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At least 883 records · Page 49

SIAM Conference on Parallel Processing for Scientific Computing, 4th, Chicago, IL, Dec. 11-13, 1989, Proceedings

Attention is given to such topics as an evaluation of block algorithm variants in LAPACK and presents a large-grain parallel sparse system solver, a multiprocessor method for the solution of the generalized Eigenvalue problem on an interval, and a parallel QR algorithm for iterative subspace methods on the CM2. A discussion of numerical methods includes the topics of asynchronous numerical solutions of PDEs on parallel computers, parallel homotopy curve tracking on a hypercube, and solving Navier-Stokes equations on the Cedar Multi-Cluster system. A section on differential equations includes a discussion of a six-color procedure for the parallel solution of elliptic systems using the finite quadtree structure, data parallel algorithms for the finite element method, and domain decomposition methods in aerodynamics. Topics dealing with massively parallel computing include hypercube vs. 2-dimensional meshes and massively parallel computation of conservation laws. Performance and tools are also discussed.

Dongarra, Jack↗

Application of linear multifrequency-grey acceleration to preconditioned Krylov iterations for thermal radiation transport

The thermal radiative transfer (TRT) equations comprise a radiation equation coupled to the material internal energy equation. Linearization of these equations produces effective, thermally-redistributed scattering through absorption-reemission. In this paper, we investigate the effectiveness and efficiency of Linear-Multi-Frequency-Grey (LMFG) acceleration that has been reformulated for use as a preconditioner to Krylov iterative solution methods. We introduce two general frameworks, the scalar flux formulation (SFF) and the absorption rate formulation (ARF), and investigate their iterative properties in the absence and presence of true scattering. SFF has a group-dependent state size but may be formulated without inner iterations in the presence of scattering, while ARF has a group-independent state size but requires inner iterations when scattering is present. We compare and evaluate the computational cost and efficiency of LMFG applied to these two formulations using a direct solver for the preconditioners. Finally, this work is novel because the use of LMFG for the radiation transport equation, in conjunction with Krylov methods, involves special considerations not required for radiation diffusion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Numerical methods of solving a system of multi-dimensional nonlinear equations of the diffusion type

The principles of conservation and stability of difference schemes achieved using the iteration control method were examined. For the schemes obtained of the predictor-corrector type, the conversion was proved for the control sequences of approximate solutions to the precise solutions in the Sobolev metrics. Algorithms were developed for reducing the differential problem to integral relationships, whose solution methods are known, were designed. The algorithms for the problem solution are classified depending on the non-linearity of the diffusion coefficients, and practical recommendations for their effective use are given.

Agapov, A. V.↗

The Fractional Step Method Applied to Simulations of Natural Convective Flows

This paper describes research done to apply the Fractional Step Method to finite-element simulations of natural convective flows in pure liquids, permeable media, and in a directionally solidified metal alloy casting. The Fractional Step Method has been applied commonly to high Reynold's number flow simulations, but is less common for low Reynold's number flows, such as natural convection in liquids and in permeable media. The Fractional Step Method offers increased speed and reduced memory requirements by allowing non-coupled solution of the pressure and the velocity components. The Fractional Step Method has particular benefits for predicting flows in a directionally solidified alloy, since other methods presently employed are not very efficient. Previously, the most suitable method for predicting flows in a directionally solidified binary alloy was the penalty method. The penalty method requires direct matrix solvers, due to the penalty term. The Fractional Step Method allows iterative solution of the finite element stiffness matrices, thereby allowing more efficient solution of the matrices. The Fractional Step Method also lends itself to parallel processing, since the velocity component stiffness matrices can be built and solved independently of each other. The finite-element simulations of a directionally solidified casting are used to predict macrosegregation in directionally solidified castings. In particular, the finite-element simulations predict the existence of 'channels' within the processing mushy zone and subsequently 'freckles' within the fully processed solid, which are known to result from macrosegregation, or what is often referred to as thermo-solutal convection. These freckles cause material property non-uniformities in directionally solidified castings; therefore many of these castings are scrapped. The phenomenon of natural convection in an alloy under-going directional solidification, or thermo-solutal convection, will be explained. The development of the momentum and continuity equations for natural convection in a fluid, a permeable medium, and in a binary alloy undergoing directional solidification will be presented. Finally, results for natural convection in a pure liquid, natural convection in a medium with a constant permeability, and for directional solidification will be presented.

Westra, Douglas G.↗

Toward large-scale simulation of residual stress and distortion in wire and arc additive manufacturing

In this study, we aim to advance the structural analysis of wire and arc additive manufacturing (WAAM) by considering the thermomechanical features inherent in direct energy deposition. Simulation approaches including the iterative substructure method (ISM), dynamic mesh refining method (DMRM), and graphics processing unit (GPU) based explicit finite element method (FEM) were developed for accelerating additive manufacturing stress analysis that is very time consuming by conventional numerical methods. ISM and DMRM take advantage of the strong nonlinearity phenomenon near the moving heat source by reducing the global iterations and refining the local mesh, respectively. In addition to the use of GPUs, the explicit FEM is accelerated by a time scaling technique based on the inherent strain concept. The residual stress and distortion of two large builds were analyzed, showing very consistent numerical results and good agreement with experiments. Compared with the commercial software Abaqus, the novel approaches reduced the computational cost substantially without compromising accuracy. The GPU code showed the highest computational efficiency (30~70×), while DMRM and ISM had acceleration factors of 9× and 3×, respectively. Finally, such high-fidelity modeling approaches will be very useful for building up a digital twin of WAAM to reduce development time and cost.

36 MATERIALS SCIENCE↗

Parallel Algebraic Multigrid for Fusion and Higher-Order PDEs

Multigrid methods play a key role in large-scale scientific simulation because they are among the fastest and most scalable approaches for solving the underlying sparse linear systems of equations that arise from a wide array of Partial Differential Equation (PDE) discretizations. Algebraic multigrid (AMG) is a special type of multigrid method that depends only on the description of the linear system, giving it better portability and broader applicability than geometric multigrid, as it requires no explicit knowledge of the problem geometry. Even though these methods are widely used today, there are still applications where further development is needed. In this report, we focus on PDEs with higher-order terms (e.g., fourth order), concentrating on a PDE that arises in tokamak edge plasma simulations (a tokamak is a machine that confines a plasma using magnetic fields and is believed to be the leading plasma confinement concept for future fusion power plants). General multigrid relaxes a linear system on coarser grids and reverses this process with interpolation, but standard AMG methods struggle with the aforementioned higher-order PDEs. We investigate cyclic coarsening and interpolation heuristics, as well as new iterative approximation methods of refining the solution at each grid to improve the existing multigrid approach. To this end, we ensure that these techniques are transferable to a parallelized setting with LLNL’s supercomputers.

97 MATHEMATICS AND COMPUTING↗

New Flutter Analysis Technique for CFD-based Unsteady Aeroelasticity

This paper presents a flutter analysis technique for the transonic flight regime. The technique uses an iterative approach to determine the critical dynamic pressure for a given mach number. Unlike other CFD-based flutter analysis methods, each iteration solves for the critical dynamic pressure and uses this value in subsequent iterations until the value converges. This process reduces the iterations required to determine the critical dynamic pressure. To improve the accuracy of the analysis, the technique employs a known structural model, leaving only the aerodynamic model as the unknown. The aerodynamic model is estimated using unsteady aeroelastic CFD analysis combined with a parameter estimation routine. The technique executes as follows. The known structural model is represented as a finite element model. Modal analysis determines the frequencies and mode shapes for the structural model. At a given mach number and dynamic pressure, the unsteady CFD analysis is performed. The output time history of the surface pressure is converted to a nodal aerodynamic force vector. The forces are then normalized by the given dynamic pressure. A multi-input multi-output parameter estimation software, ERA, estimates the aerodynamic model through the use of time histories of nodal aerodynamic forces and structural deformations. The critical dynamic pressure is then calculated using the known structural model and the estimated aerodynamic model. This output is used as the dynamic pressure in subsequent iterations until the critical dynamic pressure is determined. This technique is demonstrated on the Aerostructures Test Wing-2 model at NASA's Dryden Flight Research Center.

Pak, Chan-gi↗

Reactivity loss validation of high burn-up PWR fuels with pile-oscillation experiments in MINERVE

The ALIX experimental program relies on the experimental validation of the spent fuel inventory, by chemical analysis of samples irradiated in a PWR between 5 and 7 cycles, and also on the experimental validation of the spent fuel reactivity loss with bum-up, obtained by pile-oscillation measurements in the MINERVE reactor. These latter experiments provide an overall validation of both the fuel inventory and of the nuclear data responsible for the reactivity loss. This program offers also unique experimental data for fuels with a burn-up reaching 85 GWd/t, as spent fuels in French PWRs never exceeds 70 GWd/t up to now. The analysis of these experiments is done in two steps with the APOLLO2/SHEM-MOC/CEA2005v4 package. In the first one, the fuel inventory of each sample is obtained by assembly calculations. The calculation route consists in the self-shielding of cross sections on the 281 energy group SHEM mesh, followed by the flux calculation by the Method Of Characteristics in a 2D-exact heterogeneous geometry of the assembly, and finally a depletion calculation by an iterative resolution of the Bateman equations. In the second step, the fuel inventory is used in the analysis of pile-oscillation experiments in which the reactivity of the ALIX spent fuel samples is compared to the reactivity of fresh fuel samples. The comparison between Experiment and Calculation shows satisfactory results with the JEFF3.1.1 library which predicts the reactivity loss within 2% for burn-up of {approx}75 GWd/t and within 4% for burn-up of {approx}85 GWd/t. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Electron Cyclotron Emission–Based Separatrix Identification in ITER with OMFIT Synthetic Modeling

Accurate determination of the separatrix location is essential for understanding edge plasma behavior and optimizing confinement in tokamaks, especially in next-generation devices such as ITER. In this study, a synthetic microwave diagnostics module was developed and implemented in the OMFIT framework to assess the feasibility of an electron cyclotron emission–based separatrix detection method in ITER plasmas. Simulations were carried out using ITER H-mode equilibrium scenarios with different plasma density profiles and different pedestal widths. Here, the results show that the electron emission temperature profiles consistently exhibit an inversion pattern near the edge, with a well-defined minimum point that could serve as a proxy for the separatrix location. However, unlike in the DIII-D, the minimum point in ITER is systematically offset by approximately 2 cm into the scrape-off layer, independent of density or pedestal width, which is within the radial resolution range (2 to 5 cm) determined by the 500-MHz channel spacing. While the method does not provide the exact separatrix location, it offers a reliable indicator of the boundary region and has potential applications for real-time boundary monitoring in ITER and other future fusion devices.

Electron cyclotron emission↗

Counterrotating prop-fan simulations which feature a relative-motion multiblock grid decomposition enabling arbitrary time-steps

Improvements are presented of a computer algorithm developed for the time-accurate flow analysis of rotating machines. The flow model is a finite volume method utilizing a high-resolution approximate Riemann solver for interface flux definitions. The numerical scheme is a block LU implicit iterative-refinement method which possesses apparent unconditional stability. Multiblock composite gridding is used to orderly partition the field into a specified arrangement of blocks exhibiting varying degrees of similarity. Block-block relative motion is achieved using local grid distortion to reduce grid skewness and accommodate arbitrary time step selection. A general high-order numerical scheme is applied to satisfy the geometric conservation law. An even-blade-count counterrotating unducted fan configuration is chosen for a computational study comparing solutions resulting from altering parameters such as time step size and iteration count. The solutions are compared with measured data.

Janus, J. Mark↗

Adaptive Algebraic Smoothers

methods based on Local Sensitivity Analysis (LSA). The method can be used in the context of geometric and algebraic multigrid methods for constructing smoothers, and in the context of Krylov methods for constructing block preconditioners. It is suitable for both constant and variable coecient problems. Furthermore, the method can be applied to systems arising from both scalar and coupled system partial differential equations (PDEs), as well as linear systems that do not arise from PDEs. The simplicity of the method will allow it to be easily incorporated into existing multigrid and Krylov solvers while providing a powerful tool for adaptively constructing methods tuned to a problem.

99 GENERAL AND MISCELLANEOUS↗

A multi-dimensional Smolyak collocation method in curvilinear coordinates for computing vibrational spectra

In this paper, we improve the collocation method for computing vibrational spectra that was presented in Avila and Carrington, Jr. [J. Chem. Phys. 139, 134114 (2013)]. Using an iterative eigensolver, energy levels and wavefunctions are determined from values of the potential on a Smolyak grid. The kinetic energy matrix-vector product is evaluated by transforming a vector labelled with (nondirect product) grid indices to a vector labelled by (nondirect product) basis indices. Both the transformation and application of the kinetic energy operator (KEO) scale favorably. Collocation facilitates dealing with complicated KEOs because it obviates the need to calculate integrals of coordinate dependent coefficients of differential operators. The ideas are tested by computing energy levels of HONO using a KEO in bond coordinates.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Application of Variance Reduction Techniques in RMC Burnup and Thermal-Hydraulic Coupled Calculation

In reactor analog simulation, the Monte Carlo method has relatively high fidelity since it can reduce calculation errors resulting from using approximation methods by describing complex geometry and neutron energy spectra. The Monte Carlo method is, in essence, a stochastic simulation of the neutron transport process, and statistical uncertainty of all the computed results must be provided. In large-scale reactor computation, this method can accurately estimate integral quantities such as the effective multiplication factor (K{sub eff}), and it can limit the uncertainty within an acceptable range via reasonably selecting simulation particles. Nevertheless, it faces great challenges in estimating local quantities like neutron flux and fission power, with uncertainty of estimators beyond acceptance. To decrease the uncertainty of local quantities by increasing simulation particles may cost much time and reduce efficiency. The main reasons are as follows. Firstly, the scale of reactors is so large that common pressurized water reactors have tens of thousands of lattice cells; secondly, uneven distribution of neutron flux and fission power causes uneven distribution of uncertainty. Smith K. puts forward the 95/95 principle to estimate whether uncertainty calculated with Monte Carlo Code satisfies the requirement. According to the principle, with a confidence level of 95%, statistical errors of power density in more than 95% of the regions should be less than 1%. To meet the requirement of the principle, the uniform fission site (UFS) method is raised currently. UFS aims at redistributing fission sources to uniformize the fission source sampling, which can make statistical variance distribution more uniform. This method, which is easy to use, will not obviously increase computation time. Many studies show that UFS has a good variance reduction effect in Monte Carlo criticality calculation, but less attention is paid to its performance in burnup calculation and thermal-hydraulic coupled calculation. Uncertainty arising from the Monte Carlo method has a large impact on burnup calculation and thermal-hydraulic coupled calculation. Variance propagates between burnup steps and between iterative steps of coupled calculation, which causes asymmetry of results of the physical symmetrical regions and instability of coupled iterative convergence errors. To further verify the effect of UFS, this study uses it in the RMC (the Reactor Monte Carlo code) burnup calculation module and the neutronics/thermohydraulics coupled calculation module, and conducts two-dimensional pressurized water reactor burnup calculation and BEAVRS benchmark thermalhydraulic coupled calculation. In this way, it verifies the improvement effect of UFS on variance propagation. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Thermal feedback coupling in a transient Monte Carlo high-order/low-order scheme

Transient simulations of nuclear systems face the computational challenge of resolving both space and time during reactivity changes. A common strategy for tackling this issue is to split the neutron flux into shape and amplitude functions. This split can be solved with high- order/low-order methods. While this multi-fidelity approach has traditionally been reserved for deterministic methods, it is also possible to implement in Monte Carlo as an efficient alternative to Dynamic Monte Carlo. This work implements the frequency transform method with thermal feedback in high-order/low-order Monte Carlo by blending static coupling methods such as single-batch Monte Carlo, with a simple thermal-fluids calculation. While previous work focused solely on prescribed transients, the addition of time-dependent thermal-fluids allows transients to be self-propagating. Tests were run in a fluids-initiated transient to showcase the basic functionalities of this methodology. Preliminary results behave as expected, paving the way for studying more sophisticated thermal-fluids coupling methods. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Analysis of Real Ship Rolling Dynamics under Wave Excitement Force Composed of Sums of Cosine Functions

The ship motion equation with a cosine wave excitement force describes the slip moments in regular waves. A new kind of wave excitement force model, with the form as sums of cosine functions was proposed to describe ship rolling in irregular waves. Ship rolling time series were obtained by solving the ship motion equation with the fourth-order-Runger-Kutta method. These rolling time series were synthetically analyzed with methods of phase-space track, power spectrum, primary component analysis, and the largest Lyapunove exponent. Simulation results show that ship rolling presents some chaotic characteristic when the wave excitement force was applied by sums of cosine functions. The result well explains the course of ship rolling's chaotic mechanism and is useful for ship hydrodynamic study.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Large-scale sparse singular value computations

Four numerical methods for computing the singular value decomposition (SVD) of large sparse matrices on a multiprocessor architecture are presented. Lanczos and subspace iteration-based methods for determining several of the largest singular triplets (singular values and corresponding left and right-singular vectors) for sparse matrices arising from two practical applications: information retrieval and seismic reflection tomography are emphasized. The target architectures for implementations are the CRAY-2S/4-128 and Alliant FX/80. The sparse SVD problem is well motivated by recent information-retrieval techniques in which dominant singular values and their corresponding singular vectors of large sparse term-document matrices are desired, and by nonlinear inverse problems from seismic tomography applications which require approximate pseudo-inverses of large sparse Jacobian matrices.

Berry, Michael W.↗

The Equivalence of the Radial Return and Mendelson Methods for Integrating the Classical Plasticity Equations

The radial return and Mendelson methods for integrating the equations of classical plasticity, which appear independently in the literature, are shown to be identical. Both methods are presented in detail as are the specifics of their algorithmic implementation. Results illustrate the methods' equivalence across a range of conditions and address the question of when the methods require iteration in order for the plastic state to remain on the yield surface. FORTRAN code implementations of the radial return and Mendelson methods are provided in the appendix.

Bednarcyk, Brett A.↗

SU-E-J-130: Automating Liver Segmentation Via Combined Global and Local Optimization

Purpose: The aim of this work is to develop a robust algorithm for accurate segmentation of liver with special attention paid to the problems with fuzzy edges and tumor. Methods: 200 CT images were collected from radiotherapy treatment planning system. 150 datasets are selected as the panel data for shape dictionary and parameters estimation. The remaining 50 datasets were used as test images. In our study liver segmentation was formulated as optimization process of implicit function. The liver region was optimized via local and global optimization during iterations. Our method consists five steps: 1)The livers from the panel data were segmented manually by physicians, and then We estimated the parameters of GMM (Gaussian mixture model) and MRF (Markov random field). Shape dictionary was built by utilizing the 3D liver shapes. 2)The outlines of chest and abdomen were located according to rib structure in the input images, and the liver region was initialized based on GMM. 3)The liver shape for each 2D slice was adjusted using MRF within the neighborhood of liver edge for local optimization. 4)The 3D liver shape was corrected by employing SSR (sparse shape representation) based on liver shape dictionary for global optimization. Furthermore, H-PSO(Hybrid Particle Swarm Optimization) was employed to solve the SSR equation. 5)The corrected 3D liver was divided into 2D slices as input data of the third step. The iteration was repeated within the local optimization and global optimization until it satisfied the suspension conditions (maximum iterations and changing rate). Results: The experiments indicated that our method performed well even for the CT images with fuzzy edge and tumors. Comparing with physician delineated results, the segmentation accuracy with the 50 test datasets (VOE, volume overlap percentage) was on average 91%–95%. Conclusion: The proposed automatic segmentation method provides a sensible technique for segmentation of CT images. This work is supported by NIH/NIBIB (1R01-EB016777), National Natural Science Foundation of China (No.61471226 and No.61201441), Research funding from Shandong Province (No.BS2012DX038 and No.J12LN23), and Research funding from Jinan City (No.201401221 and No.20120109)

60 APPLIED LIFE SCIENCES↗