To exploit the potential of multicore architectures, recent dense linear algebra libraries have u... more To exploit the potential of multicore architectures, recent dense linear algebra libraries have used tile algorithms, which consist in scheduling a Directed Acyclic Graph (DAG) of tasks of fine granularity where nodes represent tasks, either panel factorization or update of a block-column, and edges represent dependencies among them. Although past approaches already achieve high performance on moderate and large square matrices, their way of processing a panel in sequence leads to limited performance when factorizing tall and skinny matrices or small square matrices. We present a new fully asynchronous method for computing a QR factorization on shared-memory multicore architectures that overcomes this bottleneck. Our contribution is to adapt an existing algorithm that performs a panel factorization in parallel (named Communication-Avoiding QR and initially designed for distributed-memory machines), to the context of tile algorithms using asynchronous computations. An experimental study shows significant improvement (up to almost 10 times faster) compared to state-of-the-art approaches. We aim to eventually incorporate this work into the Parallel Linear Algebra for Scalable Multi-core Architectures (PLASMA) library.
To exploit the potential of multicore architectures, recent dense linear algebra libraries have u... more To exploit the potential of multicore architectures, recent dense linear algebra libraries have used tile algorithms, which consist of scheduling a Directed Acyclic Graph (DAG) of fine granularity tasks where nodes represent tasks, either panel factorization or update of a block-column, and edges represent dependencies among them. Although past approaches already achieve high performance on moderate and large square matrices, their way of processing a panel in sequence leads to limited performance when factorizing tall and skinny matrices or small square matrices. We present a new, fully asynchronous method for computing a QR factorization on shared-memory multicore architectures that overcomes this bottleneck. Our contribution is to adapt an existing algorithm that performs a panel factorization in parallel (named Communication-Avoiding QR and initially designed for distributed-memory machines) to the context of tile algorithms using asynchronous computations. An experimental study shows significant improvement (up to almost 10 times faster) compared to state-of-the-art approaches. We aim to eventually incorporate this work into the Parallel Linear Algebra for Scalable Multi-core Architectures (PLASMA) library.
The emergence and continuing use of multi-core architectures require changes in the existing soft... more The emergence and continuing use of multi-core architectures require changes in the existing software and sometimes even a redesign of the established algorithms in order to take advantage of now prevailing parallelism. The Parallel Linear Algebra for Scalable Multi-core Architectures (PLASMA) is a project that aims to achieve both high performance and portability across a wide range of multi-core architectures. We present in this paper a comparative study of PLASMA's performance against established linear algebra packages (LAPACK and ScaLAPACK), against new approaches at parallel execution (Task Based Linear Algebra Subroutines -TBLAS), and against equivalent commercial software offerings (MKL, ESSL and PESSL). Our experiments were conducted on one-sided linear algebra factorizations (LU, QR and Cholesky) and used multi-core architectures (based on Intel Xeon EMT64 and IBM Power6). The performance results show improvements brought by new algorithms on up to 32 cores -the largest multi-core system we could access. * Research reported here was partially supported by the National Science Foundation and Microsoft Research.
The emergence and continuing use of multi-core architectures and graphics processing units requir... more The emergence and continuing use of multi-core architectures and graphics processing units require changes in the existing software and sometimes even a redesign of the established algorithms in order to take advantage of now prevailing parallelism. Parallel Linear Algebra for Scalable Multi-core Architectures (PLASMA) and Matrix Algebra on GPU and Multics Architectures (MAGMA ) are two projects that aims to achieve high performance and portability across a wide range of multi-core architectures and hybrid systems respectively. We present in this document a comparative study of PLASMA's performance against established linear algebra packages and some preliminary results of MAGMA on hybrid multi-core and GPU systems.
With cost effective distributed memory computer systems reaching high performances, it may become... more With cost effective distributed memory computer systems reaching high performances, it may become feasible in the near future to provide routinely reliable blood flow simulations during angiographic procedures to enhance standard medical imaging techniques. The long term goal of our work is to produce a fast parallel image base Navier-Stokes flow solver for these kinds of clinical procedures. To achieve such performance, our method relies on the proper combination of three techniques that are the L2 penalty method to deal with complex geometry, a level set method to extract the geometry of the arteries, and a fast scalable domain decomposition solver for the parallel processing of the discrete equations. We developed a web application with a database back-end to store both the original medical images and the results of these simulations. This will assist the endovascular surgeon by providing quickly blood flow indicators such as pressure or shear stresses at the wall of the artery, in addition to existing image analysis technique aimed at improving therapy.
We present a method to combine fluid dynamics and image analysis into a single fast simulation en... more We present a method to combine fluid dynamics and image analysis into a single fast simulation environment. Our target applications are hemodynamic studies. Our method combines an NS solver that relies on the L2 penalty approach pioneered by Caltagirone and co-workers, and a level set method based on the Mumford-Shah energy model. Working in Cartesian coordinates regardless of grid no matter the complexity of the geometry, one can use fast parallel domain decomposition solvers in a fairly robust and consistent way. The input of the simulation tool is a set of JPEG images, and the output can be various flow components as well as shear stress indicators on the vessel or domain wall. In two space dimensions the code runs close to real time.
... In order to avoid redundancy as much as possible in the computation, we fix a size of one mes... more ... In order to avoid redundancy as much as possible in the computation, we fix a size of one mesh once and for all the overlap between ... the best subdomain solver from all existing methods, but rather to use the best solver from Sparskit(Krylov solver tool developped by Saad33) or ...
To exploit the potential of multicore architectures, recent dense linear algebra libraries have u... more To exploit the potential of multicore architectures, recent dense linear algebra libraries have used tile algorithms, which consist in scheduling a Directed Acyclic Graph (DAG) of tasks of fine granularity where nodes represent tasks, either panel factorization or update of a block-column, and edges represent dependencies among them. Although past approaches already achieve high performance on moderate and large square matrices, their way of processing a panel in sequence leads to limited performance when factorizing tall and skinny matrices or small square matrices. We present a new fully asynchronous method for computing a QR factorization on shared-memory multicore architectures that overcomes this bottleneck. Our contribution is to adapt an existing algorithm that performs a panel factorization in parallel (named Communication-Avoiding QR and initially designed for distributed-memory machines), to the context of tile algorithms using asynchronous computations. An experimental study shows significant improvement (up to almost 10 times faster) compared to state-of-the-art approaches. We aim to eventually incorporate this work into the Parallel Linear Algebra for Scalable Multi-core Architectures (PLASMA) library.
To exploit the potential of multicore architectures, recent dense linear algebra libraries have u... more To exploit the potential of multicore architectures, recent dense linear algebra libraries have used tile algorithms, which consist of scheduling a Directed Acyclic Graph (DAG) of fine granularity tasks where nodes represent tasks, either panel factorization or update of a block-column, and edges represent dependencies among them. Although past approaches already achieve high performance on moderate and large square matrices, their way of processing a panel in sequence leads to limited performance when factorizing tall and skinny matrices or small square matrices. We present a new, fully asynchronous method for computing a QR factorization on shared-memory multicore architectures that overcomes this bottleneck. Our contribution is to adapt an existing algorithm that performs a panel factorization in parallel (named Communication-Avoiding QR and initially designed for distributed-memory machines) to the context of tile algorithms using asynchronous computations. An experimental study shows significant improvement (up to almost 10 times faster) compared to state-of-the-art approaches. We aim to eventually incorporate this work into the Parallel Linear Algebra for Scalable Multi-core Architectures (PLASMA) library.
The emergence and continuing use of multi-core architectures require changes in the existing soft... more The emergence and continuing use of multi-core architectures require changes in the existing software and sometimes even a redesign of the established algorithms in order to take advantage of now prevailing parallelism. The Parallel Linear Algebra for Scalable Multi-core Architectures (PLASMA) is a project that aims to achieve both high performance and portability across a wide range of multi-core architectures. We present in this paper a comparative study of PLASMA's performance against established linear algebra packages (LAPACK and ScaLAPACK), against new approaches at parallel execution (Task Based Linear Algebra Subroutines -TBLAS), and against equivalent commercial software offerings (MKL, ESSL and PESSL). Our experiments were conducted on one-sided linear algebra factorizations (LU, QR and Cholesky) and used multi-core architectures (based on Intel Xeon EMT64 and IBM Power6). The performance results show improvements brought by new algorithms on up to 32 cores -the largest multi-core system we could access. * Research reported here was partially supported by the National Science Foundation and Microsoft Research.
The emergence and continuing use of multi-core architectures and graphics processing units requir... more The emergence and continuing use of multi-core architectures and graphics processing units require changes in the existing software and sometimes even a redesign of the established algorithms in order to take advantage of now prevailing parallelism. Parallel Linear Algebra for Scalable Multi-core Architectures (PLASMA) and Matrix Algebra on GPU and Multics Architectures (MAGMA ) are two projects that aims to achieve high performance and portability across a wide range of multi-core architectures and hybrid systems respectively. We present in this document a comparative study of PLASMA's performance against established linear algebra packages and some preliminary results of MAGMA on hybrid multi-core and GPU systems.
With cost effective distributed memory computer systems reaching high performances, it may become... more With cost effective distributed memory computer systems reaching high performances, it may become feasible in the near future to provide routinely reliable blood flow simulations during angiographic procedures to enhance standard medical imaging techniques. The long term goal of our work is to produce a fast parallel image base Navier-Stokes flow solver for these kinds of clinical procedures. To achieve such performance, our method relies on the proper combination of three techniques that are the L2 penalty method to deal with complex geometry, a level set method to extract the geometry of the arteries, and a fast scalable domain decomposition solver for the parallel processing of the discrete equations. We developed a web application with a database back-end to store both the original medical images and the results of these simulations. This will assist the endovascular surgeon by providing quickly blood flow indicators such as pressure or shear stresses at the wall of the artery, in addition to existing image analysis technique aimed at improving therapy.
We present a method to combine fluid dynamics and image analysis into a single fast simulation en... more We present a method to combine fluid dynamics and image analysis into a single fast simulation environment. Our target applications are hemodynamic studies. Our method combines an NS solver that relies on the L2 penalty approach pioneered by Caltagirone and co-workers, and a level set method based on the Mumford-Shah energy model. Working in Cartesian coordinates regardless of grid no matter the complexity of the geometry, one can use fast parallel domain decomposition solvers in a fairly robust and consistent way. The input of the simulation tool is a set of JPEG images, and the output can be various flow components as well as shear stress indicators on the vessel or domain wall. In two space dimensions the code runs close to real time.
... In order to avoid redundancy as much as possible in the computation, we fix a size of one mes... more ... In order to avoid redundancy as much as possible in the computation, we fix a size of one mesh once and for all the overlap between ... the best subdomain solver from all existing methods, but rather to use the best solver from Sparskit(Krylov solver tool developped by Saad33) or ...
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