caa a22 4500 606167331 CHVBK 20210128100702.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s10665-014-9699-0 doi (NATIONALLICENCE)springer-10.1007/s10665-014-9699-0 Partitioning strategies for the block Cimmino algorithm [Elektronische Daten] [L. Drummond, Iain Duff, Ronan Guivarch, Daniel Ruiz, Mohamed Zenadi] In the context of the block Cimmino algorithm, we study preprocessing strategies to obtain block partitionings that can be applied to general linear systems of equations $$\mathbf{A}\mathbf{x}= \mathbf{b}$$ A x = b . We study strategies that transform the matrix $$\mathbf{A}\mathbf{A}^\mathrm{{T}}$$ A A T into a matrix with a block tridiagonal structure. This provides a partitioning of the linear system for row projection methods because block Cimmino is essentially equivalent to block Jacobi on the normal equations, and the resulting partition will yield a two-block partition of the original matrix. Therefore, the resulting block partitioning should improve the rate of convergence of block row projection methods such as block Cimmino. We discuss a method for obtaining a partitioning using a dropping strategy that gives more blocks at the cost of relaxing the two-block partitioning. We then use a hypergraph partitioning that works directly on the matrix $$\mathbf{A}$$ A to reduce directly the connections between blocks. We give numerical results showing the performance of these techniques both in their effect on the convergence of the block Cimmino algorithm and in their ability to exploit parallelism. Springer Science+Business Media Dordrecht, 2014 Cuthill McKee nationallicence Hypergraph partitioning nationallicence Iterative methods nationallicence Sparse matrices nationallicence Unsymmetric matrices nationallicence Drummond L. Computational Research Division, Lawrence Berkeley National Laboratory, One Cyclotron Road, 94720, Berkeley, CA, USA aut Duff Iain Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique (CERFACS), 42 Ave G. Coriolis, 31057, Toulouse Cedex, France aut Guivarch Ronan ENSEEIHT-IRIT, 2 rue Charles Camichel, BP 7122, 31071, Toulouse Cedex 7, France aut Ruiz Daniel ENSEEIHT-IRIT, 2 rue Charles Camichel, BP 7122, 31071, Toulouse Cedex 7, France aut Zenadi Mohamed ENSEEIHT-IRIT, 2 rue Charles Camichel, BP 7122, 31071, Toulouse Cedex 7, France aut Journal of Engineering Mathematics Springer Netherlands 93/1(2015-08-01), 21-39 0022-0833 93:1<21 2015 93 10665 https://doi.org/10.1007/s10665-014-9699-0 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10665-014-9699-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Drummond L. Computational Research Division, Lawrence Berkeley National Laboratory, One Cyclotron Road, 94720, Berkeley, CA, USA aut NATIONALLICENCE 700 1- Duff Iain Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique (CERFACS), 42 Ave G. Coriolis, 31057, Toulouse Cedex, France aut NATIONALLICENCE 700 1- Guivarch Ronan ENSEEIHT-IRIT, 2 rue Charles Camichel, BP 7122, 31071, Toulouse Cedex 7, France aut NATIONALLICENCE 700 1- Ruiz Daniel ENSEEIHT-IRIT, 2 rue Charles Camichel, BP 7122, 31071, Toulouse Cedex 7, France aut NATIONALLICENCE 700 1- Zenadi Mohamed ENSEEIHT-IRIT, 2 rue Charles Camichel, BP 7122, 31071, Toulouse Cedex 7, France aut NATIONALLICENCE 773 0- Journal of Engineering Mathematics Springer Netherlands 93/1(2015-08-01), 21-39 0022-0833 93:1<21 2015 93 10665