Dynamical linke cluster expansions: Algorithmic aspects and applications

Dynamical linked cluster expansions are linked cluster expansions with hopping parameter terms endowed with their own dynamics. They amount to a generalization of series expansions from 2-point to point-link-point interactions. We outline an associated multiple-line graph theory involving extended notions of connectivity and indicate an algorithmic implementation of graphs. Fields of applications are SU(N) gauge Higgs systems within variational estimates, spin glasses and partially annealed neural networks. We present results for the critical line in an SU(2) gauge Higgs model for the electroweak phase transition. The results agree well with corresponding high precision Monte Carlo results.Comment: LATTICE98(algorithms

Efficient Algorithms And Optimizations For Scientific Computing On Many-Core Processors

Designing efficient algorithms for many-core and multicore architectures requires using different strategies to allow for the best exploitation of the hardware resources on those architectures. Researchers have ported many scientific applications to modern many-core and multicore parallel architectures, and by doing so they have achieved significant speedups over running on single CPU cores. While many applications have achieved significant speedups, some applications still require more effort to accelerate due to their inherently serial behavior. One class of applications that has this serial behavior is the Monte Carlo simulations. Monte Carlo simulations have been used to simulate many problems in statistical physics and statistical mechanics that were not possible to simulate using Molecular Dynamics. While there are a fair number of well-known and recognized GPU Molecular Dynamics codes, the existing Monte Carlo ensemble simulations have not been ported to the GPU, so they are relatively slow and could not run large systems in a reasonable amount of time. Due to the previously mentioned shortcomings of existing Monte Carlo ensemble codes and due to the interest of researchers to have a fast Monte Carlo simulation framework that can simulate large systems, a new GPU framework called GOMC is implemented to simulate different particle and molecular-based force fields and ensembles. GOMC simulates different Monte Carlo ensembles such as the canonical, grand canonical, and Gibbs ensembles. This work describes many challenges in developing a GPU Monte Carlo code for such ensembles and how I addressed these challenges. This work also describes efficient many-core and multicore large-scale energy calculations for Monte Carlo Gibbs ensemble using cell lists. Designing Monte Carlo molecular simulations is challenging as they have less computation and parallelism when compared to similar molecular dynamics applications. The modified cell list allows for more speedup gains for energy calculations on both many-core and multicore architectures when compared to other implementations without using the conventional cell lists. The work presents results and analysis of the cell list algorithms for each one of the parallel architectures using top of the line GPUs, CPUs, and Intel’s Phi coprocessors. In addition, the work evaluates the performance of the cell list algorithms for different problem sizes and different radial cutoffs. In addition, this work evaluates two cell list approaches, a hybrid MPI+OpenMP approach and a hybrid MPI+CUDA approach. The cell list methods are evaluated on a small cluster of multicore CPUs, Intel Phi coprocessors, and GPUs. The performance results are evaluated using different combinations of MPI processes, threads, and problem sizes. Another application presented in this dissertation involves the understanding of the properties of crystalline materials, and their design and control. Recent developments include the introduction of new models to simulate system behavior and properties that are of large experimental and theoretical interest. One of those models is the Phase-Field Crystal (PFC) model. The PFC model has enabled researchers to simulate 2D and 3D crystal structures and study defects such as dislocations and grain boundaries. In this work, GPUs are used to accelerate various dynamic properties of polycrystals in the 2D PFC model. Some properties require very intensive computation that may involve hundreds of thousands of atoms. The GPU implementation has achieved significant speedups of more than 46 times for some large systems simulations

Non-local updates for quantum Monte Carlo simulations

We review the development of update schemes for quantum lattice models simulated using world line quantum Monte Carlo algorithms. Starting from the Suzuki-Trotter mapping we discuss limitations of local update algorithms and highlight the main developments beyond Metropolis-style local updates: the development of cluster algorithms, their generalization to continuous time, the worm and directed-loop algorithms and finally a generalization of the flat histogram method of Wang and Landau to quantum systems.Comment: 14 pages, article for the proceedings of the "The Monte Carlo Method in the Physical Sciences: Celebrating the 50th Anniversary of the Metropolis Algorithm", Los Alamos, June 9-11, 200

Radiation therapy calculations using an on-demand virtual cluster via cloud computing

Computer hardware costs are the limiting factor in producing highly accurate radiation dose calculations on convenient time scales. Because of this, large-scale, full Monte Carlo simulations and other resource intensive algorithms are often considered infeasible for clinical settings. The emerging cloud computing paradigm promises to fundamentally alter the economics of such calculations by providing relatively cheap, on-demand, pay-as-you-go computing resources over the Internet. We believe that cloud computing will usher in a new era, in which very large scale calculations will be routinely performed by clinics and researchers using cloud-based resources. In this research, several proof-of-concept radiation therapy calculations were successfully performed on a cloud-based virtual Monte Carlo cluster. Performance evaluations were made of a distributed processing framework developed specifically for this project. The expected 1/n performance was observed with some caveats. The economics of cloud-based virtual computing clusters versus traditional in-house hardware is also discussed. For most situations, cloud computing can provide a substantial cost savings for distributed calculations.Comment: 12 pages, 4 figure