Achieving Efficient Strong Scaling with PETSc using Hybrid MPI/OpenMP Optimisation

The increasing number of processing elements and decreas- ing memory to core ratio in modern high-performance platforms makes efficient strong scaling a key requirement for numerical algorithms. In order to achieve efficient scalability on massively parallel systems scientific software must evolve across the entire stack to exploit the multiple levels of parallelism exposed in modern architectures. In this paper we demonstrate the use of hybrid MPI/OpenMP parallelisation to optimise parallel sparse matrix-vector multiplication in PETSc, a widely used scientific library for the scalable solution of partial differential equations. Using large matrices generated by Fluidity, an open source CFD application code which uses PETSc as its linear solver engine, we evaluate the effect of explicit communication overlap using task-based parallelism and show how to further improve performance by explicitly load balancing threads within MPI processes. We demonstrate a significant speedup over the pure-MPI mode and efficient strong scaling of sparse matrix-vector multiplication on Fujitsu PRIMEHPC FX10 and Cray XE6 systems

On the validity of tidal turbine array configurations obtained from steady-state adjoint optimisation

Extracting the optimal amount of power from an array of tidal turbines requires an intricate understanding of tidal dynamics and the effects of turbine placement on the local and regional scale flow. Numerical models have contributed significantly towards this understanding, and more recently, adjoint-based modelling has been employed to optimise the positioning of the turbines in an array in an automated way and improve on simple, regular man-made configurations. Adjoint-based optimisation of high-resolution and ideally 3D transient models is generally a very computationally expensive problem. As a result, existing work on the adjoint optimisation of tidal turbine placement has been mostly limited to steady-state simulations in which very high, non-physical values of the background viscosity are required to ensure that a steady-state solution exists. However, such compromises may affect the reliability of the modelled turbines, their wakes and interactions, and thus bring into question the validity of the computed optimal turbine positions. This work considers a suite of idealised simulations of flow past tidal turbine arrays in a 2D channel. It compares four regular array configurations, detailed by Divett et al. (2013), with the configuration found through adjoint optimisation in a steady-state, high-viscosity setup. The optimised configuration produces considerably more power. The same configurations are then used to produce a suite of transient simulations that do not use constant high-viscosity, and instead use large eddy simulation (LES) to parameterise the resulting turbulent structures. It is shown that the LES simulations produce less power than that predicted by the constant high-viscosity runs. Nevertheless, they still follow the same trends in the power curve throughout time, with optimised layouts continuing to perform significantly better than simplified configuration

ADM formulation of the General Relativity

Se realiza el estudio del formalismo ADM para la Teoría de la Relatividad General mediante el método de las foliaciones en las superficies de Cauchy. Se presenta explícitamente el desarrollo matemático que conduce, finalmente, a la formulación hamiltoniana de la Relatividad General.The study of the ADM formalism for the General Relativity Theory through the foliation methods on the Cauchy surfacesis is realized. The mathematical development that leads to the Hamiltonian formulation of General Relativity is presented explicitly

The trade-off between tidal-turbine array yield and impact on flow: A multi-objective optimisation problem

Abstract This paper introduces a new approach for investigating trade-offs between different societal objectives in the design of tidal-turbine arrays. This method is demonstrated through the trade-off between the yield of an array, and the extent to which that array alters the flow. This is posed as a multi-objective optimisation problem, and the problem is investigated using the array layout optimisation tool OpenTidalFarm. Motivated by environmental concerns, OpenTidalFarm is adapted to not only maximise array yield but also to minimise the effect of the array upon the hydrodynamics of the region, specifically the flow velocity. A linear scalarisation of the multi-objective optimisation problem is solved for a series of different weightings of the two conflicting objectives. Two idealised test scenarios are evaluated and in each case a set of Pareto solutions is found. These arrays are assessed for the power they generate and the severity of change they cause in the flow velocity. These analyses allow for the identification of trade-offs between these two objectives, while the methods proposed can similarly be applied to the two key societal objectives of energy production and conservation, thus providing information that could be valuable to stakeholders and policymakers when making decisions on array design

Tidal resource extraction in the Pentland Firth, UK : Potential impacts on flow regime and sediment transport in the Inner Sound of Stroma

Large-scale extraction of power from tidal streams within the Pentland Firth is expected to be underway in the near future. The Inner Sound of Stroma in particular has attracted significant commercial interest. To understand potential environmental impacts of the installation of a tidal turbine array a case study based upon the Inner Sound is considered. A numerical computational fluid dynamics model, Fluidity, is used to conduct a series of depth-averaged simulations to investigate velocity and bed shear stress changes due to the presence of idealised tidal turbine arrays. The number of turbines is increased from zero to 400. It is found that arrays in excess of 85 turbines have the potential to affect bed shear stress distributions in such a way that the most favourable sites for sediment accumulation migrate from the edges of the Inner Sound towards its centre. Deposits of fine gravel and coarse sand are indicated to occur within arrays of greater than 240 turbines with removal of existing deposits in the shallower channel margins also possible. The effects of the turbine array may be seen several kilometres from the site which has implications not only on sediment accumulation, but also on the benthic fauna

The trade-off between tidal-turbine array yield and environmental impact: a habitat suitability modelling approach

In the drive towards a carbon-free society, tidal energy has the potential to become a valuable part of the UK energy supply. Developments are subject to intense scrutiny, and potential environmental impacts must be assessed. Unfortunately many of these impacts are still poorly understood, including the implications that come with altering the hydrodynamics. Here, methods are proposed to quantify ecological impact and to incorporate its minimisation into the array design process. Four tidal developments in the Pentland Firth are modelled with the array optimisation tool OpenTidalFarm, that designs arrays to generate the maximum possible profit. Maximum entropy modelling is used to create habitat suitability maps for species that respond to changes in bedshear stress. Changes in habitat suitability caused by an altered tidal regime are assessed. OpenTidalFarm is adapted to simultaneously optimise array design to maximise both this habitat suitability and to maximise the profit of the array. The problem is thus posed as a multi-objective optimisation problem, and a set of Pareto solutions found, allowing trade-offs between these two objectives to be identified. The methods proposed generate array designs that have reduced negative impact, or even positive impact, on the habitat suitability of specific species or habitats of interest

Firedrake-Fluids v0.1: numerical modelling of shallow water flows using an automated solution framework

This model description paper introduces a new finite element model for the simulation of non-linear shallow water flows, called Firedrake-Fluids. Unlike traditional models that are written by hand in static, low-level programming languages such as Fortran or C, Firedrake-Fluids uses the Firedrake framework to automatically generate the model's code from a high-level abstract language called Unified Form Language (UFL). By coupling to the PyOP2 parallel unstructured mesh framework, Firedrake can then target the code towards a desired hardware architecture to enable the efficient parallel execution of the model over an arbitrary computational mesh. The description of the model includes the governing equations, the methods employed to discretise and solve the governing equations, and an outline of the automated solution process. The verification and validation of the model, performed using a set of well-defined test cases, is also presented along with a road map for future developments and the solution of more complex fluid dynamical systems

Assessment of spurious mixing in adaptive mesh simulations of the two-dimensional lock-exchange

AbstractNumerical simulations are used to evaluate the impact of adaptive meshes on the two-dimensional lock-exchange flow. In particular, the diapycnal mixing is quantified through calculation of the background potential energy. The choice of metric, which guides the mesh adapt, is fundamental to the success of an adaptive mesh simulation. The performance of different Hessian-based metrics is assessed and cases that both outperform and underperform, compared to fixed mesh simulations, are evaluated. The differences in performance result from the different forms of the metric and the extent to which smaller-scale fluctuations can influence the adapted mesh. The best performing metric produces levels of diapycnal mixing that are comparable to high resolution fixed mesh simulations that use one to two orders of magnitude more mesh vertices. Comparison of the mixing with the numerical simulations of Özgökmen et al. (2007) also demonstrates the validity of the adaptive mesh simulations