1,721,096 research outputs found
Gilles de Rome, Théorèmes sur l’être et l’essence. Introduction, traduction et notes de Stéphane Mercier
No full textPini Giorgio, Thirion Benoît. Gilles de Rome, Théorèmes sur l’être et l’essence. Introduction, traduction et notes de Stéphane Mercier. In: Revue Philosophique de Louvain. Troisième série, tome 110, n°2, 2012. pp. 372-374
Computation of minimun eigenvalue through minimization of Rayleigh's quotient for large sparse matrices using vector computer
No full textRayleigh Quotient Minimization methods for the calculation of minimal eigenpair achieve great efficiency when ad hoc preconditioners are employed. The performance of different preconditioners on a vector computer is compared and analyzed from a computational standpoint. The numerical experiments are carried out on large symmetric sparse positive definite matrices arising from finite element discretizations of practical problems. Diagonal, polynomial and Kershaw preconditioners are considered for the generalized and the classical eigenvalue problems. Speed-up factors and MFLOPS are calculated. The results show that a good vectorization level of the computational code is achieved. The speed-up factors obtained with the best schemes are generally high and uniformly distributed. Numerical experiments suggest that the highest efficiency for the solution of the classical problem is achieved in vector computers by diagonal preconditioning. This conclusion differs from the results that can be obtained in scalar computers. All the computations were performed on a CRAY X-MP/48 supercomputer
Transpose-free Lanczos-type schemes on transputer network
No full textWe present the parallel implementation on a transputer network of two preconditioned Lanczos-type schemes for the solution of unsymmetric sparse Linear systems: Bi-CGSTAB and TFQMR Solution of a number of sample tests shows that Bi-CGSTAB with ILU preconditioning is generally Faster than TFQMR, but do not achieve. a high degree of parallelize!ion. Better paraLlelization is obtained with the diagonal preconditioner, which uses less memory and allows therefore the solution of larger problems. With this preconditioner the TFQMR algorithm is found to be more robust than Bi-CGSTAB, but not always globally more efficient. The speed Ups obtained with 8 processors in this case reached a maximum of approximately 6.82, showing the high degree of parallelization achievable with the diagonal preconditioner. As in most massively parallel scenarios, however, the attainable speed ups are strongly dependent on the problem granularity
A parallel algorithm for the partial eigensolution of sparse symmetric matrices on the CRAY Y-MP
No full textA parallel algorithm for the calculation of the p leftmost eigenpairs of large, sparse F.E.M. matrices is presented. Test problems are carried out on symmetric, positive definite matrices whose dimensions range from N = 222 to N = 4560. The method, which is intrinsically parallel, is based on the simultaneous minimization of the Rayleigh quotient obtained using an appropriate preconditioned version of the conjugate gradient scheme. The parallel implementation on a CRAY Y-MP8/432 supercomputer is described. The computational efficiency is evaluated with different test matrices and CPU number varying from 1 to 4. The average parallel speedups obtained with 2, 3, and 4 processors are respectively 1.72, 2.24, 2.63. They suggest that a high percentage of the code is efficiently parallelized
Prismatic versus tetrahedral elements in three-dimensional finite element analyses of subsurface systems
No full textA mesh of prismatic or tetrahedral elements automatically generated from an initial triangular grid is used to integrate 3-D flow equation in space. Many numerical comparisons between these two models have been performed. The results show that integration with tetrahedrons is as accurate as integration with prisms but much more efficient. The CPU time of solution with prismatic elements is about three times greater than that required employing tetrahedral elemen
Leftmost eigenvalue of real and complex sparse matrices on parallel computer using approximate inverse preconditioning
No full textAn efficient parallel approach for the computation of the eigenvalue of smallest absolute magnitude of sparse real and complex matrices is provided. The proposed strategy tries to improve the efficiency of the reverse power method. At each inverse power iteration the linear system is solved either by the conjugate gradient scheme (symmetric case) or by the Bi-CGSTAB method (symmetric case). Both solvers are preconditioned employing the approximate inverse factorization and thus are easily parallelized. The satisfactory speed-ups obtained on the CRAY T3E supercomputer show the high degree of parallelization reached by the proposed algorithm
Calculation of condition numbers of sparse matrices on the nCUBE 2
No full textIn this note we discuss the development and implementation of an efficient and highly parallelizable algorithm for the calculation of some
of the most used condition numbers for large sparse matrices. In the
process the inverse matrix could be also evaluated. A number of numerical
experiments are carried out on an nCUBE 2 parallel computer. Symmetric and
nonsymmetric matrices are used with dimensions ranging from 500 to 3000.
The maximum speed up obtained in the tests is approximately 113 when
128 processors are employed. This result shows the high degree of
parallelization that can be achieved by the proposed algorithm
Domain decomposition and nested grids in a parallel environment
No full textA new algorithm for domain decomposition to solve steady flow problems in randomly heterogeneous porous media has recently been proposed. In the present paper we explain the most significant results of its parallel implementation. In each macro-triangle three adjoint problems are solved by a finite element technique. These adjoint problems are completely independent and my be solved concurrently on a parallel computer. The results obtained are subsequently transferred over the boundaries of subdomains and conveniently assembled over the nodes of the macromesh. We obtain a nonsymmetric linear system wich gives the potential values over the nodes of the macromesh.
The code has been implemented, using specific parallelization directives, on a Cray Y-MP8/432. The average parallel spedups obtained in the numerical experiments using 2, 3, and 4 processors are, respectively, 1.991, 2.978, and 3.973. These values demonstrate the excellent level of parallelization achieved by the code and the high efficiency of the proposed algorithm
Parallel evaluation of leftmost eigenpairs of large unsymmetric matrices
No full textA parallel algorithm for the efficient calculation of m (m .le.15) eigenvalues of smallest absolute magnitude for large sparse unsymmetric matrices is implemented and presented. The procedure employes a modification of the reverse simultaneous iteration scheme, which involves, among other things, the solution of m systems of linear equations. This phase is by far the most computationally demanding of the entire algorithm. However, efficient parallelization can be achieved, highly reducing the overall computational load. Numerical experiments consider the calculation of the m = 12 and m = 15 leftmost eigenvalues and eigenvectors of seven test matrices of varying size between n = 512 and n = 3564. All the computations are performed on a 4 CPU CRAY YMP8/432 machine. The accuracy of the eigenpairs found with the proposed algorithm is independent of the number of CPUs employed. Wall clock time and speed-up measurements show that the scheme is efficient and robust and is well parallelized. In fact, average speed-up factors of up to 3.72 were obtained
- …
