Abstract
CFD simulations are a fundamental engineering application, implying huge workloads, often with dynamic behaviour due to runtime mesh refinement. Parallel processing over heterogeneous distributed memory clusters is often used to process such workloads. The execution of dynamic workloads over a set of heterogeneous resources leads to load imbalances that severely impacts execution time, when static uniform load distribution is used. This paper proposes applying dynamic, heterogeneity aware, load balancing techniques within CFD simulations. nSharma, a software package that fully integrates with OpenFOAM, is presented and assessed. Performance gains are demonstrated, achieved by reducing busy times standard deviation among resources, i.e., heterogeneous computing resources are kept busy with useful work due to an effective workload distribution. To best of authors’ knowledge, nSharma is the first implementation and integration of heterogeneity aware load balancing in OpenFOAM and will be made publicly available in order to foster its adoption by the large community of OpenFOAM users.

Abstract
Despite great advances in computer-assisted proof systems, writing formal proofs using a traditional computer is still challenging due to mouse-and-keyboard interaction. This leads to scientists often resorting to pen and paper to write their proofs. However, when handwriting a proof, there is no formal guarantee that the proof is correct. In this paper we address this issue and present the initial steps towards a system that allows users to handwrite proofs using a pen-based device and that communicates with an external theorem prover to support the users throughout the proof writing process. We focus on calculational proofs, whereby a theorem is proved by a chain of formulae, each transformed in some way into the next. We present the implementation of a proof-of-concept prototype that can formally verify handwritten calculational proofs without the need to learn the specific syntax of theorem provers.

Abstract
It is known since the late 1960's that the dual of the category of compact Hausdoroff spaces and continuous maps is a variety - not finitary, but bounded by aleph(1). In this note we show that the dual of the category of partially ordered compact spaces and monotone continuous maps is an aleph(1)-ary quasivariety, and describe partially its algebraic theory. Based on this description, we extend these results to categories of Vietoris coalgebras and homomorphisms on ordered compact spaces. We also characterise the aleph(1)-copresentable partially ordered compact spaces.

Abstract
The recently introduced notions of guarded traced (monoidal) category and guarded (pre-)iterative monad aim at unifying di erent instances of partial iteration whilst keeping in touch with the established theory of total iteration and preserving its merits. In this paper we use these notions and the corresponding stock of results to examine di erent types of iteration for hybrid computations. As a starting point we use an available notion of hybrid monad restricted to the category of sets, and modify it in order to obtain a suitable notion of guarded iteration with guardedness interpreted as progressiveness in time – we motivate this modification by our intention to capture Zeno behaviour in an arguably general and feasible way. We illustrate our results with a simple programming language for hybrid computations and interpret it over the developed semantic foundations. © Sergey Goncharov, Julian Jakob, and Renato Neves.

Abstract

Abstract