Adaptive control in rollforward recovery for extreme scale multigrid

With the increasing number of compute components, failures in future exa-scale computer systems are expected to become more frequent. This motivates the study of novel resilience techniques. Here, we extend a recently proposed algorithm-based recovery method for multigrid iterations by introducing an adaptive control. After a fault, the healthy part of the system continues the iterative solution process, while the solution in the faulty domain is re-constructed by an asynchronous on-line recovery. The computations in both the faulty and healthy subdomains must be coordinated in a sensitive way, in particular, both under and over-solving must be avoided. Both of these waste computational resources and will therefore increase the overall time-to-solution. To control the local recovery and guarantee an optimal re-coupling, we introduce a stopping criterion based on a mathematical error estimator. It involves hierarchical weighted sums of residuals within the context of uniformly refined meshes and is well-suited in the context of parallel high-performance computing. The re-coupling process is steered by local contributions of the error estimator. We propose and compare two criteria which differ in their weights. Failure scenarios when solving up to $6.9\cdot10^{11}$ unknowns on more than 245\,766 parallel processes will be reported on a state-of-the-art peta-scale supercomputer demonstrating the robustness of the method

Volume 2: Explicit, multistage upwind schemes for Euler and Navier-Stokes equations

The objective of this study was to develop a high-resolution-explicit-multi-block numerical algorithm, suitable for efficient computation of the three-dimensional, time-dependent Euler and Navier-Stokes equations. The resulting algorithm has employed a finite volume approach, using monotonic upstream schemes for conservation laws (MUSCL)-type differencing to obtain state variables at cell interface. Variable interpolations were written in the k-scheme formulation. Inviscid fluxes were calculated via Roe's flux-difference splitting, and van Leer's flux-vector splitting techniques, which are considered state of the art. The viscous terms were discretized using a second-order, central-difference operator. Two classes of explicit time integration has been investigated for solving the compressible inviscid/viscous flow problems--two-state predictor-corrector schemes, and multistage time-stepping schemes. The coefficients of the multistage time-stepping schemes have been modified successfully to achieve better performance with upwind differencing. A technique was developed to optimize the coefficients for good high-frequency damping at relatively high CFL numbers. Local time-stepping, implicit residual smoothing, and multigrid procedure were added to the explicit time stepping scheme to accelerate convergence to steady-state. The developed algorithm was implemented successfully in a multi-block code, which provides complete topological and geometric flexibility. The only requirement is C degree continuity of the grid across the block interface. The algorithm has been validated on a diverse set of three-dimensional test cases of increasing complexity. The cases studied were: (1) supersonic corner flow; (2) supersonic plume flow; (3) laminar and turbulent flow over a flat plate; (4) transonic flow over an ONERA M6 wing; and (5) unsteady flow of a compressible jet impinging on a ground plane (with and without cross flow). The emphasis of the test cases was validation of code, and assessment of performance, as well as demonstration of flexibility

Modern Power System Dynamic Performance Improvement through Big Data Analysis

Higher penetration of Renewable Energy (RE) is causing generation uncertainty and reduction of system inertia for the modern power system. This phenomenon brings more challenges on the power system dynamic behavior, especially the frequency oscillation and excursion, voltage and transient stability problems. This dissertation work extracts the most useful information from the power system features and improves the system dynamic behavior by big data analysis through three aspects: inertia distribution estimation, actuator placement, and operational studies.First of all, a pioneer work for finding the physical location of COI in the system and creating accurate and useful inertia distribution map is presented. Theoretical proof and dynamic simulation validation have been provided to support the proposed method for inertia distribution estimation based on measurement PMU data. Estimation results are obtained for a radial system, a meshed system, IEEE 39 bus-test system, the Chilean system, and a real utility system in the US. Then, this work provided two control actuator placement strategy using measurement data samples and machine learning algorithms. The first strategy is for the system with single oscillation mode. Control actuators should be placed at the bus that are far away from the COI bus. This rule increased damping ratio of eamples systems up to 14\% and hugely reduced the computational complexity from the simulation results of the Chilean system. The second rule is created for system with multiple dynamic problems. General and effective guidance for planners is obtained for IEEE 39-bus system and IEEE 118-bus system using machine learning algorithms by finding the relationship between system most significant features and system dynamic performance. Lastly, it studied the real-time voltage security assessment and key link identification in cascading failure analysis. A proposed deep-learning framework has Achieved the highest accuracy and lower computational time for real-time security analysis. In addition, key links are identified through distance matrix calculation and probability tree generation using 400,000 data samples from the Western Electricity Coordinating Council (WECC) system