Papers by Timothy J Williams
… oriented methods for …, 1999
Rapid Application Development and Enhanced Code Interoperability using the POOMA Framework* Julia... more Rapid Application Development and Enhanced Code Interoperability using the POOMA Framework* Julian C. Cummings, James A. Crotinger, Scott W. Haney, William F. Humphrey, Steve R. Karmesin, John VW Reynders, Stephen A. Smith and Timothy J. Williams* ...
Gyrokinetic particle-in-cell (PIC) simulations have been proven to be an important and useful too... more Gyrokinetic particle-in-cell (PIC) simulations have been proven to be an important and useful tool for studying low frequency waves and instabilities below ion cyclotron frequency. The gyrokinetic formalism eliminates the cyclotron motion by analytically averaging the equation of motion in time, while keeping finite-Larmor radius effects, and therefore allows a time step of integration to be significantly longer than the
POOMA is an object-oriented C++ class library for doing large scale scientific computations. At i... more POOMA is an object-oriented C++ class library for doing large scale scientific computations. At its highest level it provides the user with data-parallel objects for simulating PDE's and containers of particles for kinetic simulations. These objects translate data-parallel statements into local computation, communication, and synchronization for execution on a variety of serial or parallel architectures. This allows development on workstations
We describe GTC++, a global-cross-section, gyrokinetic, PIC code for simulating tokamak microinst... more We describe GTC++, a global-cross-section, gyrokinetic, PIC code for simulating tokamak microinstabilities. In GTC++, we use objects to represent physical and numerical abstractions such as the magnetic geometry and the gyrokinetic particle-mesh interactions. The basic software infrastructure is the POOMA Framework (Parallel Object-Oriented Methods and Applications). This C++ class library provides high-level data-parallel programming interfaces for particles and for fields discretized on meshes, and it encapsulates parallelism. Sophisticated internal implementations provide high serial and parallel performance. We compare performance with a hand-parallelized Fortran90/MPI code. We describe the design of the GTC++ code---its specialized classes and mechanisms, as well as its use of POOMA's generic particle and field classes. We show reuse of software components also used in hydrodynamic and Monte Carlo codes with radically different physics. We show how our new code design is re...
We have ported a three#dimensional, electrostatic, gyrokinetic, particle#in#cell #PIC# plasma sim... more We have ported a three#dimensional, electrostatic, gyrokinetic, particle#in#cell #PIC# plasma simulation code from the Cray2 to the BBN TC2000 and the Thinking Machines CM2. On the TC2000, we employed the PFP split#join programming paradigm#1#; on the CM2 we employed the CM Fortran data# parallel programming language. Though our hopes to produce codes ten or more times faster than the Cray2 code were not realized, we did produce codes which run faster than the Cray2 code on much less expensive hardware---proof of the promise of massively parallel computing. We are now able to run plasma physics simulations with these parallel codes, including some which are not practical on the Cray2. 1 Gyrokinetic PIC 1.1 Simulation Goals Gyrokinetic particle-in-cell #PIC# simulation#2# is an important tool for studying low-frequency #! # ! ci # plasma instabilities and the associated transport of particles and heat in tokamaks. In spite of the e#- ciency gained by not following ion cyclotron motio...
Almost all public secure communication relies on the inability to factor large numbers. There is ... more Almost all public secure communication relies on the inability to factor large numbers. There is no known analytic or classical numeric method to rapidly factor large numbers. Shor[1] has shown that a quantum computer can factor numbers in polynomial time but there is no practical quantum computer that can yet do such computations. We show that a simulated annealing[2] approach can be adapted to find factors of large numbers.
International Journal of High Performance Computing Applications
Summary ���Grid��� computing has emerged as an important new field, distinguished from convention... more Summary ���Grid��� computing has emerged as an important new field, distinguished from conventional distributed computing by its focus on large-scale resource sharing, innovative applications, and, in some cases, high performance orientation. In this article, the authors define this new field. First, they review the ���Grid problem,��� which is defined as flexible, secure, coordinated resource sharing among dynamic collections of individuals, institutions, and resources���what is referred to as virtual organizations. In such settings, unique ...
Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis on - SC '13, 2013
Reliable predictive simulation capability addressing confinement properties in magnetically confi... more Reliable predictive simulation capability addressing confinement properties in magnetically confined fusion plasmas is critically-important for ITER, a 20 billion dollar international burning plasma device under construction in France. The complex study of kinetic turbulence, which can severely limit the energy confinement and impact the economic viability of fusion systems, requires simulations at extreme scale for such an unprecedented device size. Our newly optimized, global, ab initio particle-in-cell code solving the nonlinear equations underlying gyrokinetic theory achieves excellent performance with respect to "time to solution" at the full capacity of the IBM Blue Gene/Q on 786,432 cores of Mira at ALCF and recently of the 1,572,864 cores of Sequoia at LLNL. Recent multithreading and domain decomposition optimizations in the new GTC-P code represent critically important software advances for modern, low memory per core systems by enabling routine simulations at unprecedented size (130 million grid points ITER-scale) and resolution (65 billion particles).
Physics of Fluids B: Plasma Physics, 1993
Data from several current tokamak experiments indicate that the equilibrium perpendicular velocit... more Data from several current tokamak experiments indicate that the equilibrium perpendicular velocity field can become strongly sheared accompanying the transition from the L mode to the H mode, i.e. improved, confinement, and that fluctuation levels are reduced. Linear theory suggests that velocity shear can stabilize ion-temperature-gradient (ITG) modes when the frequency shift experienced by the mode due to the radial
Proceedings of the 2nd Workshop on High Performance Computational Finance - WHPCF '09, 2009
This paper reviews real-world examples of distributed computing in the finance industry, specific... more This paper reviews real-world examples of distributed computing in the finance industry, specifically in institutional trading of fixed-income securities. Three examples illustrate small to large-scale distributed calculations: valuation of fixed-income derivatives, loading and producing time sequences of prices in statistical arbitrage on fixed-income instruments, and valuation of large portfolios of mortgagebacked securities. Two of these also serve to illustrate a recurring pattern in distributed access of financial datadistributed caching.
The primary research objective of the Numerical Tokamak Turbulence Project (NTTP) is to develop a... more The primary research objective of the Numerical Tokamak Turbulence Project (NTTP) is to develop a predictive ability in modeling turbulent transport due to drift-type instabilities in the core of tokamak fusion experiments, through the use of three-dimensional kinetic and fluid simulations and the derivation of reduced models.
The primary research objective of the Numerical Tokamak Turbulence Project (NTTP) is to develop a... more The primary research objective of the Numerical Tokamak Turbulence Project (NTTP) is to develop a predictive ability in modeling turbulent transport due to drift-type instabilities in the core of tokamak fusion experiments, through the use of three-dimensional kinetic and fluid simulations and the derivation of reduced models.
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Papers by Timothy J Williams