Related papers: Adaptive Multigrid Algorithm for the QCD Dirac-Wil…
We propose new techniques for the numerical implementation of the overlap-Dirac operator, which exploit the physical properties of the underlying theory to avoid nested algorithms. We test these procedures in the two-dimensional Schwinger…
Numerical simulations of quantum chromodynamics (QCD) on a lattice require the frequent solution of linear systems of equations with large, sparse and typically ill-conditioned matrices. Algebraic multigrid methods are meanwhile the…
Application of multigrid solvers in shifted linear systems is studied. We focus on accelerating the rational approximation needed for simulating single flavor operators. This is particularly useful, in the case of twisted mass fermions for…
We develop an algebraic multigrid method for solving the non-Hermitian Wilson discretization of the 2-dimensional Dirac equation. The proposed approach uses a bootstrap setup algorithm based on a multigrid eigensolver. It computes test…
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…
We provide an alternative Fourier analysis for multigrid applied to the Poisson problem in 1D, based on explicit derivation of spectra of the iteration matrix. The new Fourier analysis has advantages over the existing one. It is easy to…
We present a multigrid based eigensolver for computing low-modes of the Hermitian Wilson Dirac operator. For the non-Hermitian case multigrid methods have already replaced conventional Krylov subspace solvers in many lattice QCD…
Eigenvalues of the Hermitian Wilson-Dirac operator are of special interest in several lattice QCD simulations, e.g., for noise reduction when evaluating all-to-all propagators. In this paper we present a Davidson-type eigensolver that…
Lattice QCD solvers encounter critical slowing down for fine lattice spacings and small quark mass. Traditional matrix eigenvalue deflation is one approach to mitigating this problem. However, to improve scaling we study the effects of…
We propose and investigate a novel solution strategy to efficiently and accurately compute approximate solutions to semilinear optimal control problems, focusing on the optimal control of phase field formulations of geometric evolution…
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…
Complete spectra of the staggered Dirac operator $\Dirac$ are determined in quenched four-dimensional $SU(2)$ gauge fields, and also in the presence of dynamical fermions. Periodic as well as antiperiodic boundary conditions are used. An…
We establish global existence and derive sharp pointwise decay estimates of solutions to cubic Dirac and Dirac-Klein-Gordon systems on a curved background, close to the Minkowski spacetime. By squaring the Dirac operator, we reduce the…
We discuss the construction and properties of an approximate solution of the Ginsparg-Wilson equation, the so-called chirally improved lattice Dirac operator. In particular we study the behavior of its eigenmodes in smooth instanton…
We propose new techniques to implement numerically the overlap-Dirac operator which exploit the physical properties of the underlying theory to avoid nested algorithms. We test these procedures in the two-dimensional Schwinger model and the…
Many iterative parallel-in-time algorithms have been shown to be highly efficient for diffusion-dominated partial differential equations (PDEs), but are inefficient or even divergent when applied to advection-dominated PDEs. We consider the…
We propose an adaptive refinement algorithm to solve total variation regularized measure optimization problems. The method iteratively constructs dyadic partitions of the unit cube based on i) the resolution of discretized dual problems and…
In this paper we construct and analyse a level-dependent coarsegrid correction scheme for indefinite Helmholtz problems. This adapted multigrid method is capable of solving the Helmholtz equation on the finest grid using a series of…
A Dirac choice for the averaging kernel $C$ is implemented numerically. This improved kernel will be needed in gauge covariant multigrid computations for propagators of staggered fermions. Results for $C$ and the variational coarse grid…
In the present paper we concentrate on an important issue in constructing a good multigrid solver: the choice of an efficient smoother. We will introduce all-at-once multigrid solvers for optimal control problems which show robust…