Related papers: Adaptive multigrid algorithm for the lattice Wilso…
Symplectic gauge theories coupled to matter fields lead to symmetry enhancement phenomena that have potential applications in such diverse contexts as composite Higgs, top partial compositeness, strongly interacting dark matter, and…
In continuum QCD, nontrivial gauge topologies give rise to zero eigenvalues of the massless Dirac operator. In lattice QCD with Wilson fermions, these zero modes appear as exactly real eigenvalues of the Wilson-Dirac operator and hence as…
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…
In this article we propose a scalable shape optimization algorithm which is tailored for large scale problems and geometries represented by hierarchically refined meshes. Weak scalability and grid independent convergence is achieved via a…
We present results for application of block BiCGSTAB algorithm modified by the QR decomposition and the SAP preconditioner to the Wilson-Dirac equation with multiple right-hand sides in lattice QCD on a $32^3 \times 64$ lattice at almost…
We investigate the critical dynamics of the Hybrid Monte Carlo algorithm approaching the chiral limit of standard Wilson fermions. Our observations are based on time series of lengths O(5000) for a variety of observables. The lattice sizes…
We introduce the formulation of domain wall fermions in the context of lattice QCD. We prove the recovery of exact chiral symmetry in the limit of an infinite fifth direction, and derive the effective four-dimensional operator satisfying…
In lattice QCD, the trace of the inverse of the discretized Dirac operator appears in the disconnected fermion loop contribution to an observable. As simulation methods get more and more precise, these contributions become increasingly…
We present a multigrid iterative algorithm for solving a system of coupled free boundary problems for pricing American put options with regime-switching. The algorithm is based on our recently developed compact finite difference scheme…
We show how to introduce a quark chemical potential in the overlap Dirac operator. The resulting operator satisfies a Ginsparg-Wilson relation and has exact zero modes. It is no longer gamma_5-hermitian, but its nonreal eigenvalues still…
We formulate lattice theories in which chiral symmetry is realized nonlinearly on the fermion fields. In this framework the fermion mass term does not break chiral symmetry. This property allows us to use the Wilson term to remove the…
We analyse the leading logarithmic corrections to the $a^2$ scaling of lattice artefacts in QCD, following the seminal work of Balog, Niedermayer and Weisz in the O(n) non-linear sigma model. Limiting the discussion to contributions from…
We propose a lattice action including unphysical Wilson fermions with a negative mass m_0 of the order of the inverse lattice spacing. With this action, the exact zero mode of the hermitian Wilson-Dirac operator H_W(m_0) cannot appear and…
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…
We present a new multigrid scheme for solving the Poisson equation with Dirichlet boundary conditions on a Cartesian grid with irregular domain boundaries. This scheme was developed in the context of the Adaptive Mesh Refinement (AMR)…
We propose a novel general approach to locality of lattice composite fields, which in case of QCD involves locality in both quark and gauge degrees of freedom. The method is applied to gauge operators based on the overlap Dirac matrix…
Chiral perturbation theory for eigenvalue distributions, and equivalently random matrix theory, has recently been extended to include lattice effects for Wilson fermions. We test the predictions by comparison to eigenvalue distributions of…
We develop an implementation for a recently proposed Noisy Monte Carlo approach to the simulation of lattice QCD with dynamical fermions by incorporating the full fermion determinant directly. Our algorithm uses a quenched gauge field…
The CKM unitarity precision test of the Standard Model requires a systematic treatment of electromagnetic and strong corrections for semi-leptonic decays. Electromagnetic corrections require the renormalization of a semileptonic…
We consider the Dirac equation with cubic Hartree-type nonlinearity derived by uncoupling the Dirac-Klein-Gordon systems. We prove small data scattering result in full subcritical range. Main ingredients of the proof are the localized…