Related papers: Deflated GMRES with Multigrid for Lattice QCD
This work develops a nonlinear multigrid method for diffusion problems discretized by cell-centered finite volume methods on general unstructured grids. The multigrid hierarchy is constructed algebraically using aggregation of degrees of…
The construction of multigrid operators for disordered linear lattice operators, in particular the fermion matrix in lattice gauge theories, by means of algebraic multigrid and block LU decomposition is discussed. In this formalism, the…
We consider two-flavor QCD in the lattice regularization with improved Wilson fermions. In this formulation chiral symmetry is explicitly broken at order a and hence the isovector axial currents require improvement as well as a finite…
We develop a density matrix renormalization group (DMRG) algorithm for constrained quantum lattice models that successfully {\it{implements the local constraints as symmetries in the contraction of the matrix product states and matrix…
We compare extensive simulations of QCD with 8 and 12 flavors of degenerate quarks, using the DBW2 gauge action, naive staggered fermions, and the rational hybrid Monte Carlo algorithm. A variety of values of the coupling constant, quark…
Exploiting the recent lattice results for the infrared gluon propagator with light dynamical quarks, we solve the gap equation for the quark propagator. We thus model the chiral symmetry breaking mechanism with increasing number of flavours…
In this paper we consider a class of robust multilevel precontioners for the Helmholtz equation with high wave number. The key idea in this work is to use the continuous interior penalty finite element methods (CIP-FEM) studied in…
A methodology is given to test the QCD $N_f$=2 chiral transition, presently conjectured to be second order. Scaling forms for the correlation length, susceptibilities and equation of state are given which account for finite lattice spacing.…
Convolution-type integral equations commonly occur in signal processing and image processing. Discretizing these equations yields large and ill-conditioned linear systems. While the classic multigrid method is effective for solving linear…
We apply chiral perturbation theory to the pseudoscalar meson mass and decay constant data obtained in the PACS-CS Project toward 2+1 flavor lattice QCD simulations with the O(a)-improved Wilson quarks. We examine the existence of chiral…
Anisotropic lattices are an efficient means of studying the glueballs of QCD, however problems arise with simulations of the lightest, scalar state. The mass is strongly dependent on the lattice spacing, even when a mean-field improved…
We study the convergence of multigrid schemes for the Helmholtz equation, focusing in particular on the choice of the coarse scale operators. Let G_c denote the number of points per wavelength at the coarse level. If the coarse scale…
We propose various improvements of finite step-size updating for full QCD on the lattice that might turn finite step-size updating into a viable alternative to the hybrid Monte Carlo algorithm. These improvements are noise reduction of the…
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…
We present an efficient matrix-free geometric multigrid method for the elastic Helmholtz equation, and a suitable discretization. Many discretization methods had been considered in the literature for the Helmholtz equations, as well as many…
Recovery of ground-state degeneracy in two-dimensional square ice is a significant challenge in the field of geometric frustration with far-reaching fundamental implications, such as realization of vertex models and understanding the effect…
Second order accurate Cartesian grid methods have been well developed for interface problems in the literature. However, it is challenging to develop third or higher order accurate methods for problems with curved interfaces and internal…
When approximating the expectations of a functional of a solution to a stochastic differential equation, the numerical performance of deterministic quadrature methods, such as sparse grid quadrature and quasi-Monte Carlo (QMC) methods, may…
We study the computation of the static quark potential under decimations in the Monte Carlo Renormalization Group (MCRG). Employing a multi-representation plaquette action, we find that fine-tuning the decimation prescription so that the…
This is the Lattice '95 review of recent progress towards accurate QCD simulations using very coarse lattices. This development could have revolutionary implications for low energy (nonperturbative) QCD.