Related papers: Some Comments on Multigrid Methods for Computing P…
We present a new multigrid method called neural multigrid which is based on joining multigrid ideas with concepts from neural nets. The main idea is to use the Greenbaum criterion as a cost functional for the neural net. The algorithm is…
A method for computing all-point quark propagators is applied to a variety of processes of physical interest in lattice QCD. The method allows, for example, efficient calculation of disconnected parts and full momentum-space 2 and 3 point…
Efficient deterministic algorithms to construct representations of lattice path matroids over finite fields are presented. They are built on known constructions of hierarchical secret sharing schemes, a recent characterization of…
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…
Multigrid solvers face multiple challenges on parallel computers. Two fundamental ones read as follows: Multiplicative solvers issue coarse grid solves which exhibit low concurrency and many multigrid implementations suffer from an…
Various algebraic multigrid algorithms have been developed for solving problems in scientific and engineering computation over the past decades. They have been shown to be well-suited for solving discretized partial differential equations…
A geometric grid class consists of those permutations that can be drawn on a specified set of line segments of slope \pm1 arranged in a rectangular pattern governed by a matrix. Using a mixture of geometric and language theoretic methods,…
This paper introduces a novel geometric multigrid solver for unstructured curved surfaces. Multigrid methods are highly efficient iterative methods for solving systems of linear equations. Despite the success in solving problems defined on…
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…
The many-body problem is ubiquitous in the theoretical description of physical phenomena, ranging from the behavior of elementary particles to the physics of electrons in solids. Most of our understanding of many-body systems comes from…
We present a new exact algorithm for estimating all elements of the quark propagator. The advantage of the method is that the exact all-to-all propagator is reproduced in a large but finite number of inversions. The efficacy of the…
In this paper we analyse the convergence properties of V-cycle multigrid algorithms for the numerical solution of the linear system of equations arising from discontinuous Galerkin discretization of second-order elliptic partial…
The classification of the most used load balancing algorithms in distributed systems (including cloud technology, cluster systems, grid systems) is described. Comparative analysis of types of the load balancing algorithms is conducted in…
We construct operators for simulating the scattering of two hadrons with spin on the lattice. Three methods are shown to give the consistent operators for PN, PV, VN and NN scattering, where P, V and N denote pseudoscalar, vector and…
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…
A variety of unitary gauges for perturbation theory in a background field is considered in order to find those most suitable for a Hamiltonian treatment of the system. We select two convenient gauges and derive the propagators $D_{\mu\nu}$…
We develop multilevel methods for interface-driven multiphysics problems that can be coupled across dimensions and where complexity and strength of the interface coupling deteriorates the performance of standard methods. We focus on solvers…
The gluon propagator in Landau gauge is calculated in quenched QCD on a large (32^3X64) lattice at beta=6.0. In order to assess finite volume and finite lattice spacing artefacts, we also calculate the propagator on a smaller volume for two…
We describe the basic lattice structures of attractors and repellers in dynamical systems. The structure of distributive lattices allows for an algebraic treatment of gradient-like dynamics in general dynamical systems, both invertible and…
The quark propagator is at the core of lattice hadron spectrum calculations as well as studies in other nonperturbative schemes. We investigate the quark propagator with an improved staggered action (Asqtad) and an improved gluon action,…