Parallel solution of large sparse matrix equations and parallel power flow

1995 ◽  
Vol 10 (3) ◽  
pp. 1343-1349 ◽  
Author(s):  
Jun Qiang Wu ◽  
A. Bose
Keyword(s):  
Power Flow ◽  
Sparse Matrix ◽  
Matrix Equations ◽  
Parallel Solution

Parallel solution of Newton’s power flow equations on configurable chips

2007 ◽  
Vol 29 (5) ◽  
pp. 422-431 ◽  
Author(s):  
Xiaofang Wang ◽  
Sotirios G. Ziavras ◽  
Chika Nwankpa ◽  
Jeremy Johnson ◽  
Prawat Nagvajara
Keyword(s):  
Power Flow ◽  
Flow Equations ◽  
Parallel Solution

A Parallel Solution Strategy for Finite Element Models

1996 ◽  
Author(s):  
Jordan J. Cox ◽  
Jeffrey A. Talbert ◽  
Eric Mulkay
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Decomposition Methods ◽  
Finite Element Models ◽  
Unique Contribution ◽  
Matrix Equations ◽  
Parallel Solution ◽  
The Finite Element Model ◽  
Parallel Fashion

Abstract This paper presents a method for naturally decomposing finite element models into sub-models which can be solved in a parallel fashion. The unique contribution of this paper is that the decomposition strategy comes from the geometric features used to construct the solid model that the finite element model represents. Domain composition and domain decomposition methods are used to insure global compatibility. These techniques reduce the N2 behavior of traditional matrix solving techniques, where N is the number of degrees of freedom in the global set of matrix equations, to a sum of m matrices with n2 behavior, where n represents the number of degrees of freedom in the smaller sub-model matrix equations.

scholarly journals DC Large-Scale Simulation of Nonlinear Circuits on Parallel Processors

2012 ◽  
Vol 58 (3) ◽  
pp. 285-295
Author(s):  
Diego Ernesto Cortés Udave ◽  
Jan Ogrodzki ◽  
Miguel Angel Gutiérrez De Anda
Keyword(s):  
Large Scale ◽  
Complexity Analysis ◽  
Sparse Matrix ◽  
Nonlinear Models ◽  
Nonlinear Circuits ◽  
Departure Point ◽  
Parallel Solution ◽  
Matrix Operations ◽  
Time Required ◽  
Numerical Complexity

Abstract Newton-Raphson DC analysis of large-scale nonlinear circuits may be an extremely time consuming process even if sparse matrix techniques and bypassing of nonlinear models calculation are used. A slight decrease in the time required for this task may be enabled on multi-core, multithread computers if the calculation of the mathematical models for the nonlinear elements as well as the stamp management of the sparse matrix entries is managed through concurrent processes. In this paper it is shown how the numerical complexity of this problem (and thus its solution time) can be further reduced via the circuit decomposition and parallel solution of blocks taking as a departure point the Bordered-Block Diagonal (BBD) matrix structure. This BBD-parallel approach may give a considerable profit though it is strongly dependent on the system topology. This paper presents a theoretical foundation of the algorithm, its implementation, and numerical complexity analysis in virtue of practical measurements of matrix operations.

Numerical Solution of Large Scale Sparse Matrix Equations in Python

PAMM ◽  
2014 ◽  
Vol 14 (1) ◽  
pp. 959-960
Author(s):  
Björn Baran ◽  
Martin Köhler ◽  
Nitin Prasad ◽  
Jens Saak
Keyword(s):  
Numerical Solution ◽  
Large Scale ◽  
Sparse Matrix ◽  
Matrix Equations

Parallel solution of Riccati matrix equations with the matrix sign function

Automatica ◽  
1998 ◽  
Vol 34 (2) ◽  
pp. 151-156 ◽  
Author(s):  
Enrique S. Quintana-Orti ◽  
Vicente Hernandez
Keyword(s):  
Matrix Equations ◽  
Matrix Sign Function ◽  
Sign Function ◽  
Parallel Solution ◽  
The Matrix ◽  
Riccati Matrix
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