Implicit-factorization preconditioning and iterative solvers for regularized saddle-point systems

We consider conjugate-gradient like methods for solving block symmetric indefinite linear systems that arise from saddle-point problems or, in particular, regularizations thereof. Such methods require preconditioners that preserve certain sub-blocks from the original systems but allow considerable flexibility for the remaining blocks. We construct a number of families of implicit factorizations that are capable of reproducing the required sub-blocks and (some) of the remainder. These generalize known implicit factorizations for the unregularized case. Improved eigenvalue clustering is possible if additionally some of the noncrucial blocks are reproduced. Numerical experiments confirm that these implicit-factorization preconditioners can be very effective in practice.

An analysis of arithmetic averaging in approximate Riemann solvers with an application to steady, supercritical flows

An analysis of various arithmetic averaging procedures for approximate Riemann solvers is made with a specific emphasis on efficiency and a jump capturing property. The various alternatives discussed are intended for future work, as well as the more immediate problem of steady, supercritical free-surface flows. Numerical results are shown for two test problems.

Riemann solvers with primitive parameter vectors for two-dimensional compressible flows of a real gas

An analysis of averaging procedures is presented for an approximate Riemann solver for the equations governing the compressible flow of a real gas. This study extends earlier work for the Euler equations with ideal gases.

Multivariable cluster analysis for high-speed industrial machinery

The overall operation and internal complexity of a particular production machinery can be depicted in terms of clusters of multidimensional points which describe the process states, the value in each point dimension representing a measured variable from the machinery. The paper describes a new cluster analysis technique for use with manufacturing processes, to illustrate how machine behaviour can be categorised and how regions of good and poor machine behaviour can be identified. The cluster algorithm presented is the novel mean-tracking algorithm, capable of locating N-dimensional clusters in a large data space in which a considerable amount of noise is present. Implementation of the algorithm on a real-world high-speed machinery application is described, with clusters being formed from machinery data to indicate machinery error regions and error-free regions. This analysis is seen to provide a promising step ahead in the field of multivariable control of manufacturing systems.

Human versus animal: contrasting decomposition dynamics of mammalian analogues in experimental taphonomy

Taphonomic studies regularly employ animal analogues for human decomposition due to ethical restrictions relating to the use of human tissue. However, the validity of using animal analogues in soil decomposition studies is still questioned. This study compared the decomposition of skeletal muscle tissues (SMTs) from human (Homo sapiens), pork (Sus scrofa), beef (Bos taurus), and lamb (Ovis aries) interred in soil microcosms. Fixed interval samples were collected from the SMT for microbial activity and mass tissue loss determination; samples were also taken from the underlying soil for pH, electrical conductivity, and nutrient (potassium, phosphate, ammonium, and nitrate) analysis. The overall patterns of nutrient fluxes and chemical changes in nonhuman SMT and the underlying soil followed that of human SMT. Ovine tissue was the most similar to human tissue in many of the measured parameters. Although no single analogue was a precise predictor of human decomposition in soil, all models offered close approximations in decomposition dynamics.

Soils of contrasting pH affect the decomposition of buried mammalian (Ovis aries) skeletal muscle tissue

Little is known about the effect of edaphic conditions on the decomposition of buried mammalian tissues. To address this, we set up a replicated incubation study with three fresh soils of contrasting pH: a Podsol (acidic), a Cambisol (neutral), and a Rendzina (alkaline), in which skeletal muscle tissue (SMT) of known mass was allowed to decompose. Our results clearly demonstrated that soil type had a considerable effect on the decomposition of SMT buried in soil. Differences in the rate of decomposition were up to three times greater in the Podsol compared with the Rendzina. The rate of microbial respiration was correlated to the rate of soft tissue loss, which suggests that the decomposition of SMT is dependent on the microbial community present in the soil. Decompositional by-products caused the pH of the immediate soil environment to change, becoming more alkaline at first, before acidifying. Our results demonstrate the need for greater consideration of soil type in future taphonomic studies.

Optimised frequency grids for infrared radiative transfer simulations in cloudy conditions

This paper shows that radiometer channel radiances for cloudy atmospheric conditions can be simulated with an optimised frequency grid derived under clear-sky conditions. A new clear-sky optimised grid is derived for AVHRR channel 5 ð12 m m, 833 cm �1 Þ. For HIRS channel 11 ð7:33 m m, 1364 cm �1 Þ and AVHRR channel 5, radiative transfer simulations using an optimised frequency grid are compared with simulations using a reference grid, where the optimised grid has roughly 100–1000 times less frequencies than the full grid. The root mean square error between the optimised and the reference simulation is found to be less than 0.3 K for both comparisons, with the magnitude of the bias less than 0.03 K. The simulations have been carried out with the radiative transfer model Atmospheric Radiative Transfer Simulator (ARTS), version 2, using a backward Monte Carlo module for the treatment of clouds. With this module, the optimised simulations are more than 10 times faster than the reference simulations. Although the number of photons is the same, the smaller number of frequencies reduces the overhead for preparing the optical properties for each frequency. With deterministic scattering solvers, the relative decrease in runtime would be even more. The results allow for new radiative transfer applications, such as the development of new retrievals, because it becomes much quicker to carry out a large number of simulations. The conclusions are applicable to any downlooking infrared radiometer.