Related papers: Resilience for Exascale Enabled Multigrid Methods
We consider discontinuous Galerkin methods for an elliptic distributed optimal control problem and we propose multigrid methods to solve the discretized system. We prove that the $W$-cycle algorithm is uniformly convergent in the energy…
Many subsurface engineering applications involve tight-coupling between fluid flow, solid deformation, fracturing, and similar processes. To better understand the complex interplay of different governing equations, and therefore design…
In large-scale LLM pre-training systems with 100k+ GPUs, failures become the norm rather than the exception, and restart costs can dominate wall-clock training time. However, existing fault-tolerance mechanisms are largely unprepared for…
Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little…
In his article "Powerlist: A Structure for Parallel Recursion" Jayadev Misra wrote: "Many data parallel algorithms - Fast Fourier Transform, Batcher's sorting schemes and prefix sum - exhibit recursive structure. We propose a data…
As computers reach exascale and beyond, the incidence of faults will increase. Solutions to this problem are an active research topic. We focus on strategies to make the preconditioned conjugate gradient (PCG) solver resilient against node…
We develop numerical methods for elliptic systems governed by partial segregation constraints, in which three nonnegative components are required to have a vanishing pointwise product throughout the domain. This constraint enforces that at…
Synchronizations of processing elements (PEs) in massively parallel simulations, which arise due to communication or load imbalances between PEs, significantly affect the scalability of scientific applications. We have recently proposed a…
Parallel-in-time algorithms have been successfully employed for reducing time-to-solution of a variety of partial differential equations, especially for diffusive (parabolic-type) equations. A major failing of parallel-in-time approaches to…
This research paper investigates how machine learning-driven data replication strategies can enhance fault tolerance in large-scale distributed systems. Traditional replication methods, which rely on static configurations, often struggle to…
We propose a parallel adaptive constraint-tightening approach to solve a linear model predictive control problem for discrete-time systems, based on inexact numerical optimization algorithms and operator splitting methods. The underlying…
In this work, we propose an adaptive geometric multigrid method for the solution of large-scale finite cell flow problems. The finite cell method seeks to circumvent the need for a boundary-conforming mesh through the embedding of the…
The finite-difference time-domain (FDTD) algorithm is a popular numerical method for solving electromagnetic problems. FDTD simulations can suffer from instability due to the explicit nature of the method. Stability enforcement can be…
This work is concerned with phrasing the concepts of fault-tolerant quantum computation within the framework of disordered systems, Bernoulli site percolation in particular. We show how the so-called "threshold theorems" on the possibility…
In recent publications, the author and his coworkers have shown robust approximation error estimates for B-splines of maximum smoothness and have proposed multigrid methods based on them. These methods allow to solve the linear system…
Hybrid fault models are known to be an effective means for enhancing the robustness of consensus-based replicated systems. However, existing hybridization approaches suffer from limited flexibility with regard to the composition of…
Constructing fast numerical solvers for partial differential equations (PDEs) is crucial for many scientific disciplines. A leading technique for solving large-scale PDEs is using multigrid methods. At the core of a multigrid solver is the…
We present a first of its kind framework which overcomes a major challenge in the design of digital systems that are resilient to reliability failures: achieve desired resilience targets at minimal costs (energy, power, execution time,…
Iterative multiscale methods for electronic structure calculations offer several advantages for large-scale problems. Here we examine a nonlinear full approximation scheme (FAS) multigrid method for solving fixed potential and…
The increasing scale of data propels the popularity of leveraging parallelism to speed up the optimization. Minibatch stochastic gradient descent (minibatch SGD) and local SGD are two popular methods for parallel optimization. The existing…