Schumann, U. and Benner, J. (1982) Direct Solution of the Discretized PoissonNeumann Problem on a Domain Composed of Rectangles. Journal of Computational Physics, 46, pp. 114.

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Abstract
Finitedifference approximations for the twodimensional PoissonNeumann problem (l/λ) div λ grad p = q, λ>0 on R (λ<sub>n</sub> x grad p = g<sub>R</sub> on ∂R result in a large system of linear equations Lp = q. The n x n matrix L is singular with rank(L) = n  1. A solution exists if q satisfies the consistency condition v<sup>T</sup>q = 0, where L<sup>T</sup>v = 0, v ≠ 0. A directsolution scheme is described for the case where R can be decomposed into a set of rectangular domains each having a possibly different but constant material coefficient λ. We assume that this problem has to be solved repeatedly for many vectors q. The method is efficient in that the number of operations is of order n log n. This efficiency is gained by using fast elliptic solvers for each single rectangle and a proper variant of the socalled influence or capacitancematrix technique. Here, on each rectangle a separate PoissonNeumann problem has to be solved. The essential point is the manner in which the consistency condition is enforced for each rectangle. The new method has been successfully applied in a code FLUX to analyze fluidstructure interactions.
Item URL in elib:  https://elib.dlr.de/53345/  

Document Type:  Article  
Title:  Direct Solution of the Discretized PoissonNeumann Problem on a Domain Composed of Rectangles  
Authors: 
 
Date:  1982  
Journal or Publication Title:  Journal of Computational Physics  
Open Access:  Yes  
Gold Open Access:  No  
In SCOPUS:  No  
In ISI Web of Science:  No  
Volume:  46  
Page Range:  pp. 114  
Status:  Published  
Keywords:  influencematrix, capacitancematrix  
HGF  Research field:  other  
HGF  Program:  other  
HGF  Program Themes:  other  
DLR  Research area:  no assignment  
DLR  Program:  no assignment  
DLR  Research theme (Project):  no assignment  
Location:  Oberpfaffenhofen  
Institutes and Institutions:  Institute of Atmospheric Physics  
Deposited By:  Freund, Jana  
Deposited On:  20 Feb 2008  
Last Modified:  31 Jul 2019 19:21 
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