Related papers: Resilience for Exascale Enabled Multigrid Methods
FFT, FMM, and multigrid methods are widely used fast and highly scalable solvers for elliptic PDEs. However, emerging large-scale computing systems are introducing challenges in comparison to current petascale computers. Recent efforts…
Advances in microgrids powered by Distributed Energy Resources (DERs) make them an attractive response capability for improving the resilience of electricity distribution networks (DNs). This paper presents an approach to evaluate the value…
Current algorithms for large-scale industrial optimization problems typically face a trade-off: they either require exponential time to reach optimal solutions, or employ problem-specific heuristics. To overcome these limitations, we…
A long-standing challenge is the design of chips resilient to faults and glitches. Both fine-grained gate diversity and coarse-grained modular redundancy have been used in the past. However, these approaches have not been well-studied under…
In this paper, we study a fault-tolerant control for systems consisting of multiple homogeneous components such as parallel processing machines. This type of system is often more robust to uncertainty compared to those with a single…
To numerically solve a generic elliptic equation on two-dimensional domains with rectangular Cartesian grids, we propose a cut-cell geometric multigrid method that features (1) general algorithmic steps that apply to two-dimensional…
The convergence of multigrid methods degrades significantly if a small number of low quality cells are present in a finite element mesh, and this can be a barrier to the efficient and robust application of multigrid on complicated geometric…
Numerical solution of partial differential equations on parallel computers using domain decomposition usually requires synchronization and communication among the processors. These operations often have a significant overhead in terms of…
In this article, we present a parallel discretization and solution method for parabolic problems with a higher number of space dimensions. It consists of a parallel-in-time approach using the multigrid reduction-in-time algorithm MGRIT with…
Using fault-tolerant constructions, computations performed with unreliable components can simulate their noiseless counterparts though the introduction of a modest amount of redundancy. Given the modest overhead required to achieve…
In this paper, a nonlinear system of fractional ordinary differential equations with multiple scales in time is investigated. We are interested in the effective long-term computation of the solution. The main challenge is how to obtain the…
Work presented in this paper describes a general algorithm and its finite element implementation for performing concurrent multiple sub-domain simulations in linear structural dynamics. Using this approach one can solve problems in which…
Dealing with hardware and software faults is an important problem as parallel and distributed systems scale to millions of processing cores and wide area networks. Traditional methods for dealing with faults include checkpoint-restart,…
A local weighted discontinuous Galerkin gradient discretization method for solving elliptic equations is introduced. The local scheme is based on a coarse grid and successively improves the solution solving a sequence of local elliptic…
This paper introduces a novel approach to algebraic multigrid methods for large systems of linear equations coming from finite element discretizations of certain elliptic second order partial differential equations. Based on a discrete…
The solution to partial differential equations using deep learning approaches has shown promising results for several classes of initial and boundary-value problems. However, their ability to surpass, particularly in terms of accuracy,…
Erasure coding techniques are getting integrated in networked distributed storage systems as a way to provide fault-tolerance at the cost of less storage overhead than traditional replication. Redundancy is maintained over time through…
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,…
Fault tolerance for the upcoming exascale generation has long been an area of active research. One of the components of a fault tolerance strategy is checkpointing. Petascale-level checkpointing is demonstrated through a new mechanism for…
We propose a design methodology to facilitate fault tolerance of deep learning models. First, we implement a many-core fault-tolerant neuromorphic hardware design, where neuron and synapse circuitries in each neuromorphic core are enclosed…