Guido Arnold

Compact QED under scrutiny: It's first order

We report new results from our finite size scaling analysis of 4d compact pure U(1) gauge theory with Wilson action. Investigating several cumulants of the plaquette energy within the Borgs-Kotecky finite size scaling scheme we find strong evidence for a first-order phase transition and present a high precision value for the critical coupling in the thermodynamic limit.

Numerical methods for the QCD overlap operator IV: Hybrid Monte Carlo

Abstract The computational costs of calculating the matrix sign function of the overlap operator together with fundamental numerical problems related to the discontinuity of the sign function in the kernel eigenvalues are the major obstacle towards simulations with dynamical overlap fermions using the Hybrid Monte Carlo algorithm. In a previous paper of the present series we introduced optimal numerical approximation of the sign function and have developed highly advanced preconditioning and relaxation techniques which speed up the inversion of the overlap operator by nearly an order of magnitude. In this fourth paper of the series we construct an HMC algorithm for overlap fermions. We approximate the matrix sign function using the Zolotarev rational approximation, treating the smallest eigenvalues of the Wilson operator exactly within the fermionic force. Based on this we derive the fermionic force for the overlap operator. We explicitly solve the problem of the Dirac delta-function terms arising through zero crossings of eigenvalues of the Wilson operator. The main advantage of scheme is that its energy violations scale better than O ( Δ τ 2 ) and thus are comparable with the violations of the standard leapfrog algorithm over the course of a trajectory. We explicitly prove that our algorithm satisfies reversibility and area conservation. We present test results from our algorithm on 44, 64, and 84 lattices.

Numerical Methods for the QCD Overlap Operator: II. Optimal Krylov SubspaceMethods

We investigate optimal choices for the (outer) iteration method to use when solving linear systems with Neuberger’s overlap operator in QCD. Different formulations for this operator give rise to different iterative solvers, which are optimal for the respective formulation. We compare these methods in theory and practice to find the overall optimal one. For the first time, we apply the so-called SUMR method of Jagels and Reichel to the shifted unitary version of Neuberger’s operator, and show that this method is in a sense the optimal choice for propagator computations. When solving the “squared” equations in a dynamical simulation with two degenerate flavours, it turns out that the CG method should be used.

Finite size scaling analysis of compact QED

Abstract We describe results of a high-statistics finite size scaling analysis of 4d compact U(1) lattice gauge theory with Wilson action at the phase transition point. Using a multicanonical hybrid Monte Carlo algorithm we generate data samples with more than 150 tunneling events between the metastable states of the system, on lattice sizes up to 184. We performed a first analysis within the Borgs-Kotecky finite size scaling scheme. As a result, we report evidence for a first-order phase transition with a plaquette energy gap, G = 0.02667(20), at a transition coupling, βT = 1.011128(11).

Multicanonical hybrid Monte Carlo algorithm: Boosting simulations of compact QED

We demonstrate that substantial progress can be achieved in the study of the phase structure of 4-dimensional compact QED by a joint use of hybrid Monte Carlo and multicanonical algorithms, through an efficient parallel implementation. This is borne out by the observation of considerable speedup of tunnelling between the metastable states, close to the phase transition, on the Wilson line. We estimate that the creation of adequate samples (with order 100 flip-flops) becomes a matter of half a years runtime at 2 Gflops sustained performance for lattices of size up to 24^4.

Cluster-Computing und Computational Science mit der Wuppertaler Alpha-Linux-Cluster-Engine ALiCE

ZUSAMMENFASSUNG Gegenwärtig sind wir Zeugen eines Umbruchs in der Welt des Höchstleistungsrechnens. Zunehmend werden proprietäre Systeme durch kostengünstige Clustercomputer ersetzt. Eingeleitet wurde diese Entwicklung durch neue Gigabit-Netzwerke, die über Standard-Schnittstellen hunderte von PCs koppeln können. Diese Entwicklung ist von immenser Bedeutung für Arbeitsgruppen der Computational Science mit Grand-Challenge-Anwendungen. Die Universität Wuppertal, wo seit 1990 High-Performance-Rechner wie die Connection Machines CM2 und CM5 in der Computational Science eingesetzt werden, hat die Alpha-Linux-Cluster-Engine ALiCE in ihrem Institut für Angewandte Informatik (IAI) installiert. Im Endausbau besteht der Clustercomputer aus 128 DS10 Workstations des Herstellers Compaq, mit jeweils einer 616 MHz Alpha CPU. Die Workstations sind durch ein Myrinet Gigabit-Netzwerk gekoppelt. Softwareseitig kommt das ursprünglich an der Universität Karlsruhe aufgebaute und durch die Fa. ParTec AG weitergeführte Kommunikationssystem ParaStation3™ zum Einsatz und wird in Kooperation weiterentwickelt. Die wichtigsten Einsatzfelder von ALiCE liegen auf den Gebieten der computergestützten Elementarteilchenphysik, der Materialwissenschaft und des Wissenschaftlichen Rechnens. Neben genuinen Anwendungen der numerischen Mathematik spielen interdisziplinäre Projekte zwischen Angewandter Mathematik und Physik eine besondere Rolle. Insbesondere wird mit ALiCE Ausbildung in HPC für Anwendungen der Computational Science betrieben. Unsere Erfahrungen zeigen, dass kostengünstige modulare Clusterrechner wie ALiCE heute in die Spitzengruppe der schnellsten Rechner vorstoßen können, wie durch die TOP500-Liste ausgewiesen, und dass sie überdies in vielen Fällen leistungsfähiger sind als proprietäre Systeme.

Cluster computing vs. Cray T3E-a case study from numerical field theory

We compare the performance of a simulation code for lattice quantum electrodynamics, running on the cluster computer ALiCE (Alpha-Linux-Cluster-Engine) and the Cray T3E-1200 system. We present results from simulations using the novel parallelized multicanonical hybrid Monte Carlo algorithm. We merge multicanonical simulation techniques with the hybrid Monte Carlo algorithm to achieve a parallel scheme, and thus to be able to fight the notorious metastabilities by use of high performance parallel computers. We demonstrate for this application field that ALiCE is superior to the Cray T3E-1200 by factors of about 1.3 to 2.

Multicanonical hybrid Monte Carlo for compact QED

Abstract We demonstrate that substantial progress can be achieved in the study of the phase structure of 4-dimensional compact QED by a joint use of hybrid Monte Carlo and multicanonical algorithms, through an efficient parallel implementation. This is borne out by the observation of considerable speedup of tunnelling between the metastable states, close to the phase transition, on the Wilson line. Our approach leads to a general parallelization scheme for the efficient stochastic sampling of systems where (a part of) the Hamiltonian involves the total action or energy in each update step.