linear_algebra

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- | The team is the main developer of qr_mumps -- a direct solver for sparse linear systems based on the multifrontal QR factorization. qr_mumps is a parallel, multithreaded software based on the OpenMP standard and is specifically designed for multicore architectures. Parallelism is achieved by dividing the workload into fine grained tasks that are arranged in a Direct Acyclic Graph (DAG). The execution of these tasks is guided by an asynchronous and dynamic data-flow programming model which provides high efficiency and scalability. The package is distributed under the LGPL license. | + | The team is the main developer of [[http://buttari.perso.enseeiht.fr/qr_mumps|qr_mumps]] -- a direct solver for sparse linear systems based on the multifrontal QR factorization. qr_mumps is a parallel, multithreaded software based on the OpenMP standard and is specifically designed for multicore architectures. Parallelism is achieved by dividing the workload into fine grained tasks that are arranged in a Direct Acyclic Graph (DAG). The execution of these tasks is guided by an asynchronous and dynamic data-flow programming model which provides high efficiency and scalability. The package is distributed under the LGPL license. |

APO is also pursuing the study and development of novel, hybrid solution techniques for large scale sparse linear systems, specifically the Block-Cimmino method which is an iterative, row projection method in which the original linear system is divided into subsystems. At every iteration, this method computes one projection per subsystem and uses these projections to construct an approximation to the solution of the linear system. The Block-Cimmino method is a linear stationary iterative method with a symmetric and positive definite (SPD) iteration matrix. Therefore, its rate of convergence can be accelerated with the use of Block Conjugate Gradient method (Block-CG). The main target of this research is the implementation of a parallel distributed Block-Cimmino method where the Cimmino iteration matrix is used as a preconditioner for the Block-CG. | APO is also pursuing the study and development of novel, hybrid solution techniques for large scale sparse linear systems, specifically the Block-Cimmino method which is an iterative, row projection method in which the original linear system is divided into subsystems. At every iteration, this method computes one projection per subsystem and uses these projections to construct an approximation to the solution of the linear system. The Block-Cimmino method is a linear stationary iterative method with a symmetric and positive definite (SPD) iteration matrix. Therefore, its rate of convergence can be accelerated with the use of Block Conjugate Gradient method (Block-CG). The main target of this research is the implementation of a parallel distributed Block-Cimmino method where the Cimmino iteration matrix is used as a preconditioner for the Block-CG. | ||

- | The APO team is also deeply involved in the GridTLSE platform GridTLSE (http://gridtlse.org) platform -- an expertise site which aims to provide access to a range of sparse linear direct solvers and assists users in selecting the most appropriate solver for their problem. GridTLSE makes use of grid computing technology to perform the related computations. Determining the most appropriate values for the input parameters of a specific sparse linear solver is quite complex and combinatorial by nature, which makes the use of grid computing technology very attractive. TLSE platform has been designed by using the "Distributed Interactive Engineering Toolbox (DIET)" grid middleware to manage the various sparse solvers and tools installed over heterogeneous computers. GridTLSE has been supported by ANR-SOLSTICE (ANR-06-CIS6-01, 2007-2010), LEGO (ANR-05-CIGC-11 2005-2009) and ANR Cosinus COOP (ANR-09-COSI-001-04, 2009-20011) and is now used in production environments. | + | The APO team is also deeply involved in the GridTLSE platform GridTLSE (http://gridtlse.org) platform -- an expertise site which aims to provide access to a range of sparse linear direct solvers and assists users in selecting the most appropriate solver for their problem. GridTLSE makes use of grid computing technology to perform the related computations. Determining the most appropriate values for the input parameters of a specific sparse linear solver is quite complex and combinatorial by nature, which makes the use of grid computing technology very attractive. TLSE platform has been designed by using the [[http://graal.ens-lyon.fr/DIET/|"Distributed Interactive Engineering Toolbox (DIET)"]] grid middleware to manage the various sparse solvers and tools installed over heterogeneous computers. GridTLSE has been supported by ANR-SOLSTICE (ANR-06-CIS6-01, 2007-2010), LEGO (ANR-05-CIGC-11 2005-2009) and ANR Cosinus COOP (ANR-09-COSI-001-04, 2009-20011) and is now used in production environments. |

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linear_algebra.txt · Last modified: 2015/03/06 09:46 (external edit)