相关论文: Multigrid in H(div) on Axisymmetric Domains

We present a comparison of different multigrid approaches for the solution of systems arising from high-order continuous finite element discretizations of elliptic partial differential equations on complex geometries. We consider the…

This paper presents a new fast iterative solver for large systems involving kernel matrices. Advantageous aspects of H2 matrix approximations and the multigrid method are hybridized to create the H2-MG algorithm. This combination provides…

We design and investigate efficient multigrid solvers for multiphase Stokes problems discretised via mixed-degree local discontinuous Galerkin methods. Using the template of a standard multigrid V-cycle, we develop a smoother analogous to…

An application of dimensional reduction results for gradient constrained problems is provided for 3D-2D dimension reduction for supremal functionals, in the case when the domain is convex.

Multidimensional scaling visualizes dissimilarities among objects and reduces data dimensionality. While many methods address symmetric proximity data, asymmetric and especially three-way proximity data (capturing relationships across…

In this work we propose and analyze a novel Hybrid High-Order discretization of a class of (linear and) nonlinear elasticity models in the small deformation regime which are of common use in solid mechanics. The proposed method is valid in…

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…

Multigrid solvers for hierarchical hybrid grids (HHG) have been proposed to promote the efficient utilization of high performance computer architectures. These HHG meshes are constructed by uniformly refining a relatively coarse fully…

This paper addresses the problem of efficiently classifying high-dimensional data over decentralized networks. Penalized support vector machines (SVMs) are widely used for high-dimensional classification tasks. However, the double…

The Fourier analysis of the \emph{p}-multigrid acceleration technique is considered for a dual-time scheme applied to the advection-diffusion equation with various cycle configurations. It is found that improved convergence can be achieved…

In this paper we present a general convex optimization approach for solving high-dimensional multiple response tensor regression problems under low-dimensional structural assumptions. We consider using convex and weakly decomposable…

Composite minimization involves a collection of smooth functions which are aggregated in a nonsmooth manner. In the convex setting, we design an algorithm by linearizing each smooth component in accordance with its main curvature. The…

The solution to the Poisson equation arising from the spectral element discretization of the incompressible Navier-Stokes equation requires robust preconditioning strategies. One such strategy is multigrid. To realize the potential of…

We consider a standard elliptic partial differential equation and propose a geometric multigrid algorithm based on Dirichlet-to-Neumann (DtN) maps for hybridized high-order finite element methods. The proposed unified approach is applicable…

Uni- and bivariate data smoothing with spline functions is a well established method in nonparametric regression analysis. The extension to multivariate data is straightforward, but suffers from exponentially increasing memory and…

The two-dimensional layout optimization problem reinforced by the efficient space utilization demand has a wide spectrum of practical applications. Formulating the problem as a nonlinear minimization problem under planar equality and/or…

Multigrid is a powerful solver for large-scale linear systems arising from discretized partial differential equations. The convergence theory of multigrid methods for symmetric positive definite problems has been well developed over the…

Current state-of-the-art deep neural networks for image classification are made up of 10 - 100 million learnable weights and are therefore inherently prone to overfitting. The complexity of the weight count can be seen as a function of the…

High-dimensional interpolation problems appear in various applications of uncertainty quantification, stochastic optimization and machine learning. Such problems are computationally expensive and request the use of adaptive grid generation…

This paper is devoted to the multigrid convergence analysis for the linear systems arising from the conforming linear finite element discretization of the second order elliptic equations with anisotropic diffusion. The multigrid convergence…