1,721,024 research outputs found
MLD2P4 (Multi-Level Domain Decomposition Parallel Preconditioners Package based on PSBLAS)
No full textMLD2P4 (MultiLevel Domain Decomposition Parallel Preconditioners Package based on PSBLAS) provides parallel Algebraic MultiGrid (AMG) and Domain Decomposition preconditioners, to be used in the iterative solution of linear systems.
The name of the package comes from its original implementation, containing multilevel additive and hybrid Schwarz preconditioners, as well as one-level additive Schwarz preconditioners. The current version extends the original plan by including multilevel cycles and smoothers widely used in multigrid methods. A purely algebraic approach is applied to generate coarse-level corrections, so that no geometric background is needed concerning the matrix to be preconditioned.
MLD2P4 has been designed to provide scalable and easy-to-use preconditioners in the context of the PSBLAS (Parallel Sparse Basic Linear Algebra Subprograms) computational framework and is used in conjuction with the Krylov solvers available from PSBLAS. The package employs object-oriented design techniques in Fortran 2003, with interfaces to additional third party libraries such as MUMPS, UMFPACK, SuperLU, and SuperLU_Dist, which can be exploited in building multilevel preconditioners. The parallel implementation is based on a Single Program Multiple Data (SPMD) paradigm; the inter-process communication is based on MPI and is managed mainly through PSBLAS
Performance analysis of parallel Schwarz preconditioners in the LES of turbulent channel flows
No full textWe present a comparative study of parallel Schwarz preconditioners in the solution of linear systems arising in a Large Eddy Simulation (LES) procedure for turbulent plane channel flows. This procedure applies a time-splitting technique to suitably filtered Navier-Stokes equations, in order to decouple the continuity and momentum equations, and uses a semi-implicit scheme for time integration and finite volumes for space discretisation. This approach requires the solution of four sparse linear systems at each time step, accounting for a large part of the overall simulation; hence the linear system solvers are a crucial component in the whole procedure. Several preconditioners are applied in the simulation of a reference test case for the LES community, using discretisation grids of different sizes, with the aim of analysing the effects of different algorithmic choices defining the preconditioners, and identifying the most effective ones for the selected problem. The preconditioners, coupled with the GMRES method, are run within SParC-LES, a recently developed LES code based on the PSBLAS and MLD2P4 libraries for parallel sparse matrix computations and preconditioning. © 2012 Elsevier Ltd. All rights reserved
A parallel generalized relaxation method for high-performance image segmentation on GPUs
Full text linkFast and scalable software modules for image segmentation are needed for modern high-throughput screening platforms in Computational Biology. Indeed, accurate segmentation is one of the main steps to be applied in a basic software pipeline aimed to extract accurate measurements from a large amount of images. Image segmentation is often formulated through a variational principle, where the solution is the minimum of a suitable functional, as in the case of the Ambrosio–Tortorelli model. Euler–Lagrange equations associated with the above model are a system of two coupled elliptic partial differential equations whose finite-difference discretization can be efficiently solved by a generalized relaxation method, such as Jacobi or Gauss–Seidel, corresponding to a first-order alternating minimization scheme. In this work we present a parallel software module for image segmentation based on the Parallel Sparse Basic Linear Algebra Subprograms (PSBLAS), a general-purpose library for parallel sparse matrix computations, using its Graphics Processing Unit (GPU) extensions that allow us to exploit in a simple and transparent way the performance capabilities of both multi-core CPUs and of many-core GPUs. We discuss performance results in terms of execution times and speed-up of the segmentation module running on GPU as well as on multi-core CPUs, in the analysis of 2D gray-scale images of mouse embryonic stem cells colonies coming from biological experiment
BootCMatch: A software package for bootstrap AMG based on graph weighted matching
No full textThis article has two main objectives: one is to describe some extensions of an adaptive Algebraic Multigrid (AMG) method of the form previously proposed by the first and third authors, and a second one is to present a new software framework, named BootCMatch, which implements all the components needed to build and apply the described adaptive AMG both as a stand-alone solver and as a preconditioner in a Krylov method. The adaptive AMG presented is meant to handle general symmetric and positive definite (SPD) sparse linear systems, without assuming any a priori information of the problem and its origin; the goal of adaptivity is to achieve a method with a prescribed convergence rate. The presented method exploits a general coarsening process based on aggregation of unknowns, obtained by a maximum weight matching in the adjacency graph of the system matrix. More specifically, a maximum product matching is employed to define an effective smoother subspace (complementary to the coarse space), a process referred to as compatible relaxation, at every level of the recursive two-level hierarchical AMG process. Results on a large variety of test cases and comparisons with related work demonstrate the reliability and efficiency of the method and of the software
Automatic coarsening in Algebraic Multigrid utilizing quality measures for matching-based aggregations
No full textIn this paper, we discuss the convergence of an Algebraic MultiGrid (AMG) method for general symmetric positive-definite matrices. The method relies on an aggregation algorithm, named coarsening based on compatible weighted matching, which exploits the interplay between the principle of compatible relaxation and the maximum product matching in undirected weighted graphs. The results are based on a general convergence analysis theory applied to the class of AMG methods employing unsmoothed aggregation and identifying a quality measure for the coarsening; similar quality measures were originally introduced and applied to other methods as tools to obtain good quality aggregates leading to optimal convergence for M-matrices. The analysis, as well as the coarsening procedure, is purely algebraic and, in our case, allows an a posteriori evaluation of the quality of the aggregation procedure which we apply to analyze the impact of approximate algorithms for matching computation and the definition of graph edge weights. We also explore the connection between the choice of the aggregates and the compatible relaxation convergence, confirming the consistency between theories for designing coarsening procedures in purely algebraic multigrid methods and the effectiveness of the coarsening based on compatible weighted matching. We discuss various completely automatic algorithmic approaches to obtain aggregates for which good convergence properties are achieved on various test cases
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