Browsing by Author "Ruiz, Daniel"
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- An hybrid approach for the parallelization of a block iterative algorithmPublication . Balsa, Carlos; Guivarch, Ronan; Ruiz, Daniel; Zenadi, MohamedThe Cimmino method is a row projection method in which the original linear system is divided into subsystems. At every iteration, it computes one projection per subsystem and uses these projections to construct an approximation to the solution of the linear system. The usual parallelization strategy in block algorithms is to distribute the different blocks on the available processors. In this paper, we follow another approach where we do not perform explicitly this block distribution to processors within the code, but let the multi-frontal sparse solver MUMPS handle the data distribution and parallelism. The data coming from the subsystems defined by the block partition in the Block Cimmino method are gathered in an unique block diagonal sparse matrix which is analysed, distributed and factorized in parallel by MUMPS. Our target is to define a methodology for parallelism based only on the functionalities provided by general sparse solver libraries and how efficient this way of doing can be.
- An hybrid approach for the parallelization of a block iterative algorithmPublication . Balsa, Carlos; Guivarch, Ronan; Ruiz, Daniel; Zinadi, MohamedThe Cimmino method is a row projection method in which the original linear system is divided into subsystems. At every iteration, it computes one projection per subsystem and uses these projections to construct an approximation to the solution of the linear system. The usual parallelization strategy in block algorithms is to distribute the different blocks on the available processors. In this paper, we follow another approach where we do not perform explicitly this block distribution to processors within the code, but let the multi-frontal sparse solver MUMPS handle the data distribution and parallelism. The data coming from the subsystems defined by the block partition in the Block Cimmino method are gathered in an unique block diagonal sparse matrix which is analysed, distributed and factorized in parallel by MUMPS. Our target is to define a methodology for parallelism based only on the functionalities provided by general sparse solver libraries and how efficient this way of doing can be
- Inexact subspace iteration for the consecutive solution of linear systems with changing right-hand sidesPublication . Balsa, Carlos; Daydé, Michel; Palma, J.M.L.M.; Ruiz, DanielWe propose a two-phase acceleration technique for the solution of Symmetric and Positive Definite linear systems with multiple right-hand sides. In the first phase we compute some partial spectral information related to the ill conditioned part of the given coefficient matrix and, in the second phase, we use this information to improve the convergence of the Conjugate Gradient algorithm. This approach is adequate for large scale problems, like the simulation of time dependent differential equations, where it is necessary to solve consecutively several linear systems with the same coefficient matrix (or with matrices that present very close spectral properties) but with changing right-hand sides. To compute the spectral information, in the first phase, we combine the block Conjugate Gradient algorithm with the Inexact Subspace Iteration to build a purely iterative algorithm, that we call BlockCGSI. We proceed to an inner-outer convergence analysis and we show that it is possible to determine when to stop the inner iteration in order to achieve the targeted invariance in the outer iteration. The spectral information is used in a second phase to remove the effect of the smallest eigenvalues in two different ways: either by building a Spectral Low Rank Update preconditioner, or by performing a deflation of the initial residual in order to remove part of the solution corresponding to the smallest eigenvalues.
- MUMPS based approach to parallelize the block cimmino algorithmPublication . Balsa, Carlos; Guivarch, Ronan; Raimundo, João; Ruiz, DanielThe Cimmino method is a row projection method in which the original linear system is divided into subsystems. At every iteration, it computes one projection per subsystem and uses these projections to construct an approximation to the solution of the linear system. The usual parallelization strategy applied in block algorithms is to distribute the different blocks on the different available processors. In this paper, we follow another approach where we do not perform explicitely this block distribution to processors whithin the code, but let the multi-frontal sparse solver MUMPS handle the data distribution and parallelism. The data coming from the subsystems defined by the block partition in the Block Cimmino method are gathered in an unique matrix which is analysed, distributed and factorized in parallel by MUMPS. Our target is to define a methodology for parallelism based only on the functionalities provided by general sparse solver libraries and how efficient this way of doing can be. We relate the development of this new approach from an existing code written in Fortran 77 to the MUMPS-embedded version. The results of the ongoing numerical experiments will be presented in the conference