Related papers: Aggregation-based Multilevel Methods for Lattice Q…
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…
Nonlinear domain decomposition methods became popular in recent years since they can improve the nonlinear convergence behavior of Newton's method significantly for many complex problems. In this article, a nonlinear two-level Schwarz…
Multigrid methods were invented for the solution of discretized partial differential equations in ordered systems. The slowness of traditional algorithms is overcome by updates on various length scales. In this article we discuss…
The semidefinite programming (SDP) relaxation has proven to be extremely strong for many hard discrete optimization problems. This is in particular true for the quadratic assignment problem (QAP), arguably one of the hardest NP-hard…
Adaptive multi-grid methods have proven very successful in dealing with critical slow down for the Wilson-Dirac solver in lattice gauge theory. Multi-grid algorithms developed for Staggered fermions using the K\"ahler-Dirac…
This work proposes a scheme for significantly reducing the computational complexity of discretized problems involving the non-smooth forward propagation of uncertainty by combining the adaptive hierarchical sparse grid stochastic…
The spectral deferred correction (SDC) method is an iterative scheme for computing a higher-order collocation solution to an ODE by performing a series of correction sweeps using a low-order timestepping method. This paper examines a…
The past decade has witnessed a dramatic acceleration of lattice quantum chromodynamics calculations in nuclear and particle physics. This has been due to both significant progress in accelerating the iterative linear solvers using…
A hierarchical solver is proposed for solving sparse ill-conditioned linear systems in parallel. The solver is based on a modification of the LoRaSp method, but employs a deferred-compression technique, which provably reduces the…
Lattice Quantum Chromodynamics (Lattice QCD) is a quantum field theory on a finite discretized space-time box so as to numerically compute the dynamics of quarks and gluons to explore the nature of subatomic world. Solving the equation of…
We present promising initial results of our adaptive multigrid solver developed for application directly to the non-Hermitian Wilson-Dirac system in 4 dimensions, as opposed to the solver developed in [1] for the corresponding normal…
We investigate the application of the additive overlapping Schwarz domain decomposition method as a preconditioner for the large sparse linear systems arising in graph-based nonlinear least-squares problems, specifically the pose-graph…
Over the past five years, graphics processing units (GPUs) have had a transformational effect on numerical lattice quantum chromodynamics (LQCD) calculations in nuclear and particle physics. While GPUs have been applied with great success…
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…
The purpose of this paper is to study the influence of relaxation and acceleration techniques on the convergence behavior of the non-overlapping Schwarz algorithm with alternating Dirichlet-Neumann transmission conditions in the context of…
In this work, we propose a robust and easily implemented algebraic multigrid method as a stand-alone solver or a preconditioner in Krylov subspace methods for solving either symmetric and positive definite or saddle point linear systems of…
We determine the fine-tuning of the Yukawa couplings of supersymmetric QCD, discretized on a lattice. We use perturbation theory at one-loop level. The Modified Minimal Subtraction scheme ($\overline{{\rm MS}}$) is employed; by its…
The overlap Dirac operator at nonzero quark chemical potential involves the computation of the sign function of a non-Hermitian matrix. In this talk we present iterative Krylov subspace approximations, with deflation of critical…
One of the most computationally expensive steps of the low-rank ADI method for large-scale Lyapunov equations is the solution of a shifted linear system at each iteration. We propose the use of the extended Krylov subspace method for this…
Close to the chiral limit, many calculations in numerical lattice QCD can potentially be accelerated using low-mode deflation techniques. In this paper it is shown that the recently introduced domain-decomposed deflation subspaces can be…