Related papers: Non-invasive multigrid for semi-structured grids
Grid computing is distributed computing performed transparently across multiple administrative domains. Grid middleware, which is meant to enable access to grid resources, is currently widely seen as being too heavyweight and, in…
In this paper, we develop multigrid solvers for the biharmonic problem in the framework of isogeometric analysis (IgA). In this framework, one typically sets up B-splines on the unit square or cube and transforms them to the domain of…
This paper presents efficient data structures for the implementation of matrix-free finite element methods on block-structured, hybrid tetrahedral grids. It provides a complete categorization of all geometric sub-objects that emerge from…
This paper is to introduce a type of full multigrid method for the nonlinear eigenvalue problem. The main idea is to transform the solution of nonlinear eigenvalue problem into a series of solutions of the corresponding linear boundary…
The goal of this primer is to provide a relatively short exposition of the basics of multigrid methods, simplified by focusing on fundamental concepts in a variational setting. This is done by way of a quadratic energy minimization…
We discuss how multi-grid computing schemes can be used to design hierarchical coordination architectures for energy systems. These hierarchical architectures can be used to manage multiple temporal and spatial scales and mitigate…
Overlapping block smoothers efficiently damp the error contributions from highly oscillatory components within multigrid methods for the Stokes equations but they are computationally expensive. This paper is concentrated on the development…
We propose an adaptive multigrid preconditioning technology for solving linear systems arising from Discontinuous Petrov-Galerkin (DPG) discretizations. Unlike standard multigrid techniques, this preconditioner involves only trace spaces…
The dispersive character of the Hall-MHD solutions, in particular the whistler waves, is a strong restriction to numerical treatments of this system. Numerical stability demands a time step dependence of the form $\Delta t\propto (\Delta…
In this study, we present an $hp$-multigrid preconditioner for a divergence-conforming HDG scheme for the generalized Stokes and the Navier-Stokes equations using an augmented Lagrangian formulation. Our method relies on conforming…
In this work, we formulate and analyze a geometric multigrid method for the iterative solution of the discrete systems arising from the finite element discretization of symmetric second-order linear elliptic diffusion problems. We show that…
This paper presents the use of element-based algebraic multigrid (AMGe) hierarchies, implemented in the ParELAG (Parallel Element Agglomeration Algebraic Multigrid Upscaling and Solvers) library, to produce multilevel preconditioners and…
We apply an unfitted HDG discretization to a model problem in shape optimization. The method proposed uses a fixed, shape regular, non-geometry conforming mesh and a high order transfer technique to deal with the curved boundaries arising…
The family of Multiscale Hybrid-Mixed (MHM) finite element methods has received considerable attention from the mathematics and engineering community in the last few years. The MHM methods allow solving highly heterogeneous problems on…
The structural analogies of ResNets and Multigrid (MG) methods such as common building blocks like convolutions and poolings where already pointed out by He et al.\ in 2016. Multigrid methods are used in the context of scientific computing…
The paper presents AMGCL -- an opensource C++ library implementing the algebraic multigrid method (AMG) for solution of large sparse linear systems of equations, usually arising from discretization of partial differential equations on an…
Solving the indefinite Helmholtz equation is not only crucial for the understanding of many physical phenomena but also represents an outstandingly-difficult benchmark problem for the successful application of numerical methods. Here we…
The support vector machine is a flexible optimization-based technique widely used for classification problems. In practice, its training part becomes computationally expensive on large-scale data sets because of such reasons as the…
We propose a sparse interpolation construction and a practical coarsening algorithm for the algebraic multigrid (AMG) method, tailored towards H(curl). Building on the generalized AMG framework, we introduce an interior/exterior splitting…
We propose a multilevel approach for trace systems resulting from hybridized discontinuous Galerkin (HDG) methods. The key is to blend ideas from nested dissection, domain decomposition, and high-order characteristic of HDG discretizations.…