Related papers: Deep Learning Accelerated Algebraic Multigrid Meth…
Algebraic multigrid (AMG) is an $\mathcal{O}(n)$ solution process for many large sparse linear systems. A hierarchy of progressively coarser grids is constructed that utilize complementary relaxation and interpolation operators. High-energy…
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…
Algebraic multigrid (AMG) is one of the most efficient iterative methods for solving large sparse system of equations. However, how to build/check restriction and prolongation operators in practical of AMG methods for nonsymmetric {\em…
We develop a new meshfree geometric multilevel (MGM) method for solving linear systems that arise from discretizing elliptic PDEs on surfaces represented by point clouds. The method uses a Poisson disk sampling-type technique for coarsening…
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…
Algebraic multigrid (AMG) solvers and preconditioners are some of the fastest numerical methods to solve linear systems, particularly in a parallel environment, scaling to hundreds of thousands of cores. Most AMG methods and theory assume a…
This paper builds on the algebraic theory in the companion paper [Algebraic Error Analysis for Mixed-Precision Multigrid Solvers] to obtain discretization-error-accurate solutions for linear elliptic partial differential equations (PDEs) by…
The numerical simulation of structural mechanics applications via finite elements usually requires the solution of large-size and ill-conditioned linear systems, especially when accurate results are sought for derived variables interpolated…
The geometric multigrid method (GMG) is one of the most efficient solving techniques for discrete algebraic systems arising from elliptic partial differential equations. GMG utilizes a hierarchy of grids or discretizations and reduces the…
In this work, we develop algebraic solvers for linear systems arising from the discretization of second-order elliptic partial differential equations by saddle-point mixed finite element methods of arbitrary polynomial degree $p \ge 0$ on…
Hybrid CPU-GPU algorithms for Algebraic Multigrid methods (AMG) to efficiently utilize both CPU and GPU resources are presented. In particular, hybrid AMG framework focusing on minimal utilization of GPU memory with performance on par with…
Linear solvers for large and sparse systems are a key element of scientific applications, and their efficient implementation is necessary to harness the computational power of current computers. Algebraic MultiGrid (AMG) preconditioners are…
We present a novel solver technique for the anisotropic heat flux equation, aimed at the high level of anisotropy seen in magnetic confinement fusion plasmas. Such problems pose two major challenges: (i) discretization accuracy and (ii)…
Strength-of-connection algorithms play a key role in algebraic multigrid (AMG). Specifically, they determine which matrix nonzeros are classified as weak and so ignored when coarsening matrix graphs and defining interpolation sparsity…
We investigate the performance of algebraic multigrid methods for the solution of the linear system of equations arising from a Virtual Element discretization. We provide numerical experiments on very general polygonal meshes for a model…
In this paper, we consider a classical form of optimal algebraic multigrid (AMG) interpolation that directly minimizes the two-grid convergence rate and compare it with the so-called ideal form that minimizes a certain weak approximation…
Algebraic multigrid (AMG) is known to be an effective solver for many sparse symmetric positive definite (SPD) linear systems. For SPD systems, the convergence theory of AMG is well-understood in terms of the $A$-norm, but in a nonsymmetric…
Multigrid solvers are the standard in modern scientific computing simulations. Domain Decomposition Aggregation-Based Algebraic Multigrid, also known as the DD-$\alpha$AMG solver, is a successful realization of an algebraic multigrid solver…
Iterative methods are widely used for solving partial differential equations (PDEs). However, the difficulty in eliminating global low-frequency errors significantly limits their convergence speed. In recent years, neural networks have…
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…