that the preferred ordering of the grid variables and the choice of iterative method are dependent upon the magnitudes of the coupling parameters. For this model, ABF is the most robust of the non-accelerated iterative methods. Among the preconditioners employed with GMRES, the blocked ``by grid point`` version of both the ILU and MILU preconditioners are the most robust and the most time efficient over the wide range of parameter values tested. This information may aid in the choice of iterative methods and preconditioners for solving more complicated, yet analogous, coupled systems.

Authors:
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE, Washington, DC (United States)
OSTI Identifier:
10180753
Report Number(s):
ORNL/TM-12447
ON: DE93040482
DOE Contract Number:  
AC05-84OR21400
Resource Type:
Technical Report
Resource Relation:
Other Information: PBD: Aug 1993
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; PARTIAL DIFFERENTIAL EQUATIONS; ITERATIVE METHODS; ELLIPTICAL CONFIGURATION; FACTORIZATION; BOUNDARY CONDITIONS; MATRICES; SEMICONDUCTOR DEVICES; DIFFUSION; 665000; 990200; PHYSICS OF CONDENSED MATTER; MATHEMATICS AND COMPUTERS

Citation Formats

Donato, J M. A comparison of iterative methods for a model coupled system of elliptic equations. United States: N. p., 1993. Web. doi:10.2172/10180753.
Donato, J M. A comparison of iterative methods for a model coupled system of elliptic equations. United States. https://doi.org/10.2172/10180753
Donato, J M. 1993. "A comparison of iterative methods for a model coupled system of elliptic equations". United States. https://doi.org/10.2172/10180753. https://www.osti.gov/servlets/purl/10180753.
@article{osti_10180753,
title = {A comparison of iterative methods for a model coupled system of elliptic equations},
author = {Donato, J M},
abstractNote = {Many interesting areas of current industry work deal with non-linear coupled systems of partial differential equations. We examine iterative methods for the solution of a model two-dimensional coupled system based on a linearized form of the two carrier drift-diffusion equations from semiconductor modeling. Discretizing this model system yields a large non-symmetric indefinite sparse matrix. To solve the model system various point and block methods, including the hybrid iterative method Alternate Block Factorization (ABF), are applied. We also employ GMRES with various preconditioners, including block and point incomplete LU (ILU) factorizations. The performance of these methods is compared. It is seen that the preferred ordering of the grid variables and the choice of iterative method are dependent upon the magnitudes of the coupling parameters. For this model, ABF is the most robust of the non-accelerated iterative methods. Among the preconditioners employed with GMRES, the blocked ``by grid point`` version of both the ILU and MILU preconditioners are the most robust and the most time efficient over the wide range of parameter values tested. This information may aid in the choice of iterative methods and preconditioners for solving more complicated, yet analogous, coupled systems.},
doi = {10.2172/10180753},
url = {https://www.osti.gov/biblio/10180753}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Sun Aug 01 00:00:00 EDT 1993},
month = {Sun Aug 01 00:00:00 EDT 1993}
}