Related papers: Is the Multigrid Method Fault Tolerant? The Two-Gr…
The accurate assembly of the system matrix is an important step in any code that solves partial differential equations on a mesh. We either explicitly set up a matrix, or we work in a matrix-free environment where we have to be able to…
Hexahedral meshes are an ubiquitous domain for the numerical resolution of partial differential equations. Computing a pure hexahedral mesh from an adaptively refined grid is a prominent approach to automatic hexmeshing, and requires the…
Multiscale techniques have been widely shown to potentially overcome the limitation of homogenization schemes in representing the microscopic failure mechanisms in heterogeneous media as well as their influence on their structural response…
In this paper we propose a distributed dual gradient algorithm for minimizing linearly constrained separable convex problems and analyze its rate of convergence. In particular, we prove that under the assumption of strong convexity and…
Many complex systems may be described not by one, but by a number of complex networks mapped one on the other in a multilayer structure. The interactions and dependencies between these layers cause that what is true for a distinct single…
Hazard radiation can lead the system fault therefore Fault Tolerance is required. Fault Tolerant is a system, which is designed to keep operations running, despite the degradation in the specific module is happening. Many fault tolerances…
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…
Existing or planned power grids need to evaluate survivability under extreme events, like a number of peak load overloading conditions, which could possibly cause system collapses (i.e. blackouts). For realistic extreme events that are…
Convolutional and Recurrent, deep neural networks have been successful in machine learning systems for computer vision, reinforcement learning, and other allied fields. However, the robustness of such neural networks is seldom apprised,…
Over the past decade, the high performance computing community has become increasingly concerned that preserving the reliable, digital machine model will become too costly or infeasible. In this paper we discuss four approaches for…
We present W-cycle multigrid algorithms for the solution of the linear system of equations arising from a wide class of $hp$-version discontinuous Galerkin discretizations of elliptic problems. Starting from a classical framework in…
Machine learning (ML) provides us with numerous opportunities, allowing ML systems to adapt to new situations and contexts. At the same time, this adaptability raises uncertainties concerning the run-time product quality or dependability,…
Many problems in computational science and engineering involve partial differential equations and thus require the numerical solution of large, sparse (non)linear systems of equations. Multigrid is known to be one of the most efficient…
We focus in this report on two main axes. The first is dedicated to the study of the effect of replicas distribution on data grid performances. In this respect, our main contributions are as follows: 1) An overview of replication strategies…
Despite the progress in high performance computing, Computational Fluid Dynamics (CFD) simulations are still computationally expensive for many practical engineering applications such as simulating large computational domains and highly…
Algorithms are increasingly common components of high-impact decision-making, and a growing body of literature on adversarial examples in laboratory settings indicates that standard machine learning models are not robust. This suggests that…
Counterexample-guided repair aims at creating neural networks with mathematical safety guarantees, facilitating the application of neural networks in safety-critical domains. However, whether counterexample-guided repair is guaranteed to…
In this paper two types of multgrid methods, i.e., the Rayleigh quotient iteration and the inverse iteration with fixed shift, are developed for solving the Maxwell eigenvalue problem with discontinuous relative magnetic permeability and…
Traditionally power distribution networks are either not observable or only partially observable. This complicates development and implementation of new smart grid technologies, such as those related to demand response, outage detection and…
Multigrid methods are asymptotically optimal algorithms ideal for large-scale simulations. But, they require making numerous algorithmic choices that significantly influence their efficiency. Unlike recent approaches that learn optimal…