On the Strong Scalability of Maritime CFD

Since 2004, supercomputer growth hasbeen constrained by energy efficiency rather than raw hardware speeds. Tomaintain exponential growth of overall computing power, a massive growth inparallelization is under way. To keep up with these changes, computationalfluid dynamics (CFD) must improve its strong scalability – its ability tohandle lower cells-per-core ratios and achieve finer-grain parallelization. Amaritime-focused, unstructured, finite-volume code (ReFRESCO) is used toinvestigate the scalability problems for incompressible, viscous CFD using two classicaltest-cases. Existing research suggests that the linear equation-system solveris the main bottleneck to incompressible codes, due to the stiff Poisson pressure equation. Here, these results are expandedby analysing the reasons for this poor scalability. In particular, a number ofalternative linear solvers and preconditioners are tested to determine if thescalability problem can be circumvented, including GMRES, Pipelined-GMRES,Flexible-GMRES and BCGS. Conventional block-wise preconditioners are tested,along with multi-grid preconditioners and smoothers in various configurations.Memory-bandwidth constraints and global communication patterns are found to bethe main bottleneck, and no state-of-the-art solution techniques which solve thestrong-scalability problem satisfactorily could be found. There is significantincentive for more research and development in this area

Chaotic multigrid methods for the solution of elliptic equations

Supercomputer power has been doubling approximately every 14 months for several decades, increasing the capabilities of scientific modelling at a similar rate. However, to utilize these machines effectively for applications such as computational fluid dynamics, improvements to strong scalability are required. Here, the particular focus is on semi-implicit, viscous-flow CFD, where the largest bottleneck to strong scalability is the parallel solution of the linear pressure-correction equation — an elliptic Poisson equation. State-of-the-art linear solvers, such as Krylov subspace or multigrid methods, provide excellent numerical performance for elliptic equations, but do not scale efficiently due to frequent synchronization between processes. Complete desynchronization is possible for basic, Jacobi-like solvers using the theory of ‘chaotic relaxations’. These non-deterministic, chaotic solvers scale superbly, as demonstrated herein, but lack the numerical performance to converge elliptic equations — even with the relatively lax convergence requirements of the example CFD application. However, these chaotic principles can also be applied to multigrid solvers. In this paper, a ‘chaotic-cycle’ algebraic multigrid method is described and implemented as an open-source library. It is tested on a model Poisson equation, and also within the context of CFD. Two CFD test cases are used: the canonical lid-driven cavity flow and the flow simulation of a ship (KVLCC2). The chaotic-cycle multigrid shows good scalability and numerical performance compared to classical V-, W- and F-cycles. On 2048 cores the chaotic-cycle multigrid solver performs up to faster than Flexible-GMRES and faster than classical V-cycle multigrid. Further improvements to chaotic-cycle multigrid can be made, relating to coarse-grid communications and desynchronized residual computations. It is expected that the chaotic-cycle multigrid could be applied to other scientific fields, wherever a scalable elliptic-equation solver is required

Scarabaeoidea (Insecta : Coleoptera) in the Brazilian Cerrado : current state of knowledge

Besouros pertencentes à superfamília Scarabaeoidea ocupam habitats variados, possuem hábitos alimentares diversifi cados, desempenham importante papel ecológico e diversas espécies apresentam importância agrícola. No entanto, estudos com esse grupo na região do Cerrado são escassos. Nesta revisão realizou-se um levantamento dos artigos publicados nos últimos 30 anos a respeito dos Scarabaeoidea no Cerrado. Foram recuperados 64 artigos, realizados em nove unidades da federação, que focavam quatro temas principais espécies praga, aspectos bioecológicos, biodiversidade e importância ecológica, e técnicas e metodologias de coleta de Scarabaeoidea. Os resultados desta revisão indicam que poucos estudos foram realizados com os Scarabaeoidea no Cerrado brasileiro nas últimas décadas frente à importância e diversidade desse grupo de insetos.Beetles belonging to the superfamily Scarabaeoidea occupy different habitats, present feeding habits diversifi ed, play an important ecological role and several species have agricultural importance. However, studies with this group in the Brazilian Cerrado are scarce. In this review we carried out a survey of scientifi c articles published in the past 30 years concerning Scarabaeoidea in the Cerrado. Were found 64 studies in nine Brazilian states. The studies focused on four main topics: pest species, bioecology, biodiversity and ecological importance, techniques and methodologies for collecting Scarabaeoidea. The results of this review indicate that few studies have been conducted with Scarabaeoidea in the Cerrado in recent decades compared to the importance and diversity of this group of insects

Black Hole Thermodynamics and Statistical Mechanics

We have known for more than thirty years that black holes behave as thermodynamic systems, radiating as black bodies with characteristic temperatures and entropies. This behavior is not only interesting in its own right; it could also, through a statistical mechanical description, cast light on some of the deep problems of quantizing gravity. In these lectures, I review what we currently know about black hole thermodynamics and statistical mechanics, suggest a rather speculative "universal" characterization of the underlying states, and describe some key open questions.Comment: 35 pages, Springer macros; for the Proceedings of the 4th Aegean Summer School on Black Hole