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At least 1,729 records · Page 96

A projected preconditioned conjugate gradient algorithm for computing many extreme eigenpairs of a Hermitian matrix

We present an iterative algorithm for computing an invariant subspace associated with the algebraically smallest eigenvalues of a large sparse or structured Hermitian matrix A. We are interested in the case in which the dimension of the invariant subspace is large (e.g., over several hundreds or thousands) even though it may still be small relative to the dimension of A. These problems arise from, for example, density functional theory (DFT) based electronic structure calculations for complex materials. The key feature of our algorithm is that it performs fewer Rayleigh–Ritz calculations compared to existing algorithms such as the locally optimal block preconditioned conjugate gradient or the Davidson algorithm. It is a block algorithm, and hence can take advantage of efficient BLAS3 operations and be implemented with multiple levels of concurrency. We discuss a number of practical issues that must be addressed in order to implement the algorithm efficiently on a high performance computer.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A multiscale restriction-smoothed basis method for high contrast porous media represented on unstructured grids

A wide variety of multiscale methods have been proposed in the literature to reduce runtime and provide better scaling for the solution of Poisson-type equations modeling flow in porous media. We present a new multiscale restricted-smoothed basis (MsRSB) method that is designed to be applicable to both rectilinear grids and unstructured grids. Like many other multiscale methods, MsRSB relies on a coarse partition of the underlying fine grid and a set of local prolongation operators (multiscale basis functions) that map unknowns associated with the fine grid cells to unknowns associated with blocks in the coarse partition. These mappings are constructed by restricted smoothing: Starting from a constant, a localized iterative scheme is applied directly to the fine-scale discretization to compute prolongation operators that are consistent with the local properties of the differential operators. The resulting method has three main advantages: First of all, both the coarse and the fine grid can have general polyhedral geometry and unstructured topology. This means that partitions and good prolongation operators can easily be constructed for complex models involving high media contrasts and unstructured cell connections introduced by faults, pinch-outs, erosion, local grid refinement, etc. In particular, the coarse partition can be adapted to geological or flow-field properties represented on cells or faces to improve accuracy. Secondly, the method is accurate and robust when compared to existing multiscale methods and does not need expensive recomputation of local basis functions to account for transient behavior: Dynamic mobility changes are incorporated by continuing to iterate a few extra steps on existing basis functions. This way, the cost of updating the prolongation operators becomes proportional to the amount of change in fluid mobility and one reduces the need for expensive, tolerance-based updates. Finally, since the MsRSB method is formulated on top of a cell-centered, conservative, finite-volume method, it is applicable to any flow model in which one can isolate a pressure equation. Herein, we only discuss single and two-phase incompressible models. Compressible flow, e.g., as modeled by the black-oil equations, is discussed in a separate paper.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A fast band–Krylov eigensolver for macromolecular functional motion simulation on multicore architectures and graphics processors

We introduce a new iterative Krylov subspace-based eigensolver for the simulation of macromolecular motions on desktop multithreaded platforms equipped with multicore processors and, possibly, a graphics accelerator (GPU). The method consists of two stages, with the original problem first reduced into a simpler band-structured form by means of a high-performance compute-intensive procedure. This is followed by a memory-intensive but low-cost Krylov iteration, which is off-loaded to be computed on the GPU by means of an efficient data-parallel kernel. The experimental results reveal the performance of the new eigensolver. Concretely, when applied to the simulation of macromolecules with a few thousands degrees of freedom and the number of eigenpairs to be computed is small to moderate, the new solver outperforms other methods implemented as part of high-performance numerical linear algebra packages for multithreaded architectures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

High-order solution methods for grey discrete ordinates thermal radiative transfer

This work presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation is accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A tightly-coupled domain-decomposition approach for highly nonlinear stochastic multiphysics systems

Multiphysics simulations often involve nonlinear components that are driven by internally generated or externally imposed random fluctuations. When used with a domain-decomposition (DD) algorithm, such components have to be coupled in a way that both accurately propagates the noise between the subdomains and lends itself to a stable and cost-effective temporal integration. We develop a conservative DD approach in which tight coupling is obtained by using a Jacobian-free Newton–Krylov (JfNK) method with a generalized minimum residual iterative linear solver. This strategy is tested on a coupled nonlinear diffusion system forced by a truncated Gaussian noise at the boundary. Enforcement of path-wise continuity of the state variable and its flux, as opposed to continuity in the mean, at interfaces between subdomains enables the DD algorithm to correctly propagate boundary fluctuations throughout the computational domain. Reliance on a single Newton iteration (explicit coupling), rather than on the fully converged JfNK (implicit) coupling, may increase the solution error by an order of magnitude. Increase in communication frequency between the DD components reduces the explicit coupling's error, but makes it less efficient than the implicit coupling at comparable error levels for all noise strengths considered. Finally, the DD algorithm with the implicit JfNK coupling resolves temporally-correlated fluctuations of the boundary noise when the correlation time of the latter exceeds some multiple of an appropriately defined characteristic diffusion time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Efficient and robust relaxation procedures for multi-component mixtures including phase transition

We consider a thermodynamic consistent multi-component model in multi-dimensions that is a generalization of the classical two-phase flow model of Baer and Nunziato. The exchange of mass, momentum and energy between the phases is described by additional source terms. Typically these terms are handled by relaxation procedures. Available relaxation procedures suffer from efficiency and robustness resulting in very costly computations that in general only allow for one-dimensional computations. Therefore we focus on the development of new efficient and robust numerical methods for relaxation processes. We derive exact procedures to determine mechanical and thermal equilibrium states. Further we introduce a novel iterative method to treat the mass transfer for a three component mixture. All new procedures can be extended to an arbitrary number of inert ideal gases. We prove existence, uniqueness and physical admissibility of the resulting states and convergence of our new procedures. Efficiency and robustness of the procedures are verified by means of numerical computations in one and two space dimensions. - Highlights: • We develop novel relaxation procedures for a generalized, thermodynamically consistent Baer–Nunziato type model. • Exact procedures for mechanical and thermal relaxation procedures avoid artificial parameters. • Existence, uniqueness and physical admissibility of the equilibrium states are proven for special mixtures. • A novel iterative method for mass transfer is introduced for a three component mixture providing a unique and admissible equilibrium state.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A second-order-in-time, explicit approach addressing the redundancy in the low-Mach, variable-density Navier-Stokes equations

A novel algorithm for explicit temporal discretization of the variable-density, low-Mach Navier-Stokes equations is presented here in this study. Recognizing there is a redundancy between the mass conservation equation, the equation of state, and the transport equation(s) for the scalar(s) which characterize the thermochemical state, and that it destabilizes explicit methods, we demonstrate how to analytically eliminate the redundancy and propose an iterative scheme to solve the resulting transformed scalar equations. The method obtains second-order accuracy in time regardless of the number of iterations, so one can terminate this subproblem once stability is achieved. Hence, flows with larger density ratios can be simulated while still retaining the efficiency, low cost, and parallelizability of an explicit scheme. The temporal discretization algorithm is used within a pseudospectral direct numerical simulation which extends the method of Kim, Moin, and Moser for incompressible flow to the variable-density, low-Mach setting, where we demonstrate stability for density ratios up to ~25.7.

97 MATHEMATICS AND COMPUTING↗

A parallel strategy for density functional theory computations on accelerated nodes

Using the Löwdin orthonormalization of tall-skinny matrices as a proxy-app for wavefunction-based Density Functional Theory solvers, we investigate a distributed memory parallel strategy focusing on Graphics Processing Unit (GPU)-accelerated nodes as available on some of the top ranked supercomputers at the present time. Here we present numerical results in the strong limit regime, as it is particularly relevant for First-Principles Molecular Dynamics. We also examine how matrix product-based iterative solvers provide a competitive alternative to dense eigensolvers on GPUs, allowing to push the strong scaling limit of these computations to a larger number of distributed tasks. Our strategy, which relies on replicated Gram matrices and efficient collective communications using the NCCL library, leads to a time-to-solution under 0.5 s for the Löwdin orthonormalization of a tall-skinny matrix of 3000 columns on Summit at Oak Ridge Leadership Facility (OLCF). Given the similarity in computational operations between one iteration of a DFT solver and this proxy-app, this shows the possibility of solving accurately the DFT equations well under a minute for 3000 electronic wave functions, and thus perform First-Principles molecular dynamics of physical systems much larger than traditionally solved on CPU systems.

97 MATHEMATICS AND COMPUTING↗

The development of the radio frequency driven negative ion source for neutral beam injectors (invited)

Large and powerful negative hydrogen ion sources are required for the neutral beam injection (NBI) systems of future fusion devices. Simplicity and maintenance-free operation favors RF sources, which are developed intensively at the Max-Planck-Institut fuer Plasmaphysik (IPP) since many years. The negative hydrogen ions are generated by caesium-enhanced surface conversion of atoms and positive ions on the plasma grid surface. With a small scale prototype the required high ion current density and the low fraction of co-extracted electrons at low pressure as well as stable pulses up to 1 h could be demonstrated. The modular design allows extension to large source dimensions. This has led to the decision to choose RF sources for the NBI of the international fusion reactor, ITER. As an intermediate step towards the full size ITER source at IPP, the development will be continued with a half-size source on the new ELISE testbed. This will enable to gain experience for the first time with negative hydrogen ion beams from RF sources of these dimensions.

43 PARTICLE ACCELERATORS↗

Large Scale CW ECRH Systems: Meeting a Challenge

Electron Cyclotron Resonance Heating (ECRH) systems for next step-fusion devices like W7-X and ITER operate in CW-mode and provide a large flexibility to comply with various physics demands such as plasma start-up, heating and current drive, as well as configuration and MHD control. The request for many different sophisticated applications results in a growing complexity of the systems. This is in conflict with the request for high availability, reliability, and maintainability, which arises from DEMO demands. 'Advanced' ECRH-components must, therefore, comply with both the complex physics demands and operational robustness and reliability. The W7-X ECRH system is the first CW facility of an ITER relevant size and is used as a test bed for such components. Results on improvements of gyrotrons, transmission components and launchers are presented together with proposals for future developments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

ICRF heating at JET: From operations with a metallic wall to the long term perspective of a DT campaign

The first series of experiments with the ITER-like wall (ILW) will start mid-2011 with D plasmas and will continue through 2012-13 with H, {sup 4}He and D plasmas, and up to 2014-15, when a DT campaign is proposed. In this paper, the previous experience at JET is reviewed to set the scene for the future challenges of ICRF operation including change in the ICRF coupling, W impurity production and evaluation of localized power loads due the RF sheaths. development in a Beryllium/Tungsten environment of ICRF heating schemes for the non activated and the DT phases of ITER.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Analysis of a multi-machine database on divertor heat fluxes

A coordinated effort to measure divertor heat flux characteristics in fully attached, similarly shaped H-mode plasmas on C-Mod, DIII-D, and NSTX was carried out in 2010 in order to construct a predictive scaling relation applicable to next step devices including ITER, FNSF, and DEMO. Few published scaling laws are available and those that have been published were obtained under widely varying conditions and divertor geometries, leading to conflicting predictions for this critically important quantity. This study was designed to overcome these deficiencies. Analysis of the combined data set reveals that the primary dependence of the parallel heat flux width is robustly inverse with I{sub p}, which all three tokamaks independently demonstrate. An improved Thomson scattering system on DIII-D has yielded very accurate scrape off layer (SOL) profile measurements from which tests of parallel transport models have been made. It is found that a flux-limited model agrees best with the data at all collisionalities, while a Spitzer resistivity model agrees at higher collisionality where it is more valid. The SOL profile measurements and divertor heat flux scaling are consistent with a heuristic drift based model as well as a critical gradient model.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Diagnostic options for radiative divertor feedback control on NSTX-U

A radiative divertor technique is used in present tokamak experiments and planned for ITER to mitigate high heat loads on divertor plasma-facing components (PFCs) to prevent excessive material erosion and thermal damage. In NSTX, a large spherical tokamak with lithium-coated graphite PFCs and high divertor heat flux (q{sub peak} Less-Than-Or-Slanted-Equal-To 15 MW/m{sup 2}), radiative divertor experiments have demonstrated a significant reduction of divertor peak heat flux simultaneously with good core H-mode confinement using pre-programmed D{sub 2} or CD{sub 4} gas injections. In this work diagnostic options for a new real-time feedback control system for active radiative divertor detachment control in NSTX-U, where steady-state peak divertor heat fluxes are projected to reach 20-30 MW/m{sup 2}, are discussed. Based on the NSTX divertor detachment measurements and analysis, the control diagnostic signals available for NSTX-U include divertor radiated power, neutral pressure, spectroscopic deuterium recombination signatures, infrared thermography of PFC surfaces, and thermoelectric scrape-off layer current. In addition, spectroscopic 'security' monitoring of possible confinement or pedestal degradation is recommended. These signals would be implemented in a digital plasma control system to manage the divertor detachment process via an actuator (impurity gas seeding rate).

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Simultaneous imaging/reflectivity measurements to assess diagnostic mirror cleaning

Practical methods to clean ITER's diagnostic mirrors and restore reflectivity will be critical to ITER's plasma operations. We describe a technique to assess the efficacy of mirror cleaning techniques and detect any damage to the mirror surface. The method combines microscopic imaging and reflectivity measurements in the red, green, and blue spectral regions and at selected wavelengths. The method has been applied to laser cleaning of single crystal molybdenum mirrors coated with either carbon or beryllium films 150-420 nm thick. It is suitable for hazardous materials such as beryllium as the mirrors remain sealed in a vacuum chamber.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Collisionless inter-species energy transfer and turbulent heating in drift wave turbulence

We reconsider the classic problems of calculating 'turbulent heating' and collisionless inter-species transfer of energy in drift wave turbulence. These issues are of interest for low collisionality, electron heated plasmas, such as ITER, where collisionless energy transfer from electrons to ions is likely to be significant. From the wave Poynting theorem at steady state, a volume integral over an annulus r{sub 1} =-S{sub r}|{sub r{sub 1}{sup r{sub 2}}}{ne}0. Here S{sub r} is the wave energy density flux in the radial direction. Thus, a wave energy flux differential across an annular region indeed gives rise to a net heating, in contrast to previous predictions. This heating is related to the Reynolds work by the zonal flow, since S{sub r} is directly linked to the zonal flow drive. In addition to net heating, there is inter-species heat transfer. For collisionless electron drift waves, the total turbulent energy source for collisionless heat transfer is due to quasilinear electron cooling. Subsequent quasilinear ion heating occurs through linear ion Landau damping. In addition, perpendicular heating via ion polarization currents contributes to ion heating. Since at steady state, Reynolds work of the turbulence on the zonal flow must balance zonal flow frictional damping ({approx}{nu}{sub ii} {sup 2}{approx}|(e{phi}(tilde sign)/T)|{sup 4}), it is no surprise that zonal flow friction appears as an important channel for ion heating. This process of energy transfer via zonal flow has not previously been accounted for in analyses of energy transfer. As an application, we compare the rate of turbulent energy transfer in a low collisionality plasma with the rate of the energy transfer by collisions. The result shows that the collisionless turbulent energy transfer is a significant energy coupling process for ITER plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Physics of a magnetic filter for negative ion sources. II. E Multiplication-Sign B drift through the filter in a real geometry

The physics of a magnetic filter under conditions similar to those of the negative ion source for the ITER neutral beam injector is analyzed with the help of a two-dimensional particle-in-cell Monte Carlo Collisions model. A detailed analysis of the different terms of the electron momentum equations shows how diamagnetic and drift currents can be dominant in different regions of the filter. Electron transport through the filter is due to an E Multiplication-Sign B drift current on one side of the chamber induced by the presence of the chamber walls perpendicular to the electron diamagnetic current. The filter design of the ITER negative ion source, which does not allow a closed electron diamagnetic current, induces an asymmetry of the plasma that is analyzed with the particle model. It is shown that electron transport through the filter in this geometry is very different from the transport in an ideal, one-dimensional magnetic filter often considered in the literature and described in detail in the companion paper [Boeuf et al., Phys. Plasmas 19, 113509 (2012)].

43 PARTICLE ACCELERATORS↗

EBIT spectroscopy of highly charged heavy ions relevant to hot plasmas

We present spectra of highly charged iron, gadolinium, and tungsten ions obtained with electron beam ion traps. Spectroscopic studies of these ions are important to diagnose and control hot plasmas in several areas. For iron ions, the electron density dependence of the line intensity ratio in extreme ultraviolet spectra is investigated for testing the model calculation used in solar corona diagnostics. Soft x-ray spectra of gadolinium are studied to obtain atomic data required in light source development for future lithography. Tungsten is considered to be the main impurity in the ITER plasma, and thus visible and soft x-ray spectra of tungsten have been observed to explore the emission lines useful for the spectroscopic diagnostics of the ITER plasma.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Propagation of shear Alvén waves in two-ion species plasmas confined by a nonuniform magnetic field

Ray tracing calculations are performed for shear Alfvén waves in two-ion species plasmas in which the magnetic field varies with position. Three different magnetic topologies of contemporary interest are explored: a linear magnetic mirror, a pure toroidal field, and a tokamak field. The wave frequency is chosen to lie in the upper propagation band, so that reflection at the ion-ion hybrid frequency can occur for waves originally propagating along the magnetic field direction. Calculations are performed for a magnetic well configuration used in recent experiments [S. T. Vincena et al., Geophys. Res. Lett. 38, L11101 (2011) and S. T. Vincena et al., Phys. Plasmas 20, 012111 (2013)] in the Large Plasma Device (LAPD) related to the ion-ion hybrid resonator. It is found that radial spreading cannot explain the relatively low values of the resonator quality factor (Q) measured in those experiments, even when finite ion temperature is considered. This identifies that a damping mechanism is present that is at least an order of magnitude larger than dissipation due to radial energy loss. Calculations are also performed for a magnetic field with pure toroidal geometry, without a poloidal field, as in experiments being planned for the Enormous Toroidal Plasma Device. In this case, the effects of field-line curvature cause radial reflections. A poloidal field is included to explore a tokamak geometry with plasma parameters expected in ITER. When ion temperature is ignored, it is found that the ion-ion hybrid resonator can exist and trap waves for multiples bounces. The effects of finite ion temperature combine with field line curvature to cause the reflection point to move towards the tritium cyclotron frequency when electron temperature is negligible. However, for ITER parameters, it is shown that the electrons must be treated in the adiabatic limit to properly describe resonator phenomena.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗