Improving Performance of Iterative Methods by Lossy Checkponting

Iterative methods are commonly used approaches to solve large, sparse linear systems, which are fundamental operations for many modern scientific simulations. When the large-scale iterative methods are running with a large number of ranks in parallel, they have to checkpoint the dynamic variables periodically in case of unavoidable fail-stop errors, requiring fast I/O systems and large storage space. To this end, significantly reducing the checkpointing overhead is critical to improving the overall performance of iterative methods. Our contribution is fourfold. (1) We propose a novel lossy checkpointing scheme that can significantly improve the checkpointing performance of iterative methods by leveraging lossy compressors. (2) We formulate a lossy checkpointing performance model and derive theoretically an upper bound for the extra number of iterations caused by the distortion of data in lossy checkpoints, in order to guarantee the performance improvement under the lossy checkpointing scheme. (3) We analyze the impact of lossy checkpointing (i.e., extra number of iterations caused by lossy checkpointing files) for multiple types of iterative methods. (4)We evaluate the lossy checkpointing scheme with optimal checkpointing intervals on a high-performance computing environment with 2,048 cores, using a well-known scientific computation package PETSc and a state-of-the-art checkpoint/restart toolkit. Experiments show that our optimized lossy checkpointing scheme can significantly reduce the fault tolerance overhead for iterative methods by 23%~70% compared with traditional checkpointing and 20%~58% compared with lossless-compressed checkpointing, in the presence of system failures.Comment: 14 pages, 10 figures, HPDC'1

Lorentzian spin foam amplitudes: graphical calculus and asymptotics

The amplitude for the 4-simplex in a spin foam model for quantum gravity is defined using a graphical calculus for the unitary representations of the Lorentz group. The asymptotics of this amplitude are studied in the limit when the representation parameters are large, for various cases of boundary data. It is shown that for boundary data corresponding to a Lorentzian simplex, the asymptotic formula has two terms, with phase plus or minus the Lorentzian signature Regge action for the 4-simplex geometry, multiplied by an Immirzi parameter. Other cases of boundary data are also considered, including a surprising contribution from Euclidean signature metrics.Comment: 30 pages. v2: references now appear. v3: presentation greatly improved (particularly diagrammatic calculus). Definition of "Regge state" now the same as in previous work; signs change in final formula as a result. v4: two references adde

A model for silicon solar cell performance in space Final report

Model for silicon solar cell performance in spac

Oxidation and corrosion behavior of modified-composition, low-chromium 304 stainless steel alloys

The effects of substituting less strategic elements than Cr on the oxidation and corrosion resistance of AISI 304 stainless steel were investigated. Cyclic oxidation resistance was evaluated at 870 C. Corrosion resistance was determined by exposure of specimens to a boiling copper-rich solution of copper sulfate and sulfuric acid. Alloy substitutes for Cr included Al, Mn, Mo, Si, Ti, V, Y, and misch metal. A level of about 12% Cr was the minimum amount of Cr required for adequate oxidation and corrosion resistance in the modified composition 304 stainless steels. This represents a Cr saving of at least 33%. Two alloys containing 12% Cr and 2% Al plus 2% Mo and 12% Cr plus 2.65% Si were identified as most promising for more detailed evaluation

Proton-induced damage to silicon solar cell assemblies a state-of-the-art survey Quarterly report

Literature review on proton damage of irradiated silicon solar cell

Effects of uniform damage to silicon solar cells

Uniform damage to silicon solar cells by fast protons or electron

Asymptotics of 4d spin foam models

We study the asymptotic properties of four-simplex amplitudes for various four-dimensional spin foam models. We investigate the semi-classical limit of the Ooguri, Euclidean and Lorentzian EPRL models using coherent states for the boundary data. For some classes of geometrical boundary data, the asymptotic formulae are given, in all three cases, by simple functions of the Regge action for the four-simplex geometry.Comment: 10 pages, Proceedings for the 2nd Corfu summer school and workshop on quantum gravity and quantum geometry, talk given by Winston J. Fairbair

On the causal Barrett--Crane model: measure, coupling constant, Wick rotation, symmetries and observables

We discuss various features and details of two versions of the Barrett-Crane spin foam model of quantum gravity, first of the Spin(4)-symmetric Riemannian model and second of the SL(2,C)-symmetric Lorentzian version in which all tetrahedra are space-like. Recently, Livine and Oriti proposed to introduce a causal structure into the Lorentzian Barrett--Crane model from which one can construct a path integral that corresponds to the causal (Feynman) propagator. We show how to obtain convergent integrals for the 10j-symbols and how a dimensionless constant can be introduced into the model. We propose a `Wick rotation' which turns the rapidly oscillating complex amplitudes of the Feynman path integral into positive real and bounded weights. This construction does not yet have the status of a theorem, but it can be used as an alternative definition of the propagator and makes the causal model accessible by standard numerical simulation algorithms. In addition, we identify the local symmetries of the models and show how their four-simplex amplitudes can be re-expressed in terms of the ordinary relativistic 10j-symbols. Finally, motivated by possible numerical simulations, we express the matrix elements that are defined by the model, in terms of the continuous connection variables and determine the most general observable in the connection picture. Everything is done on a fixed two-complex.Comment: 22 pages, LaTeX 2e, 1 figur

Effective interactions for light nuclei: an effective (field theory) approach

One of the central open problems in nuclear physics is the construction of effective interactions suitable for many-body calculations. We discuss a recently developed approach to this problem, where one starts with an effective field theory containing only fermion fields and formulated directly in a no-core shell-model space. We present applications to light nuclei and to systems of a few atoms in a harmonic-oscillator trap. Future applications and extensions, as well as challenges, are also considered