19 research outputs found
Rectangular Full Packed Format for Cholesky's Algorithm: Factorization, Solution and Inversion
We describe a new data format for storing triangular, symmetric, and
Hermitian matrices called RFPF (Rectangular Full Packed Format). The standard
two dimensional arrays of Fortran and C (also known as full format) that are
used to represent triangular and symmetric matrices waste nearly half of the
storage space but provide high performance via the use of Level 3 BLAS.
Standard packed format arrays fully utilize storage (array space) but provide
low performance as there is no Level 3 packed BLAS. We combine the good
features of packed and full storage using RFPF to obtain high performance via
using Level 3 BLAS as RFPF is a standard full format representation. Also, RFPF
requires exactly the same minimal storage as packed format. Each LAPACK full
and/or packed triangular, symmetric, and Hermitian routine becomes a single new
RFPF routine based on eight possible data layouts of RFPF. This new RFPF
routine usually consists of two calls to the corresponding LAPACK full format
routine and two calls to Level 3 BLAS routines. This means {\it no} new
software is required. As examples, we present LAPACK routines for Cholesky
factorization, Cholesky solution and Cholesky inverse computation in RFPF to
illustrate this new work and to describe its performance on several commonly
used computer platforms. Performance of LAPACK full routines using RFPF versus
LAPACK full routines using standard format for both serial and SMP parallel
processing is about the same while using half the storage. Performance gains
are roughly one to a factor of 43 for serial and one to a factor of 97 for SMP
parallel times faster using vendor LAPACK full routines with RFPF than with
using vendor and/or reference packed routines
Features in the diffraction of a scalar plane wave from doubly-periodic Dirichlet and Neumann surfaces
The diffraction of a scalar plane wave from a doubly-periodic surface on
which either the Dirichlet or Neumann boundary condition is imposed is studied
by means of a rigorous numerical solution of the Rayleigh equation for the
amplitudes of the diffracted Bragg beams. From the results of these
calculations the diffraction efficiencies of several of the lowest order
diffracted beams are calculated as functions of the polar and azimuthal angles
of incidence. The angular dependencies of the diffraction efficiencies display
features that can be identified as Rayleigh anomalies for both types of
surfaces. In the case of a Neumann surface additional features are present that
can be attributed to the existence of surface waves on such surfaces. Some of
the results obtained through the use of the Rayleigh equation are validated by
comparing them with results of a rigorous Green's function numerical
calculation.Comment: 16 pages, 5 figure
Time-dependent radio emission from evolving jets
We investigated the time-dependent radiative and dynamical properties of
light supersonic jets launched into an external medium, using hydrodynamic
simulations and numerical radiative transfer calculations. These involved
various structural models for the ambient media, with density profiles
appropriate for galactic and extragalactic systems. The radiative transfer
formulation took full account of emission, absorption, re-emission, Faraday
rotation and Faraday conversion explicitly. High time-resolution intensity maps
were generated, frame-by-frame, to track the spatial hydrodynamical and
radiative properties of the evolving jets. Intensity light curves were computed
via integrating spatially over the emission maps. We apply the models to jets
in active galactic nuclei (AGN). From the jet simulations and the
time-dependent emission calculations we derived empirical relations for the
emission intensity and size for jets at various evolutionary stages. The
temporal properties of jet emission are not solely consequences of intrinsic
variations in the hydrodynamics and thermal properties of the jet. They also
depend on the interaction between the jet and the ambient medium. The
interpretation of radio jet morphology therefore needs to take account of
environmental factors. Our calculations have also shown that the environmental
interactions can affect specific emitting features, such as internal shocks and
hotspots. Quantification of the temporal evolution and spatial distribution of
these bright features, together with the derived relations between jet size and
emission, would enable us to set constraints on the hydrodynamics of AGN and
the structure of the ambient medium.Comment: 16 pages, 18 figures, MNRAS in press
Excited state quantum phase transitions in the bending spectra of molecules
European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No 87208
A High Order Cartesian Grid, Finite Volume Method for Elliptic Interface Problems
We present a higher-order finite volume method for solving elliptic PDEs with
jump conditions on interfaces embedded in a 2D Cartesian grid. Second, fourth,
and sixth order accuracy is demonstrated on a variety of tests including
problems with high-contrast and spatially varying coefficients, large
discontinuities in the source term, and complex interface geometries. We
include a generalized truncation error analysis based on cell-centered Taylor
series expansions, which then define stencils in terms of local discrete
solution data and geometric information. In the process, we develop a simple
method based on Green's theorem for computing exact geometric moments directly
from an implicit function definition of the embedded interface. This approach
produces stencils with a simple bilinear representation, where
spatially-varying coefficients and jump conditions can be easily included and
finite volume conservation can be enforced
Excited state quantum phase transitions in the bending spectra of molecules
We present an extension of the Hamiltonian of the two dimensional limit of
the vibron model encompassing all possible interactions up to four-body
operators. We apply this Hamiltonian to the modeling of the experimental
bending spectrum of fourteen molecules. The bending degrees of freedom of the
selected molecular species include all possible situations: linear, bent, and
nonrigid equilibrium structures; demonstrating the flexibility of the algebraic
approach, that allows for the consideration of utterly different physical cases
with a general formalism and a single Hamiltonian. For each case, we compute
predicted term values used to depict the quantum monodromy diagram, the
Birge-Sponer plot, the participation ratio. We also show the bending energy
functional obtained using the coherent --or intrinsic-- state formalism.Comment: 67 pages, 18 tables and 15 figure
Parallel unstructured solvers for linear partial differential equations
This thesis presents the development of a parallel algorithm to solve symmetric
systems of linear equations and the computational implementation of a parallel
partial differential equations solver for unstructured meshes. The proposed
method, called distributive conjugate gradient - DCG, is based on a single-level
domain decomposition method and the conjugate gradient method to obtain a
highly scalable parallel algorithm.
An overview on methods for the discretization of domains and partial differential
equations is given. The partition and refinement of meshes is discussed and
the formulation of the weighted residual method for two- and three-dimensions
presented. Some of the methods to solve systems of linear equations are introduced,
highlighting the conjugate gradient method and domain decomposition
methods. A parallel unstructured PDE solver is proposed and its actual implementation
presented. Emphasis is given to the data partition adopted and the
scheme used for communication among adjacent subdomains is explained. A series
of experiments in processor scalability is also reported.
The derivation and parallelization of DCG are presented and the method validated
throughout numerical experiments. The method capabilities and limitations
were investigated by the solution of the Poisson equation with various source
terms. The experimental results obtained using the parallel solver developed as
part of this work show that the algorithm presented is accurate and highly scalable,
achieving roughly linear parallel speed-up in many of the cases tested
Genome-wide analysis of genetic diversity and artificial selection in Large White pigs in Russia
Breeding practices adopted at different farms are aimed at maximizing the profitability of pig farming. In this work, we have analyzed the genetic diversity of Large White pigs in Russia. We compared genomes of historic and modern Large White Russian breeds using 271 pig samples. We have identified 120 candidate regions associated with the differentiation of modern and historic pigs and analyzed genomic differences between the modern farms. The identified genes were associated with height, fitness, conformation, reproductive performance, and meat quality
Parallel unstructured solvers for linear partial differential equations
This thesis presents the development of a parallel algorithm to solve symmetric systems of linear equations and the computational implementation of a parallel partial differential equations solver for unstructured meshes. The proposed method, called distributive conjugate gradient - DCG, is based on a single-level domain decomposition method and the conjugate gradient method to obtain a highly scalable parallel algorithm. An overview on methods for the discretization of domains and partial differential equations is given. The partition and refinement of meshes is discussed and the formulation of the weighted residual method for two- and three-dimensions presented. Some of the methods to solve systems of linear equations are introduced, highlighting the conjugate gradient method and domain decomposition methods. A parallel unstructured PDE solver is proposed and its actual implementation presented. Emphasis is given to the data partition adopted and the scheme used for communication among adjacent subdomains is explained. A series of experiments in processor scalability is also reported. The derivation and parallelization of DCG are presented and the method validated throughout numerical experiments. The method capabilities and limitations were investigated by the solution of the Poisson equation with various source terms. The experimental results obtained using the parallel solver developed as part of this work show that the algorithm presented is accurate and highly scalable, achieving roughly linear parallel speed-up in many of the cases tested.EThOS - Electronic Theses Online ServiceGBUnited Kingdo