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This work develops a nonlinear multigrid method for diffusion problems discretized by cell-centered finite volume methods on general unstructured grids. The multigrid hierarchy is constructed algebraically using aggregation of degrees of…
Implicit time integration is key to robustly simulating stiff materials and large deformations, but its performance is often dominated by repeatedly solving large linear systems. Adaptive coarsening can reduce this cost by concentrating…
This work concerns the development of an Algebraic Multilevel method for computing stationary vectors of Markov chains. We present an efficient Bootstrap Algebraic Multilevel method for this task. In our proposed approach, we employ a…
Algebraic multigrid (AMG) methods are among the most efficient solvers for linear systems of equations and they are widely used for the solution of problems stemming from the discretization of Partial Differential Equations (PDEs). The most…
Algebraic multigrid (AMG) methods derive their optimal efficiency from the interplay between a relaxation process and a corresponding coarse grid correction. In many standard formulations, relaxation and coarse-graining are analyzed and…
Adaptive meshing includes local refinement as well as coarsening of meshes. Typically, coarsening algorithms are based on an explicit refinement history. In this work, we deal with local coarsening algorithms that build on the refinement…
Algebraic multigrid (AMG) methods are powerful solvers with linear or near-linear computational complexity for certain classes of linear systems, Ax=b. Broadening the scope of problems that AMG can effectively solve requires the development…
In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the physical…
Multigrid modeling algorithms are a technique used to accelerate relaxation models running on a hierarchy of similar graphlike structures. We introduce and demonstrate a new method for training neural networks which uses multilevel methods.…
Over the course of the past decade, a variety of randomized algorithms have been proposed for computing approximate least-squares (LS) solutions in large-scale settings. A longstanding practical issue is that, for any given input, the user…
Model averaging has gained significant attention in recent years due to its ability of fusing information from different models. The critical challenge in frequentist model averaging is the choice of weight vector. The bootstrap method,…
A weighted regression procedure is proposed for regression type problems where the innovations are heavy-tailed. This method approximates the least absolute regression method in large samples, and the main advantage will be if the sample is…
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…
Algebraic curve interpolation is described by specifying the location of N points in the plane and constructing an algebraic curve of a function f that should pass through them. In this paper, we propose a novel approach to construct the…
Model uncertainty quantification is an essential component of effective data assimilation. Model errors associated with sub-grid scale processes are often represented through stochastic parameterizations of the unresolved process. Many…
Algebraic multigrid (AMG) is one of the most widely used solution techniques for linear systems of equations arising from discretized partial differential equations. The popularity of AMG stems from its potential to solve linear systems in…
A central goal of neuroscience is to understand how activity in the nervous system is related to features of the external world, or to features of the nervous system itself. A common approach is to model neural responses as a weighted…
Traditionally, the least squares regression is mainly concerned with studying the effects of individual predictor variables, but strongly correlated variables generate multicollinearity which makes it difficult to study their effects.…
Adaptive mesh refinement (AMR) is widely used to efficiently resolve localized features in time-dependent partial differential equations (PDEs) by selectively refining and coarsening the mesh. However, in long-horizon simulations, repeated…
In distributed, or privacy-preserving learning, we are often given a set of probabilistic models estimated from different local repositories, and asked to combine them into a single model that gives efficient statistical estimation. A…