1,643 research outputs found
Domain Decomposition Based High Performance Parallel Computing\ud
The study deals with the parallelization of finite element based Navier-Stokes codes using domain decomposition and state-ofart sparse direct solvers. There has been significant improvement in the performance of sparse direct solvers. Parallel sparse direct solvers are not found to exhibit good scalability. Hence, the parallelization of sparse direct solvers is done using domain decomposition techniques. A highly efficient sparse direct solver PARDISO is used in this study. The scalability of both Newton and modified Newton algorithms are tested
Analysis of A Splitting Approach for the Parallel Solution of Linear Systems on GPU Cards
We discuss an approach for solving sparse or dense banded linear systems
on a Graphics Processing Unit (GPU) card. The
matrix is possibly nonsymmetric and
moderately large; i.e., . The ${\it split\ and\
parallelize}{\tt SaP}{\bf A}{\bf A}_ii=1,\ldots,P{\bf A}_i{\tt SaP::GPU}{\tt PARDISO}{\tt SuperLU}{\tt MUMPS}{\tt SaP::GPU}{\tt MKL}{\tt SaP::GPU}{\tt SaP::GPU}$ is publicly available and distributed as
open source under a permissive BSD3 license.Comment: 38 page
A domain decomposing parallel sparse linear system solver
The solution of large sparse linear systems is often the most time-consuming
part of many science and engineering applications. Computational fluid
dynamics, circuit simulation, power network analysis, and material science are
just a few examples of the application areas in which large sparse linear
systems need to be solved effectively. In this paper we introduce a new
parallel hybrid sparse linear system solver for distributed memory
architectures that contains both direct and iterative components. We show that
by using our solver one can alleviate the drawbacks of direct and iterative
solvers, achieving better scalability than with direct solvers and more
robustness than with classical preconditioned iterative solvers. Comparisons to
well-known direct and iterative solvers on a parallel architecture are
provided.Comment: To appear in Journal of Computational and Applied Mathematic
Selected inversion as key to a stable Langevin evolution across the QCD phase boundary
We present new results of full QCD at nonzero chemical potential. In PRD 92,
094516 (2015) the complex Langevin method was shown to break down when the
inverse coupling decreases and enters the transition region from the deconfined
to the confined phase. We found that the stochastic technique used to estimate
the drift term can be very unstable for indefinite matrices. This may be
avoided by using the full inverse of the Dirac operator, which is, however, too
costly for four-dimensional lattices. The major breakthrough in this work was
achieved by realizing that the inverse elements necessary for the drift term
can be computed efficiently using the selected inversion technique provided by
the parallel sparse direct solver package PARDISO. In our new study we show
that no breakdown of the complex Langevin method is encountered and that
simulations can be performed across the phase boundary.Comment: 8 pages, 6 figures, Proceedings of the 35th International Symposium
on Lattice Field Theory, Granada, Spai
FERM3D: A finite element R-matrix electron molecule scattering code
FERM3D is a three-dimensional finite element program, for the elastic
scattering of a low energy electron from a general polyatomic molecule, which
is converted to a potential scattering problem. The code is based on tricubic
polynomials in spherical coordinates. The electron-molecule interaction is
treated as a sum of three terms: electrostatic, exchange. and polarisation. The
electrostatic term can be extracted directly from ab initio codes
({\sc{GAUSSIAN 98}} in the work described here), while the exchange term is
approximated using a local density functional. A local polarisation potential
based on density functional theory [C. Lee, W. Yang and R. G. Parr, {Phys. Rev.
B} {37}, (1988) 785] describes the long range attraction to the molecular
target induced by the scattering electron. Photoionisation calculations are
also possible and illustrated in the present work. The generality and
simplicity of the approach is important in extending electron-scattering
calculations to more complex targets than it is possible with other methods.Comment: 30 pages, 4 figures, preprint, Computer Physics Communications (in
press
A two step viscothermal acoustic FE method
Previously, the authors presented a finite element for viscothermal acoustics. This element has the velocity vector, the temperature and the pressure as degrees of freedom. It can be used, for example, to model sound propagation in miniature acoustical transducers. Unfortunately, the large number of coupled degrees of freedom can make the models big and time consuming to solve. A method with reduced calculation time has been developed. It is possible to partially decouple the temperature degree of freedom, as result of the differences in the characteristic length scales of acoustics and heat conduction. This leads to a method that uses two sequential steps. In the first step, a scalar field containing information about the thermal effects is calculated (not the temperature). This is a relatively small FE calculation. In the second step, the actual viscothermal acoustical equations are solved. This calculation uses the field calculated in the first step and has the velocity vector and the pressure as the degrees of freedom. The temperature is not a degree of freedom anymore, but it can be easily calculated in a post processing step. The required computational effort is reduced significantly, while the difference in the results, compared to the fully coupled method, is negligible. Along with the theoretical basis for the method, a specific FE calculation is presented to illustrate its accuracy and improvement in calculation time
On large-scale diagonalization techniques for the Anderson model of localization
We propose efficient preconditioning algorithms for an eigenvalue problem arising in quantum physics, namely the computation of a few interior eigenvalues and their associated eigenvectors for large-scale sparse real and symmetric indefinite matrices of the Anderson model
of localization. We compare the Lanczos algorithm in the 1987 implementation by Cullum and Willoughby with the shift-and-invert techniques in the implicitly restarted Lanczos method and in the JacobiāDavidson method. Our preconditioning approaches for the shift-and-invert symmetric indefinite linear system are based on maximum weighted matchings and algebraic multilevel incomplete
LDLT factorizations. These techniques can be seen as a complement to the alternative idea of using more complete pivoting techniques for the highly ill-conditioned symmetric indefinite Anderson matrices. We demonstrate the effectiveness and the numerical accuracy of these algorithms. Our numerical examples reveal that recent algebraic multilevel preconditioning solvers can accelerate the computation of a large-scale eigenvalue problem corresponding to the Anderson model of localization
by several orders of magnitude
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