Paul Mycek

Numerical and experimental study of the interaction between two marine current turbines

Abstract The understanding of interaction effects between marine energy converters represents the next step in the research process that should eventually lead to the deployment of such devices. Although some a priori considerations have been suggested recently, very few real condition studies have been carried out concerning this issue. Trials were run on 1/30th scale models of three-bladed marine current turbine prototypes in a flume tank. The present work focuses on the case where a turbine is placed at different locations in the wake of a first one. The interaction effects in terms of performance and wake of the second turbine are examined and compared to the results obtained on the case of one single turbine. Besides, a three-dimensional software, based on a vortex method is currently being developed, and will be used in the near future to model more complex layouts. The experimental study shows that the second turbine is deeply affected by the presence of an upstream device and that a compromise between individual device performance and inter-device spacing is necessary. Numerical results show good agreement with the experiment and are promising for the future modelling of turbine farms.

Fault Resilient Domain Decomposition Preconditioner for PDEs

The move towards extreme-scale computing platforms challenges scientific simulations in many ways. Given the recent tendencies in computer architecture development, one needs to reformulate legacy codes in order to cope with large amounts of communication, system faults, and requirements of low-memory usage per core. In this work, we develop a novel framework for solving PDEs via domain decomposition that reformulates the solution as a state of knowledge with a probabilistic interpretation. Such reformulation allows resiliency with respect to potential faults without having to apply fault detection, avoids unnecessary communication, and is generally well-suited for rigorous uncertainty quantification studies that target improvements of predictive fidelity of scientific models. We demonstrate our algorithm for one-dimensional PDE examples where artificial faults have been implemented as bit flips in the binary representation of subdomain solutions.

Discrete A Priori Bounds for the Detection of Corrupted PDE Solutions in Exascale Computations

A priori bounds are derived for the discrete solution of second-order elliptic partial differential equations (PDEs). The bounds have two contributions. First, the influence of boundary conditions is taken into account through a discrete maximum principle. Second, the contribution of the source field is evaluated in a fashion similar to that used in the treatment of the continuous a priori operators. Closed form expressions are, in particular, obtained for the case of a conservative, second-order finite difference approximation of the diffusion equation with variable scalar diffusivity. The bounds are then incorporated into a resilient domain decomposition framework, in order to verify the admissibility of local PDE solutions. The computations demonstrate that the bounds are able to detect most system faults, and thus considerably enhance the resilience and the overall performance of the solver.

A resilient domain decomposition polynomial chaos solver for uncertain elliptic PDEs

Abstract A resilient method is developed for the solution of uncertain elliptic PDEs on extreme scale platforms. The method is based on a hybrid domain decomposition, polynomial chaos (PC) framework that is designed to address soft faults. Specifically, parallel and independent solves of multiple deterministic local problems are used to define PC representations of local Dirichlet boundary-to-boundary maps that are used to reconstruct the global solution. A LAD-lasso type regression is developed for this purpose. The performance of the resulting algorithm is tested on an elliptic equation with an uncertain diffusivity field. Different test cases are considered in order to analyze the impacts of correlation structure of the uncertain diffusivity field, the stochastic resolution, as well as the probability of soft faults. In particular, the computations demonstrate that, provided sufficiently many samples are generated, the method effectively overcomes the occurrence of soft faults.

ULFM-MPI Implementation of a Resilient Task-Based Partial Differential Equations Preconditioner

We present a task-based domain-decomposition preconditioner for partial differential equations (PDEs) resilient to silent data corruption (SDC) and hard faults. The algorithm exploits a reformulation of the PDE as a sampling problem, followed by a regression-based solution update that is resilient to SDC. We adopt a server-client model implemented using the User Level Fault Mitigation MPI (MPI-ULFM). All state information is held by the servers, while clients only serve as computational units. The task-based nature of the algorithm and the capabilities of ULFM are complemented at the algorithm level to support missing tasks, making the application resilient to hard faults affecting the clients. Weak and strong scaling tests up to ~115k cores show an excellent performance of the application with efficiencies above 90%, demonstrating the suitability to run at large scale. We demonstrate the resilience of the application for a 2D elliptic PDE by injecting SDC using a random single bit-flip model, and hard faults in the form of clients crashing. We show that in all cases, the application converges to the right solution. We analyze the overhead caused by the faults, and show that, for the test problem considered, the overhead incurred due to SDC is minimal compared to that from the hard faults.

Exploring the interplay of resilience and energy consumption for a task-based partial differential equations preconditioner

Abstract We discuss algorithm-based resilience to silent data corruptions (SDCs) in a task-based domain-decomposition preconditioner for partial differential equations (PDEs). The algorithm exploits a reformulation of the PDE as a sampling problem, followed by a solution update through data manipulation that is resilient to SDCs. The implementation is based on a server-client model where all state information is held by the servers, while clients are designed solely as computational units. Scalability tests run up to ∼51 K cores show a parallel efficiency greater than 90%. We use a 2D elliptic PDE and a fault model based on random single and double bit-flip to demonstrate the resilience of the application to synthetically injected SDC. We discuss two fault scenarios: one based on the corruption of all data of a target task, and the other involving the corruption of a single data point. We show that for our application, given the test problem considered, a four-fold increase in the number of faults only yields a 2% change in the overhead to overcome their presence, from 7% to 9%. We then discuss potential savings in energy consumption via dynamic voltage/frequency scaling, and its interplay with fault-rates, and application overhead.