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Matlab*P : Interactive Supercomputing on the Grid |
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| Matlab*P is an interactive system to enable computational scientists and engineers to use a high-level language to program cluster computers. Parallelism is available via data-parallel operations on distributed objects, and via task-parallel operations on multiple objects. We are currently prototyping a version of Matlab*P that allows interactive use of multiple clusters in a computational grid. Joint work with: Wasim Mohiuddin and Imran S. Patel |
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Efficient solutions of industrial electromagnetism problems on parallel computers |
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| For solving dense complex systems, such as those involved in certain formulations in electromagnetism, we test the efficiency of a new preconditioning technique. The idea is to shift the smallest eigenvalues of the original preconditioned system close to one and results in faster convergence of the Krylov solvers. For that purpose, we consider an eigendecomposition using ARPACK to make a spectral low-rank update of the initial preconditioner. Numerical experiments on parallel distributed memory computers will be presented on large real-life industrial problems. Joint work with: Iain Duff, Luc Giraud, and Julien Langou |
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Experiments on Sparse Matrix Partitioning |
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| We have undertaken experiments to determine the comparative quality of some sparse matrix partitioners which implement multilevel recursive algorithms in their partitioning. A large selection of application-derived matrices are partitioned and then permuted so that the resulting form exhibits a block structure. This form is useful for computing sparse matrix-vector multiplications, which are used in iterative methods for solving a sparse linear system, in a parallel computing environment where each block is assigned to a single computing node. |
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LSTRS: Matlab Software for Large-Scale Trust-Region Subproblems |
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| We describe the features of a Matlab 6 implementation of the method LSTRS from: M. Rojas, S.A. Santos and D.C. Sorensen. A new matrix-free method for the large-scale trust-region subproblem, SIAM J. Optim. 11(3): 611-646, 2000. The iterative method LSTRS requires the solution of a large-scale eigenvalue problem at each step. In the software, the eigensolver can be chosen among different methods, or can also be provided by the user. The Hessian matrix can be provided explicitly, or in the form of a routine for matrix-vector multiplication. Therefore, the software preserves the matrix-free nature of the algorithm, which makes it suitable for sparse computations. As in the method, storage is fixed. We present a brief description of the method, the features of the software, and examples to illustrate its use. Joint work with: Sandra A. Santos and Danny C. Sorensen |
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A numerical evaluation of HSL packages for the direct-solution of large sparse, symmetric linear systems of equations |
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| In recent years a number of new direct solvers for the solution of large sparse, symmetric linear systems of equations have been added to the mathematical software library HSL (www.cse.clrc.ac.uk/nag/hsl/hsl.shtml). These include solvers that are designed for the solution of positive-definite systems as well as solvers that are principally intended for solving indefinite problems. Faced with such a choice, it can be difficult for users to know which solver is the most appropriate for their use. We report on using performance profiles as a tool for evaluating and comparing the performance of the HSL solvers on an extensive set of test problems taken from a range of practical applications. Our aim is to make recommendations as to the efficacy of the various HSL packages. This study forms part of a wider on-going comparison of both HSL and non-HSL codes for the direct-solution of symmetric linear systems. Joint work with: Nicholas I. M. Gould |
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Two-Phase Solver versus Two-Level Preconditioner for solving Large Sparse and S.P.D Linear Systems |
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| We intend to solve the linear system $$ Ax= b$$ where $A$ is large sparse and symmetric positive definite. We consider solution techniques that exploit spectral information about the matrix $A$. The first approach is a two-phase algorithm using a deflation-type idea. In a first stage we compute a partial spectral decomposition, that enables us to get an efficient solver. The numerical ingredients are classical in linear algebra; we combine Chebyshev iterations with block Lanczos to compute accurately an invariant subspace associated with the smallest eigenvalues of $A$. Then, the solution on this small subspace is computed using a direct solver while the solution in the orthogonal complemente is obtained with Chebyshev iterations that benefits from the reduced condition number. An alternative technique consists in designing a preconditioner that would require a less accurate eigen-calculation. In this poster we present the numerical behaviour of the two approaches, illustrate their complementarity and indicate how they can be combined to construct a efficient iterative solver. Joint work with: Luc Giraud and Daniel Ruiz |
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New nonsymmetric reordering strategies with a multilevel approach |
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| We present a technique for solving highly indefinite and unstructured linear systems by preconditionined Krylov subspace methods. In contrast with existing techniques that are based on one-sided permutations, the new approach does not attempt to preorder the matrix at the outset all at once. Instead the rows/ columns are attributed a measure and the best once are used first. In this manner the "matching" is done progressively. Once the best rows/columns are matched, then a partial elimination is undertaken and the process is repeated at the next "level". The frameworks of ARMS and partial elimination are exploited. Numerical experiments will be reported using some of the test matrices viewed as hard to handle by iterative solvers. This is preliminary work and the few viewgraphs presented will only give an idea of the method along with some numerical results. |
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algweb@cerfacs.fr Last Update: June 5, 2003 |
