Related papers: Some Comments on Multigrid Methods for Computing P…
The solution of systems of linear(ized) equations lies at the heart of many problems in Scientific Computing. In particular for systems of large dimension, iterative methods are a primary approach. Stationary iterative methods are generally…
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…
Multi-hadron operators are crucial for reliably extracting the masses of excited states lying above multi-hadron thresholds in lattice QCD Monte Carlo calculations. The construction of multi-hadron operators with significant coupling to the…
A coarse grid correction (CGC) approach is proposed to enhance the efficiency of the matrix exponential and $\varphi$ matrix function evaluations. The approach is intended for iterative methods computing the matrix-vector products with…
Simulation has become the evaluation method of choice for many areas of distributing computing research. However, most existing simulation packages have several limitations on the size and complexity of the system being modeled. Fine…
This paper considers computational methods that split a vector field into three components in the case when both the vector field and the split components might be unbounded. We first employ classical Taylor expansion which, after some…
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…
We discuss the non perturbative approach to the problem of high-energy hadron-hadron (dipole-dipole) scattering at low momentum transfer by means of numerical simulations in Lattice Gauge Theory.
Constraint propagation algorithms implement logical inference. For efficiency, it is essential to control whether and in what order basic inference steps are taken. We provide a high-level framework that clearly differentiates between…
Multi-level numerical methods that obtain the exact solution of a linear system are presented. The methods are devised by combining ideas from the full multi-grid algorithm and perfect reconstruction filters. The problem is stated as…
We discuss a new lattice implementation of the linear covariant gauge, recently introduced in [1]. In particular, we present details of the numerical procedure for fixing the gauge. We also report on preliminary results for the transverse…
Beyond perturbation theory gauge-fixing becomes more involved due to the Gribov-Singer ambiguity: The appearance of additional gauge copies requires to define a procedure how to handle them. For the case of Landau gauge the structure and…
Gas Transmission Networks are large-scale complex systems, and corresponding design and control problems are challenging. In this paper, we consider the problem of control and management of these systems in crisis situations. We present…
Combinatorial rigidity theory seeks to describe the rigidity or flexibility of bar-joint frameworks in R^d in terms of the structure of the underlying graph G. The goal of this article is to broaden the foundations of combinatorial rigidity…
In this manuscript, we present a collective multigrid algorithm to solve efficiently the large saddle-point systems of equations that typically arise in PDE-constrained optimization under uncertainty, and develop a novel convergence…
We summarize the higher-loop perturbative computation of the ghost and gluon propagators in SU(3) Lattice Gauge Theory. Our final aim is to compare with results from lattice simulations in order to expose the genuinely non-perturbative…
Lattice QCD calculations have been conducted using large-scale classical computers based on the Lagrangian formalism of field theory for the past 40 years. On the other hand, the advent of quantum computers has brought increasing attention…
During the past few years, we have observed the emergence of new applications that use multicast transmission. For a multicast routing algorithm to be applicable in optical networks, it must route data only to group members, optimize and…
Accuracy is the most important parameter among few others which defines the effectiveness of a machine learning algorithm. Higher accuracy is always desirable. Now, there is a vast number of well established learning algorithms already…
A conceptually simple model for strongly interacting compact U(1) lattice gauge theory is expressed as operators acting on qubits. The number of independent gauge links is reduced to its minimum through the use of Gauss's law. The model can…