80 research outputs found
Successive eigenvalue relaxation: a new method for the generalized eigenvalue problem and convergence estimates
We present a new subspace iteration method for the efficient computation of several smallest eigenvalues of the generalized eigenvalue problem Au = lambda Bu for symmetric positive definite operators A and B. We call this method successive eigenvalue relaxation, or the SER method (homoechon of the classical successive over-relaxation,
or SOR method for linear systems). In particular, there are two significant features of SER which render it computationally attractive: (i) it can effectively deal with
preconditioned large-scale eigenvalue problems, and (ii) its practical implementation does not require any information about the preconditioner used: it can routinely
accommodate sophisticated preconditioners designed to meet more exacting requirements (e.g. three-dimensional elasticity problems with small thickness parameters).
We endow SER with theoretical convergence estimates allowing for multiple and clusters of eigenvalues and illustrate their usefulness in a numerical example for a
discretized partial differential equation exhibiting clusters of eigenvalues
Block Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX) in hypre and PETSc
We describe our software package Block Locally Optimal Preconditioned
Eigenvalue Xolvers (BLOPEX) publicly released recently. BLOPEX is available as
a stand-alone serial library, as an external package to PETSc (``Portable,
Extensible Toolkit for Scientific Computation'', a general purpose suite of
tools for the scalable solution of partial differential equations and related
problems developed by Argonne National Laboratory), and is also built into {\it
hypre} (``High Performance Preconditioners'', scalable linear solvers package
developed by Lawrence Livermore National Laboratory). The present BLOPEX
release includes only one solver--the Locally Optimal Block Preconditioned
Conjugate Gradient (LOBPCG) method for symmetric eigenvalue problems. {\it
hypre} provides users with advanced high-quality parallel preconditioners for
linear systems, in particular, with domain decomposition and multigrid
preconditioners. With BLOPEX, the same preconditioners can now be efficiently
used for symmetric eigenvalue problems. PETSc facilitates the integration of
independently developed application modules with strict attention to component
interoperability, and makes BLOPEX extremely easy to compile and use with
preconditioners that are available via PETSc. We present the LOBPCG algorithm
in BLOPEX for {\it hypre} and PETSc. We demonstrate numerically the scalability
of BLOPEX by testing it on a number of distributed and shared memory parallel
systems, including a Beowulf system, SUN Fire 880, an AMD dual-core Opteron
workstation, and IBM BlueGene/L supercomputer, using PETSc domain decomposition
and {\it hypre} multigrid preconditioning. We test BLOPEX on a model problem,
the standard 7-point finite-difference approximation of the 3-D Laplacian, with
the problem size in the range .Comment: Submitted to SIAM Journal on Scientific Computin
Genetic diversity and origin of the feral horses in Theodore Roosevelt National Park
Feral horses in Theodore Roosevelt National Park (TRNP) represent an iconic era of the North Dakota Badlands. Their uncertain history raises management questions regarding origins, genetic diversity, and long-term genetic viability. Hair samples with follicles were collected from 196 horses in the Park and used to sequence the control region of mitochondrial DNA (mtDNA) and to profile 12 autosomal short tandem repeat (STR) markers. Three mtDNA haplotypes found in the TRNP horses belonged to haplogroups L and B. The control region variation was low with haplotype diversity of 0.5271, nucleotide diversity of 0.0077 and mean pairwise difference of 2.93. We sequenced one mitochondrial genome from each haplotype determined by the control region. Two complete mtDNA sequences of haplogroup L were closely related to the mtDNA of American Paint horse. The TRNP haplotype B did not have close matches in GenBank. The phylogenetic test placed this sequence in a group consisting of two horses from China, one from Yakutia, and one from Italy raising a possibility of historical transportation of horses from Siberia and East Asia to North America. Autosomal STR loci were polymorphic and indicated that the TRNP horses were distinctly different from 48 major horse breeds. Heterozygosity, mean number of alleles, and other measures of diversity indicated that TRNP herd diversity was below that observed for most other feral herds and domestic breeds. Both mtDNA and STRs demonstrated that the existing genetic data sets of horses are insufficient to determine the exact origins of the TRNP horses. However, measures of nuclear and mitochondrial diversity have elucidated management needs. It is recommended that new genetic stock be introduced and that adaptive management principles are employed to ensure that unique mitochondrial lineages are preserved and genetic diversity is increased and maintained over time
Motion-corrected reconstruction of parametric images from dynamic PET data with the Synergistic Image Reconstruction Framework (SIRF)
Motion correction has been added to a PET-MR reconstruction tool, SIRF, by incorporating a registration package, NiftyReg. New functionality has been demonstrated in the context of estimating kinetic parameters in the left temporal lobe, comparing direct and indirect reconstructions and evaluating the impact of using motion correction.Principal component analysis was used to detect motion and to determine time frames, while STIR's parametric-OSEM was used to perform the motion-corrected direct parametric reconstruction.It was found that the variance in the left temporal lobe decreased when motion correction was performed, and the same was true of direct reconstructions compared to indirect.With SIRF, the entirety of the demonstrated functionality can be performed from a single Matlab or Python script
Versatile regularisation toolkit for iterative image reconstruction with proximal splitting algorithms
Ill-posed image recovery requires regularisation to ensure stability. The presented open-source regularisation toolkit consists of state-of-the-art variational algorithms which can be embedded in a plug-and-play fashion
into the general framework of proximal splitting methods. The packaged regularisers aim to satisfy various prior expectations of the investigated objects, e.g., their structural characteristics, smooth or non-smooth surface morphology.
The flexibility of the toolkit helps with the design of more advanced model-based iterative reconstruction methods
for different imaging modalities while operating with simpler building blocks. The toolkit is written for CPU and
GPU architectures and wrapped for Python/MATLAB. We demonstrate the functionality of the toolkit in application
to Positron Emission Tomography (PET) and X-ray synchrotron computed tomography (CT)
Recent Progress in STIR 5.0
STIR is an open source software for Emission Tomography data manipulation and image reconstruction, covering both PET and SPECT. In this work recent additions to the STIR code base are highlighted, namely the ability to read General Electric (GE) Raw Data Format 9 (RDF9) files, incorporation of GPU operators for forward and back projection, as well as work towards quantitative imaging for both PET and SPECT
Motion estimation and correction for simultaneous PET/MR using SIRF and CIL
SIRF is a powerful PET/MR image reconstruction research tool for processing data and developing new algorithms. In this research, new developments to SIRF are presented, with focus on motion estimation and correction. SIRF's recent inclusion of the adjoint of the resampling operator allows gradient propagation through resampling, enabling the MCIR technique. Another enhancement enabled registering and resampling of complex images, suitable for MRI. Furthermore, SIRF's integration with the optimization library CIL enables the use of novel algorithms. Finally, SPM is now supported, in addition to NiftyReg, for registration. Results of MR and PET MCIR reconstructions are presented, using FISTA and PDHG, respectively. These demonstrate the advantages of incorporating motion correction and variational and structural priors. This article is part of the theme issue 'Synergistic tomographic image reconstruction: part 2'
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COMPASS, the COMmunity Petascale project for Accelerator Science and Simulation, a board computational accelerator physics initiative
Accelerators are the largest and most costly scientific instruments of the Department of Energy, with uses across a broad range of science, including colliders for particle physics and nuclear science and light sources and neutron sources for materials studies. COMPASS, the Community Petascale Project for Accelerator Science and Simulation, is a broad, four-office (HEP, NP, BES, ASCR) effort to develop computational tools for the prediction and performance enhancement of accelerators. The tools being developed can be used to predict the dynamics of beams in the presence of optical elements and space charge forces, the calculation of electromagnetic modes and wake fields of cavities, the cooling induced by comoving beams, and the acceleration of beams by intense fields in plasmas generated by beams or lasers. In SciDAC-1, the computational tools had multiple successes in predicting the dynamics of beams and beam generation. In SciDAC-2 these tools will be petascale enabled to allow the inclusion of an unprecedented level of physics for detailed prediction
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