An automatable generic strategy for dynamic load balancing in parallel structured mesh CFD codes

Parallel computing is now widely used in numerical simulation, particularly for application codes based on finite difference and finite element methods. A popular and successful technique employed to parallelize such codes onto large distributed memory systems is to partition the mesh into sub-domains that are then allocated to processors. The code then executes in parallel, using the SPMD methodology, with message passing for inter-processor interactions. In order to improve the parallel efficiency of an imbalanced structured mesh CFD code, a new dynamic load balancing (DLB) strategy has been developed in which the processor partition range limits of just one of the partitioned dimensions uses non-coincidental limits, as opposed to coincidental limits. The ‘local’ partition limit change allows greater flexibility in obtaining a balanced load distribution, as the workload increase, or decrease, on a processor is no longer restricted by the ‘global’ (coincidental) limit change. The automatic implementation of this generic DLB strategy within an existing parallel code is presented in this chapter, along with some preliminary results.

Shape-optimized mesh partitioning and load balancing for parallel adaptive FEM

We present a dynamic distributed load balancing algorithm for parallel, adaptive Finite Element simulations in which we use preconditioned Conjugate Gradient solvers based on domain-decomposition. The load balancing is designed to maintain good partition aspect ratio and we show that cut size is not always the appropriate measure in load balancing. Furthermore, we attempt to answer the question why the aspect ratio of partitions plays an important role for certain solvers. We define and rate different kinds of aspect ratio and present a new center-based partitioning method of calculating the initial distribution which implicitly optimizes this measure. During the adaptive simulation, the load balancer calculates a balancing flow using different versions of the diffusion algorithm and a variant of breadth first search. Elements to be migrated are chosen according to a cost function aiming at the optimization of subdomain shapes. Experimental results for Bramble's preconditioner and comparisons to state-of-the-art load balancers show the benefits of the construction.

Dynamic load-balancing of finite element applications with the DRAMA library

The DRAMA library, developed within the European Commission funded (ESPRIT) project DRAMA, supports dynamic load-balancing for parallel (message-passing) mesh-based applications. The target applications are those with dynamic and solution-adaptive features. The focus within the DRAMA project was on finite element simulation codes for structural mechanics. An introduction to the DRAMA library will illustrate that the very general cost model and the interface designed specifically for application requirements provide simplified and effective access to a range of parallel partitioners. The main body of the paper will demonstrate the ability to provide dynamic load-balancing for parallel FEM problems that include: adaptive meshing, re-meshing, the need for multi-phase partitioning.

Load-balancing for mesh-based applications on heterogeneous cluster computers

This paper discusses load-balancing issues when using heterogeneous cluster computers. There is a growing trend towards the use of commodity microprocessor clusters. Although today's microprocessors have reached a theoretical peak performance in the range of one GFLOPS/s, heterogeneous clusters of commodity processors are amongst the most challenging parallel systems to programme efficiently. We will outline an approach for optimising the performance of parallel mesh-based applications for heterogeneous cluster computers and present case studies with the GeoFEM code. The focus is on application cost monitoring and load balancing using the DRAMA library.

Dynamic mesh partitioning and load-balancing for parallel computational mechanics codes

In this Chapter we discuss the load-balancing issues arising in parallel mesh based computational mechanics codes for which the processor loading changes during the run. We briefly touch on geometric repartitioning ideas and then focus on different ways of using a graph both to solve the load-balancing problem and the optimisation problem, both locally and globally. We also briefly discuss whether repartitioning is always valid. Sample illustrative results are presented and we conclude that repartitioning is an attractive option if the load changes are not too dramatic and that there is a certain trade-off between partition quality and volume of data that the underlying application needs to migrate.

Load sharing in cluster service provision

The factors that are driving the development and use of grids and grid computing, such as size, dynamic features, distribution and heterogeneity, are also pushing to the forefront service quality issues. These include performance, reliability and security. Although grid middleware can address some of these issues on a wider scale, it has also become imperative to ensure adequate service provision at local level. Load sharing in clusters can contribute to the provision of a high quality service, by exploiting both static and dynamic information. This paper is concerned with the presentation of a load sharing scheme, that can satisfy grid computing requirements. It follows a proactive, non preemptive and distributed approach. Load information is gathered continuously before it is needed, and a task is allocated to the most appropriate node for execution. Performance and reliability are enhanced by the decentralised nature of the scheme and the symmetric roles of the nodes. In addition, the scheme exhibits transparency characteristics that facilitate integration with the grid.

Implementation of a proactive load sharing scheme

This paper presents a proactive approach to load sharing and describes the architecture of a scheme, Concert, based on this approach. A proactive approach is characterized by a shift of emphasis from reacting to load imbalance to avoiding its occurrence. In contrast, in a reactive load sharing scheme, activity is triggered when a processing node is either overloaded or underloaded. The main drawback of this approach is that a load imbalance is allowed to develop before costly corrective action is taken. Concert is a load sharing scheme for loosely-coupled distributed systems. Under this scheme, load and task behaviour information is collected and cached in advance of when it is needed. Concert uses Linux as a platform for development. Implemented partially in kernel space and partially in user space, it achieves transparency to users and applications whilst keeping the extent of kernel modifications to a minimum. Non-preemptive task transfers are used exclusively, motivated by lower complexity, lower overheads and faster transfers. The goal is to minimize the average response-time of tasks. Concert is compared with other schemes by considering the level of transparency it provides with respect to users, tasks and the underlying operating system.

Parallel CFD fire modelling on office PCs with dynamic load balancing

Parallel processing techniques have been used in the past to provide high performance computing resources for activities such as Computational Fluid Dynamics. This is normally achieved using specialized hardware and software, the expense of which would be difficult to justify for many fire engineering practices. In this paper, we demonstrate how typical office-based PCs attached to a local area network have the potential to offer the benefits of parallel processing with minimal costs associated with the purchase of additional hardware or software. A dynamic load balancing scheme was devised to allow the effective use of the software on heterogeneous PC networks. This scheme ensured that the impact between the parallel processing task and other computer users on the network was minimized thus allowing practical parallel processing within a conventional office environment. Copyright © 2006 John Wiley & Sons, Ltd.

Zinc polycarboxylate dental cement for the controlled release of an active organic substance: proof of concept

The potential of employing zinc polycarboxylate dental cement as a controlled release material has been studied. Benzalkonium chloride was used as the active ingredient, and incorporated at concentrations of 1, 2 and 3% by mass within the cement. At these levels, there was no observable effect on the speed of setting. Release was followed using an ion-selective electrode to determine changes in chloride ion concentration with time. This technique showed that the additive was released when the cured cement was placed in water, with release occurring by a diffusion mechanism for the first 3 h, but continuing beyond that for up to 1 week. Diffusion coefficients were in the range 5.62 × 10(−6) cm(2) s(−1) (for 1% concentration) to 10.90 × 10(−6) cm(2) s(−1) (for 3% concentration). Up to 3% of the total loading of benzalkonium chloride was released from the zinc polycarboxylate after a week, which is similar to that found in previous studies with glass-ionomer cement. It is concluded that zinc polycarboxylate cement is capable of acting as a useful material for the controlled release of active organic compounds.

The kinetics of water loss from zinc phosphate and zinc polycarboxylate dental cements

The water desorption behaviour of three different zinc oxide dental cements (two polycarboxylates, one phosphate) has been studied in detail. Disc-shaped specimens of each material were prepared and allowed to lose water by being subjected to a low humidity desiccating atmosphere over concentrated sulfuric acid. In all three cements, water loss was found to follow Fick's second law for at least 6 h (until M(t)/M(infinity) values were around 0.5), with diffusion coefficients ranging from 6.03 x 10(-8 )cm(2 )s(-1) (for the zinc phosphate) to 2.056 x 10(-7 )cm(2 )s(-1) (for one of the zinc polycarboxylates, Poly F Plus). Equilibration times for desorption were of the order of 8 weeks, and equilibrium water losses ranged from 7.1% for zinc phosphate to 16.9% and 17.4% for the two zinc polycarboxylates.

The interaction of zinc oxide-based dental cements with aqueous solutions of potassium fluoride

The ability of zinc oxide-based dental cements (zinc phosphate and zinc polycarboxylate) to take up fluoride from aqueous solution has been studied. Only zinc phosphate cement was found to take up any measurable fluoride after 5 h exposure to the solutions. The zinc oxide filler of the zinc phosphate also failed to take up fluoride from solution. The key interaction for this uptake was thus shown to involve the phosphate groups of the set cement. However, whether this took the form of phosphate/fluoride exchange, or the formation of oxyfluoro-phosphate groups was not clear. Fluoride uptake followed radicaltime kinetics for about 2 h in some cases, but was generally better modelled by the Elovich equation, dq(t)/dt = alpha exp(-beta q(t)). Values for alpha varied from 3.80 to 2.48 x 10(4), and for beta from 7.19 x 10(-3) to 0.1946, though only beta showed any sort of trend, becoming smaller with increasing fluoride concentration. Fluoride was released from the zinc phosphate cements in processes that were diffusion based up to M(t)/M(infinity) of about 0.4. No further release occurred when specimens were placed in fresh volumes of deionised water. Only a fraction of the fluoride taken up was re-released, demonstrating that most of the fluoride taken up becomes irreversibly bound within the cement.

Water transport in zinc oxy-chloride cements

The water uptake and water loss behaviour in three different formulations of zinc oxy-chloride cement have been studied in detail. Specimens of each material were subjected to a high humidity atmosphere (93% RH) over saturated aqueous sodium sulfate, and a low humidity desiccating atmosphere over concentrated sulfuric acid. In high humidity, the cement formulated from the nominal 75% ZnCl2 solutions gained mass, eventually becoming too sticky to weigh further. The specimens at 25% and 50% ZnCl2 by contrast lost mass by a diffusion process, though by 1 week the 50% cement had stated to gain mass and was also too sticky to weigh. In low humidity, all three cements lost mass, again by a diffusion process. Both water gain and water loss followed Fick's law for a considerable time. In the case of water loss under desiccating conditions, this corresponded to values of Mt/MĄ well above 0.5. However, plots did not go through the origin, showing that there was an induction period before true diffusion began. Diffusion coefficients varied from 1.56 x 10-5 (75% ZnCl2) to 2.75 x 10-5 cm2/s (50% ZnCl2), and appeared to be influenced not simply by composition. The drying of the 25% and 50% ZnCl2 cements in high humidity conditions occurred at a much lower rate, with a value of D of 2.5 x 10-8 cm2/s for the 25% ZnCl2 cement. This cement was found to equilibrate slowly, but total water loss did not differ significantly from that of the cements stored under desiccating conditions. Equilibration times for water loss in desiccating conditions were of the order of 2-4 hours, depending on ZnCl2 content; equilibrium water losses were respectively 28.8 [25% ZnCl2], 16.2 [50%] and 12.4 [75%] which followed the order of ZnCl2 content. It is concluded that the water transport processes are strongly influenced by the ZnCl2 content of the cement.

Breast milk levels of zinc and omega-6 polyunsaturated fatty acids and growth of healthy Chinese infants

AIM: To examine the concentrations of zinc and omega-6 polyunsaturated fatty acids (omega-6 PUFAs) in breast milk, the impact of zinc on omega-6 PUFA metabolism, and the growth rate of infants. METHODS: Forty-one mother-term infant pairs from a rural area of northern Beijing, China, who were 1 month (n = 18, group I) and 3 months (n = 23, group II) old and exclusively breastfed, were studied. The dietary records and the concentrations of zinc and omega-6 PUFAs in the milk of lactating women and the increase in weight and length of their infants during 1 and 3 postnatal months were analysed. RESULTS: The dietary intakes of mothers in the two groups were the same, i.e. high in carbohydrate and low in fat, protein and energy. The maternal zinc intake was 7.5mg/d and thus reached only 34.6% of the current Recommended Nutrient Intake (RNI). The levels of zinc and arachidonic acid (AA, C20:4 omega-6) in the milk of group I were significantly higher than those in group II. Furthermore, significant positive correlations were found between the concentrations of zinc and AA in the breast milk and between the level of milk AA and weight gain. CONCLUSION: Zinc may be a co-factor and essential for essential fatty acids (EFA) metabolism. Thus suboptimal zinc intake may cause EFA imbalance. Further studies of Chinese rural mother-infant pairs are necessary to determine whether zinc supplementation should be recommended when lactation exceeds 3 months.