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Title: Implementing sparse matrix techniques in the ERATO code

Abstract

The ERATO code computes the stability of an equilibrium with respect to the linear MHD equation. The ERATO code is divided into 5 programs (ERATO1 through ERATO5). This report documents some minor changes made in ERATO3 and a major reorganization of ERATO4. The changes were made to reduce drastically the amount of secondary storage needed by the codes and at the same time improve the efficiency of ERATO4. The ultimate goal is to allow the successful completion of runs with finer meshes than are currently possible. ERATO4 takes given matrices, A and B, and a shift parameter, ..omega../sub 0/, and computes the Choleski factorization (U/sup T/DU) of the matrix A - ..omega../sub 0/B. It then uses the factorization to implement inverse iteration to find the eigenvalue of the generalized eigenvalue problem A - lambda B closest to ..omega../sub 0/ and its corresponding eigenvector. The matrices A and B are highly structured and quite sparse. Both are symmetric and B is positive definite. Each block consists of 16 square subblocks. 9 figures. (RWR)

Authors:
Publication Date:
Research Org.:
Union Carbide Corp., Oak Ridge, TN (USA). Computer Sciences Div.
OSTI Identifier:
5404400
Report Number(s):
ORNL/CSD/TM-117
TRN: 80-007674
DOE Contract Number:
W-7405-ENG-26
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; COMPUTER CODES; E CODES; MATRICES; EIGENVALUES; FACTORIZATION; CALCULATION METHODS; EIGENVECTORS; EQUILIBRIUM; ITERATIVE METHODS; MAGNETOHYDRODYNAMICS; STABILITY; FLUID MECHANICS; HYDRODYNAMICS; MECHANICS; 658000* - Mathematical Physics- (-1987); 990200 - Mathematics & Computers; 640430 - Fluid Physics- Magnetohydrodynamics

Citation Formats

Scott, D.S.. Implementing sparse matrix techniques in the ERATO code. United States: N. p., 1980. Web. doi:10.2172/5404400.
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Scott, D.S.. Implementing sparse matrix techniques in the ERATO code. United States. doi:10.2172/5404400.
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Scott, D.S.. Tue . "Implementing sparse matrix techniques in the ERATO code". United States. doi:10.2172/5404400. https://www.osti.gov/servlets/purl/5404400.
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@article{osti_5404400,
title = {Implementing sparse matrix techniques in the ERATO code},
author = {Scott, D.S.},
abstractNote = {The ERATO code computes the stability of an equilibrium with respect to the linear MHD equation. The ERATO code is divided into 5 programs (ERATO1 through ERATO5). This report documents some minor changes made in ERATO3 and a major reorganization of ERATO4. The changes were made to reduce drastically the amount of secondary storage needed by the codes and at the same time improve the efficiency of ERATO4. The ultimate goal is to allow the successful completion of runs with finer meshes than are currently possible. ERATO4 takes given matrices, A and B, and a shift parameter, ..omega../sub 0/, and computes the Choleski factorization (U/sup T/DU) of the matrix A - ..omega../sub 0/B. It then uses the factorization to implement inverse iteration to find the eigenvalue of the generalized eigenvalue problem A - lambda B closest to ..omega../sub 0/ and its corresponding eigenvector. The matrices A and B are highly structured and quite sparse. Both are symmetric and B is positive definite. Each block consists of 16 square subblocks. 9 figures. (RWR)},
doi = {10.2172/5404400},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Tue Apr 01 00:00:00 EST 1980},
month = {Tue Apr 01 00:00:00 EST 1980}
}
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Technical Report:
View Technical Report (0.37 MB)
DOI:  10.2172/5404400
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