Related papers: AMGCL: an Efficient, Flexible, and Extensible Alge…
We propose a data-driven and machine-learning-based approach to compute non-Galerkin coarse-grid operators in algebraic multigrid (AMG) methods, addressing the well-known issue of increasing operator complexity. Guided by the AMG theory on…
FPGAs are increasingly prevalent in cloud deployments, serving as Smart NICs or network-attached accelerators. Despite their potential, developing distributed FPGA-accelerated applications remains cumbersome due to the lack of appropriate…
We describe main issues and design principles of an efficient implementation, tailored to recent generations of Nvidia Graphics Processing Units (GPUs), of an Algebraic Multigrid (AMG) preconditioner previously proposed by one of the…
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…
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) 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…
The electrical and electronic engineering has used parallel programming to solve its large scale complex problems for performance reasons. However, as parallel programming requires a non-trivial distribution of tasks and data, developers…
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 present a novel deep learning-based algorithm to accelerate - through the use of Artificial Neural Networks (ANNs) - the convergence of Algebraic Multigrid (AMG) methods for the iterative solution of the linear systems of equations…
Multigrid methods have proven to be an invaluable tool to efficiently solve large sparse linear systems arising in the discretization of partial differential equations (PDEs). Algebraic multigrid methods and in particular adaptive algebraic…
This paper reviews the adaptive sparse grid discontinuous Galerkin (aSG-DG) method for computing high dimensional partial differential equations (PDEs) and its software implementation. The C\texttt{++} software package called AdaM-DG,…
Fully realizing the potential of multigrid solvers often requires custom algorithms for a given application model, discretizations and even regimes of interest, despite considerable effort from the applied math community to develop fully…
There are many ways to represent a molecule as input to a machine learning model and each is associated with loss and retention of certain kinds of information. In the interest of preserving three-dimensional spatial information, including…
Algebraic multigrid (AMG) is often viewed as a scalable $\mathcal{O}(n)$ solver for sparse linear systems. Yet, parallel AMG lacks scalability due to increasingly large costs associated with communication, both in the initial construction…
We present a comparison of several modern C++ libraries providing high-level interfaces for programming multi- and many-core architectures on top of CUDA or OpenCL. The comparison focuses on the solution of ordinary differential equations…
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…
The efficient solution of sparse, linear systems resulting from the discretization of partial differential equations is crucial to the performance of many physics-based simulations. The algorithmic optimality of multilevel approaches for…
Algebraic multigrid (AMG) is often an effective solver for symmetric positive definite (SPD) linear systems resulting from the discretization of general elliptic PDEs, or the spatial discretization of parabolic PDEs. However, convergence…
Structured Cartesian grids are a fundamental component in numerical simulations. Although these grids facilitate straightforward discretization schemes, their na\"{i}ve use in sparse domains leads to excessive memory overhead and…
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…