1,721,023 research outputs found
Using gradient directions to get global convergence of Newton-type methods
No full textThe renewed interest in Steepest Descent (SD) methods following the work of Barzilai and Borwein [2] has driven us to consider a globalization strategy based on SD, which is applicable to any line-search method. In particular, we combine Newton-type directions with scaled SD steps to have suitable descent directions. Scaling the SD directions with a suitable step length makes a significant difference with respect to similar globalization approaches, in terms of both theoretical features and computational behavior. We apply our strategy to Newton's method and the BFGS method, with computational results that appear interesting compared with the results of well-established globalization strategies devised ad hoc for those methods
A Parallel Implementation of a Multigrid Multiblock Euler Solver on Distributed Memory Machines
No full textThis paper presents a parallel Multigrid solver for the computation of steady compressible inviscid flows around 2D and 3D aerodynamic configurations, on MIMD distributed memory machines. It is a parallel version of a large CFD code, ZEN Flow Solver, developed by the Italian Aerospace Research Center (CIRA). The sequential solver uses a multiblock structured grid and a cell-centered finite volume scheme, and implements an explicit time-marching procedure, based on a Full Multigrid algorithm. The parallel version has been developed using a domain decomposition technique, based on the multiblock structure of the grid. Moreover, a convergence criterion has been introduced in the Multigrid algorithm. The parallel solver has been implemented using the PVM communication environment. Experiments have been carried out using a Convex Meta Series, a cluster of HP PA-RISC workstations. Numerical results and parallel efficiency concerning a 2D and a 3D test case are analysed here. © 1997 Elsevier Science B.V
PINEAPL: A European Project to develop a Parallel Numerical Library for Industrial Applications
No full textin Lecture Notes in Computer Science, Springe
On the development of PSBLAS-based parallel two-level Schwarz preconditioners
No full textDesign and implementation issues that concern the development of a package of parallel algebraic two-level Schwarz preconditioners are discussed. The computations are based on the Parallel Sparse BLAS (PSBLAS) library. The package implements various versions of Additive Schwarz preconditioners and applies a smoothed aggregation technique to generate a coarse-level correction. The coarse matrix can be either replicated on the processors or distributed among them; the corresponding system is solved by factorization or block Jacobi sweeps, respectively. The design of the package started from a description of the preconditioners in terms of parallel basic Linear Algebra operators, in order to develop software based on standard kernels. Suitable preconditioner data structures were defined to fully exploit the existing PSBLAS functionalities; however, the implementation of the preconditioner required also an extension of the set of basic library kernels. The results of experiments carried out on different test matrices show that the package is competitive in terms of runtime efficiency
Directional TGV-Based Image Restoration under Poisson Noise
Full text linkWe are interested in the restoration of noisy and blurry images where the texture mainly follows a single direction (i.e., directional images). Problems of this type arise, for example, in microscopy or computed tomography for carbon or glass fibres. In order to deal with these problems, the Directional Total Generalized Variation (DTGV) was developed by Kongskov et al. in 2017 and 2019, in the case of impulse and Gaussian noise. In this article we focus on images corrupted by Poisson noise, extending the DTGV regularization to image restoration models where the data fitting term is the generalized Kullback–Leibler divergence. We also propose a technique for the identification of the main texture direction, which improves upon the techniques used in the aforementioned work about DTGV. We solve the problem by an ADMM algorithm with proven convergence and subproblems that can be solved exactly at a low computational cost. Numerical results on both phantom and real images demonstrate the effectiveness of our approach
On preconditioner updates for sequences of saddle-point linear systems
No full textUpdating preconditioners for the solution of sequences of large and sparse saddlepoint
linear systems via Krylov methods has received increasing attention in the last few
years, because it allows to reduce the cost of preconditioning while keeping the efficiency
of the overall solution process. This paper provides a short survey of the two approaches
proposed in the literature for this problem: updating the factors of a preconditioner
available in a block LDL' form, and updating a preconditioner via a limited-memory
technique inspired by quasi-Newton methods
TGV-based restoration of Poissonian images with automatic estimation of the regularization parameter
No full textThe problem of restoring images corrupted by Poisson noise is common in many application fields and, because of its intrinsic ill posedness, it requires regularization techniques for its solution. The effectiveness of such techniques depends on the value of the regularization parameter balancing data fidelity and regularity of the solution. Here we consider the Total Generalized Variation regularization introduced in [SIAM J. Imag. Sci, 3(3), 492-526, 2010], which has demonstrated its ability of preserving sharp features as well as smooth transition variations, and introduce an automatic strategy for defining the value of the regularization parameter. We solve the corresponding optimization problem by using a 3-block version of ADMM. Preliminary numerical experiments support the proposed approach
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