Catálogo de publicaciones - libros

It is well known that the Lanczos process suffers from loss of orthogonality in the case of finite-precision arithmetic. Several approaches have been proposed in order to address this issue, thus enabling the successful computation of approximate eigensolutions. However, these techniques have been studied mainly in the context of long Lanczos runs, but not for restarted Lanczos eigensolvers. Several variants of the explicitly restarted Lanczos algorithm employing different reorthogonalization strategies have been implemented in SLEPc, the Scalable Library for Eigenvalue Computations. The aim of this work is to assess the numerical robustness of the proposed implementations as well as to study the impact of reorthogonalization in parallel efficiency.

Numerical methods, parallel and distributed computing.

Software reusability has proven to be an effective practice to speed-up the development of complex high-performance scientific and engineering applications. We promote the reuse of high quality software and general purpose libraries through the Advance CompuTational Software (ACTS) Collection. ACTS tools have continued to provide solutions to many of today’s computational problems. In addition, ACTS tools have been successfully ported to a variety of computer platforms; therefore tremendously facilitating the porting of applications that rely on ACTS functionalities. In this contribution we discuss a high-level user interface that provides a faster code prototype and user familiarization with ACTS tools. The high-level user interfaces have been built using Python. Here we focus on Python based interfaces to ScaLAPACK, the PyScaLAPACK component of PyACTS. We briefly introduce their use, functionalities, and benefits. We illustrate a few simple example of their use, as well as exemplar utilization inside large scientific applications. We also comment on existing Python interfaces to other ACTS tools. We present some comparative performance results of PyACTS based versus direct LAPACK and ScaLAPACK code implementations.

We present an experimental study of two versions of a second-degree iterative method applied to the resolution of the sparse linear systems related to the 3D multi-group time-dependent Neutron Diffusion Equation (TNDE), which is important for studies of stability and security of nuclear reactors. In addition, the second-degree iterative methods have been combined with an adaptable technique, in order to improve their convergence and accuracy. The authors consider that second-degree iterative methods can be applied and extended to the study of transient analysis with more than two energy groups and they might represent a saving in spatial cost for nuclear core simulations. These methods have been coded in PETSc [1][2][3].

We have addressed in this paper the implementation of red-black multigrid smoothers on high-end microprocessors. Most of the previous work about this topic has been focused on cache memory issues due to its tremendous impact on performance. In this paper, we have extended these studies taking () into account. With the introduction of , new possibilities arise, which makes a revision of the different alternatives highly advisable. A new strategy is proposed that focuses on inter-thread sharing to tolerate the increasing penalties caused by memory accesses. Performance results on an based system reveal that our alternative scheme can compete with and even improve sophisticated schemes based on tailored loop fusion and tiling transformations aimed at improving temporal locality.

In this paper, we describe block matrix algorithms for the iterative solution of linear-quadratic optimal control problems arising from the control of parabolic partial differential equations over a finite control horizon. After spatial discretization, by finite element or finite difference methods, the original problem reduces to an optimal control problem for coupled ordinary differential equations, where can be quite . As a result, its solution by conventional control algorithms can be prohibitively expensive in terms of computational cost and memory requirements.

We describe two iterative algorithms. The first algorithm employs a CG method to solve a symmetric positive definite reduced linear system for the unknown control variable. A preconditioner is described, which we prove has a rate of convergence independent of the space and time discretization parameters, however, double iteration is required. The second algorithm is designed to avoid double iteration by introducing an auxiliary variable. It yields a symmetric indefinite system, and for this system a positive definite block preconditioner is described. We prove that the resulting rate of convergence is independent of the space and time discretization parameters, when MINRES acceleration is used. Numerical results are presented for test problems.

In this work we consider the numerical solution of a radiative transfer equation for modeling the emission of photons in stellar atmospheres. Mathematically, the problem is formulated in terms of a weakly singular Fredholm integral equation defined on a Banach space. Computational approaches to solve the problem are discussed, using direct and iterative strategies that are implemented in open source packages.

32A55, 45B05, 65D20, 65R20, 68W10.

Cosmological simulators are currently an important component in the study of the formation of galaxies and planetary systems. However, existing simulators do not scale effectively on more recent machines containing thousands of processors. In this paper, we introduce a new parallel simulator called ChaNGa (Charm N-body Gravity). This simulator is based on the infrastructure, which provides a powerful runtime system that automatically maps computation to physical processors. Using features, in particular its measurement-based load balancers, we were able to scale the gravitational force calculation of ChaNGa on up to one thousand processors, with astronomical datasets containing millions of particles. As we pursue the completion of a production version of the code, our current experimental results show that ChaNGa may become a powerful resource for the astronomy community.

Despite their dominance of high-end computing (HEC) through the 1980’s, vector systems have been gradually replaced by microprocessor-based systems. However, while peak performance of microprocessors has grown exponentially, the gradual slide in sustained performance delivered to scientific applications has become a growing concern among HEC users. Recently, the Earth Simulator and Cray X1/X1E parallel vector processor systems have spawned renewed interest in vector technology for scientific applications. In this work, we compare the performance of two Lattice-Boltzmann applications and the Cactus astrophysics package on vector based systems including the Cray X1/X1E, Earth Simulator, and NEC SX-8, with commodity-based processor clusters including the IBM SP Power3, IBM Power5, Intel Itanium2, and AMD Opteron processors. We examine these important scientific applications to quantify the effective performance and investigate if efficiency benefits are applicable to a broader array of numerical methods.

We describe an efficient numerical simulator, based on an operator splitting technique, for three-phase flow in heterogeneous porous media that takes into account capillary forces, general relations for the relative permeability functions and variable porosity and permeability fields. Our numerical procedure combines a non-oscillatory, second order, conservative central difference scheme for the system of hyperbolic conservation laws modeling the convective transport of the fluid phases with locally conservative mixed finite elements for the approximation of the parabolic and elliptic problems associated with the diffusive transport of fluid phases and the pressure-velocity calculation. This numerical procedure has been used to investigate the existence and stability of non-classical waves (also called transitional or undercompressive waves) in heterogeneous two-dimensional flows, thereby extending previous results for one-dimensional problems.

The aim of this work is to perform numerical simulations of the propagation of a laser beam in a plasma. At each time step, one has to solve a Helmholtz equation with variable coefficients in a domain which may contain more than hundred millions of cells.

One uses an iterative method of Krylov type to deal with this system. At each inner iteration, the preconditioning amounts essentially to solve a linear system which corresponds to the same five-diagonal symmetric non-hermitian matrix. If and denote the number of discretization points in each spatial direction, this matrix is block tri-diagonal and the diagonal blocks are equal to a square matrix of dimension which corresponds to the discretization form of a one-dimension wave operator. The corresponding linear system is solved by a block cyclic reduction method.

The crucial point is the product of a full square matrix of dimension by a set of vectors where corresponds to the basis of the eigenvectors of the tri-diagonal symmetric matrix . We show some results which are obtained on a parallel architecture. Simulations with 200 millions of cells have run on 200 processors and the results are presented.