On experiments with a parallel direct solver for diagonally dominant banded linear systems

1996 ◽  
pp. 11-21 ◽  
Author(s):  
Peter Arbenz
Keyword(s):  
Linear Systems ◽  
Direct Solver ◽  
Diagonally Dominant ◽  
Banded Linear Systems

An asynchronous direct solver for banded linear systems

2017 ◽  
Vol 76 (1) ◽  
pp. 211-235 ◽  
Author(s):  
Michael A. Jandron ◽  
Anthony A. Ruffa ◽  
James Baglama
Keyword(s):  
Linear Systems ◽  
Direct Solver ◽  
Banded Linear Systems

PSPASES: Building a High Performance Scalable Parallel Direct Solver for Sparse Linear Systems

1999 ◽  
pp. 3-18 ◽  
Author(s):  
Mahesh V. Joshi ◽  
George Karypis ◽  
Vipin Kumar ◽  
Anshul Gupta ◽  
Fred Gustavson
Keyword(s):  
Linear Systems ◽  
High Performance ◽  
Sparse Linear Systems ◽  
Direct Solver

Banded Linear Systems

2015 ◽  
pp. 91-163
Author(s):  
Efstratios Gallopoulos ◽  
Bernard Philippe ◽  
Ahmed H. Sameh
Keyword(s):  
Linear Systems ◽  
Banded Linear Systems

Some Remarks About the Decoupling Approximation of Damped Linear Systems

2009 ◽  
Author(s):  
Matthias Morzfeld ◽  
Nopdanai Ajavakom ◽  
Fai Ma
Keyword(s):  
Linear Systems ◽  
Approximation Error ◽  
Driving Frequency ◽  
Finite Range ◽  
Diagonal Dominance ◽  
Damping Matrix ◽  
Modal Damping ◽  
Diagonally Dominant ◽  
Decoupling Approximation ◽  
Damped Systems

A common approximation in the analysis of non-classically damped systems is to ignore the off-diagonal elements of the modal damping matrix. This procedure is termed the decoupling approximation. It is generally believed that errors due to the decoupling approximation should be negligible if the modal damping matrix is diagonally dominant. In addition, the errors are expected to decrease as the modal damping matrix becomes more diagonally dominant. It is shown numerically in this paper that, over a finite range, errors due to the decoupling approximation can increase monotonically at any specified rate while the modal damping matrix becomes more diagonally dominant with its off-diagonal elements decreasing continuously in magnitude. These unexpected drifts in errors due to the decoupling approximation can be observed at any driving frequency. Small off-diagonal elements in the modal damping matrix may not be sufficient to ensure small errors due to the decoupling approximation. Error-criteria based solely upon diagonal dominance of the modal damping matrix cannot be accurate.

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