Related papers: Is the Multigrid Method Fault Tolerant? The Two-Gr…
Quantifying the potential benefits of microgrids in the design phase can support the transition of passive distribution networks into microgrids. At current, reliability and resilience are the main drivers for this transition. Therefore,…
The presence of uncertainty in material properties and geometry of a structure is ubiquitous. The design of robust engineering structures, therefore, needs to incorporate uncertainty in the optimization process. Stochastic gradient descent…
In recent publications, the author and his coworkers have proposed a multigrid method for solving linear systems arizing from the discretization of partial differential equations in isogeometric analysis and have proven that the convergence…
The convergence rate of a multigrid method depends on the properties of the smoother and the so-called grid transfer operator. In this paper we define and analyze new grid transfer operators with a generic cutting size which are applicable…
100% inverter-based renewable units are becoming more prevalent, introducing new challenges in the protection of microgrids that incorporate these resources. This is particularly due to low fault currents and bidirectional flows. Previous…
Multicalibration gradient boosting has recently emerged as a scalable method that empirically produces approximately multicalibrated predictors and has been deployed at web scale. Despite this empirical success, its convergence properties…
A fast multigrid solver is presented for high-order accurate Stokes problems discretised by local discontinuous Galerkin (LDG) methods. The multigrid algorithm consists of a simple V-cycle, using an element-wise block Gauss-Seidel smoother.…
Traditional fault diagnosis methods struggle to handle fault data, with complex data characteristics such as high dimensions and large noise. Deep learning is a promising solution, which typically works well only when labeled fault data are…
Predicting and classifying faults in electricity networks is crucial for uninterrupted provision and keeping maintenance costs at a minimum. Thanks to the advancements in the field provided by the smart grid, several data-driven approaches…
Understanding application resilience (or error tolerance) in the presence of hardware transient faults on data objects is critical to ensure computing integrity and enable efficient application-level fault tolerance mechanisms. However, we…
The ability to detect faults is an important safety feature for event-based multi-agent systems. In most existing algorithms, each agent tries to detect faults by checking its own behavior. But what if one agent becomes unable to recognize…
This article investigates the performance of grid computing systems whose interconnections are given by random and scale-free complex network models. Regular networks, which are common in parallel computing architectures, are also used as a…
In this paper a local Fourier analysis for multigrid methods on tetrahedral grids is presented. Different smoothers for the discretization of the Laplace operator by linear finite elements on such grids are analyzed. A four-color smoother…
The smart grid concept has transformed the traditional power grid into a massive cyber-physical system that depends on advanced two-way communication infrastructure to integrate a myriad of different smart devices. While the introduction of…
In this manuscript, we present a collective multigrid algorithm to solve efficiently the large saddle-point systems of equations that typically arise in PDE-constrained optimization under uncertainty, and develop a novel convergence…
It has been an open question in deep learning if fault-tolerant computation is possible: can arbitrarily reliable computation be achieved using only unreliable neurons? In the grid cells of the mammalian cortex, analog error correction…
Due to the increasing share of renewables, the analysis of the dynamical behavior of power grids gains importance. Effective risk assessments necessitate the analysis of large number of fault scenarios. The computational costs inherent in…
In this paper we propose distributed dual gradient algorithms for linearly constrained separable convex problems and analyze their rate of convergence under different assumptions. Under the strong convexity assumption on the primal…
This paper provides a rounding-error analysis for two-grid methods that use one relaxation step both before and after coarsening. The analysis is based on floating point arithmetic and focuses on a two-grid scheme that is perturbed on the…
The robustness of fault detection algorithms against uncertainty is crucial in the real-world industrial environment. Recently, a new probabilistic design scheme called distributionally robust fault detection (DRFD) has emerged and received…