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At least 1,387 records · Page 77

Comparative study of the convergence rates of two numerical techniques

The paper examines the applicability of the three-step Stetter (1968) method to the problem of hypersonic viscous flow over a blunt axisymmetric body used for planetary entry probes at zero angle of attack. The flow-field results using the two-step finite-difference MacCormack (1969) method are reported by Kumar and Graves (1977). Only the computational efficiency of Stetter's method is compared with that of MacCormack's in terms of the iterative time steps and computing time required for the steady-state solution. Advantages of Stetter's method over MacCormack's are established.

Kumar, A.↗

Iterative Linearization for Phasor-Defined Optimal Power Dispatch

Optimal power flow (OPF) problems, which dispatch power targets to controllable generating units across a network, must generally account for non-convex constraints on power flow. Furthermore, adapting those problems so as to make them solvable with convex optimization techniques is an area of much academic and operational interest. In this paper, we present a method for solving OPF as a quadratic program by iteratively refining and re-initializing a linearized model of power flow based on the outputs of an associated nonlinear solver. The linear model on which we demonstrate this method is an adapted version of an approximation designed for use with unbalanced distribution networks. As an important benefit, the model allows for the explicit inclusion of nodal voltage phasor values in both the OPF problem's objective and its constraints, which opens the door to the idea of phasor-based control (PBC) design. We show in simulations on the IEEE 13-node test feeder that our method quickly converges to a set of phasor targets that are sufficiently precise for use in operations at the distribution level.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Novel SOLPS-ITER simulations of X-point target and snowflake divertors

Abstract The design and understanding of alternative divertor configurations may be crucial for achieving acceptable steady-state heat and particle material loads for magnetic confinement fusion reactors. Multiple X-point alternative divertor geometries such as snowflakes and X-point targets have great potential in reducing power loads, but have not yet been simulated widely in codes with kinetic neutrals. This paper discusses recent changes made to the SOLPS-ITER code to allow for the simulation of X-point target and low-field side snowflake divertor geometries. Snowflake simulations using this method are presented, in addition to the first SOLPS-ITER simulation of the X-point target. Analysis of these results show reasonable consistency with the simple modelling and theoretical predictions, supporting the validity of the methodology implemented.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A time-parallel method for scalable heat transfer simulations of additive manufacturing

Here, a major challenge in simulating the thermal behavior in additive manufacturing processes is the disparate length and time scales between transport phenomena occurring in the melt pool and the component. A common simulation approach relies on spatial decomposition for parallel computing, but due to the nature of heat transfer in AM, where most of the computational expenditure is localized near the melt pool, the computational speedup from spatial parallelization saturates quickly. Therefore, additional parallelism by means of time-domain decomposition is needed to fully take advantage of high-performance computing (HPC) resources. This work introduces a time-parallel method to improve the computational scalability of additive manufacturing simulations on HPC systems, while maintaining high temporal resolution of heat transfer near the melt pool. The method, inspired by the nonlinear paraexp formalism, performs an iterative superposition of nonlinear solutions to the initial value problem, integrating the heat equation across overlapping time-parallel intervals. For a single layer of the NIST AMB2018–01 L7 benchmark problem, the method achieves a 38.51x speedup in wall-clock time with a maximum error in the global temperature solution of 0.99%. This reduces the total solution time from 196.72 min to 5.11 min on 128 nodes of the ORNL Frontier supercomputer. The tradeoff between accuracy and total wall-clock time is investigated and recommendations for time-parallel deployment for AM problems are made.

Additive manufacturing↗

Compressed basis GMRES on high-performance graphics processing units

Krylov methods provide a fast and highly parallel numerical tool for the iterative solution of many large-scale sparse linear systems. To a large extent, the performance of practical realizations of these methods is constrained by the communication bandwidth in current computer architectures, motivating the investigation of sophisticated techniques to avoid, reduce, and/or hide the message-passing costs (in distributed platforms) and the memory accesses (in all architectures). This article leverages Ginkgo’s memory accessor in order to integrate a communication-reduction strategy into the (Krylov) GMRES solver that decouples the storage format (i.e., the data representation in memory) of the orthogonal basis from the arithmetic precision that is employed during the operations with that basis. Given that the execution time of the GMRES solver is largely determined by the memory accesses, the cost of the datatype transforms can be mostly hidden, resulting in the acceleration of the iterative step via a decrease in the volume of bits being retrieved from memory. Together with the special properties of the orthonormal basis (whose elements are all bounded by 1), this paves the road toward the aggressive customization of the storage format, which includes some floating-point as well as fixed-point formats with mild impact on the convergence of the iterative process. We develop a high-performance implementation of the “compressed basis GMRES” solver in the Ginkgo sparse linear algebra library using a large set of test problems from the SuiteSparse Matrix Collection. We demonstrate robustness and performance advantages on a modern NVIDIA V100 graphics processing unit (GPU) of up to 50% over the standard GMRES solver that stores all data in IEEE double-precision.

97 MATHEMATICS AND COMPUTING↗

Robust and Simple ADMM Penalty Parameter Selection

We present a new method for online selection of the penalty parameter for the alternating direction method of multipliers (ADMM) algorithm. ADMM is a widely used method for solving a range of optimization problems, including those that arise in signal and image processing. In its standard form, ADMM includes a scalar hyperparameter, known as the penalty parameter, which usually has to be tuned to achieve satisfactory empirical convergence. In this work, we develop a framework for analyzing the ADMM algorithm applied to a quadratic problem as an affine fixed point iteration. Using this framework, we develop a new method for automatically tuning the penalty parameter by detecting when it has become too large or small. We analyze this and several other methods with respect to their theoretical properties, i.e., robustness to problem transformations, and empirical performance on several optimization problems. Our proposed algorithm is based on a theoretical framework with clear, explicit assumptions and approximations, is theoretically covariant/invariant to problem transformations, is simple to implement, and exhibits competitive empirical performance.

42 ENGINEERING↗

Analysis of energy states in modulation doped multiquantum well heterostructures

A precise and effective numerical procedure to model the band diagram of modulation doped multiquantum well heterostructures is presented. This method is based on a self-consistent iterative solution of the Schroedinger equation and the Poisson equation. It can be used rather easily in any arbitrary modulation-doped structure. In addition to confined energy subbands, the unconfined states can be calculated as well. Examples on realistic device structures are given to demonstrate capabilities of this procedure. The numerical results are in good agreement with experiments. With the aid of this method the transitions involving both the confined and unconfined conduction subbands in a modulation doped AlGaAs/GaAs superlattice, and in a strained layer InGaAs/GaAs superlattice are identified. These results represent the first observation of unconfined transitions in modulation doped multiquantum well structures.

Ji, G.↗

Nonlinear Elimination Applied to Radiation Diffusion

We apply a nonlinearly preconditioned, quasi-Newton framework to accelerate the numerical solution of the thermal radiative transfer (TRT) equations. This framework was inspired by the unpublished method that has existed for years in Teton, Lawrence Livermore National Laboratory’s deterministic TRT code. In this paper, we cast this iteration scheme within a formal nonlinear preconditioning framework and compare its performance against other iteration schemes in the framework. With proper choices of iteration controls for the various levels of the solver, we can recover the standard linearized one-step method, a full nonlinear Newton scheme, as well as the method in Teton. In brief, the nonlinear preconditioning TRT scheme formally eliminates the material temperature equation from the nonlinear system in a nonlinear analog of a Schur complement. This nonlinear elimination step involves solving a decoupled nonlinear equation for each spatial degree of freedom and is therefore inexpensive. By applying a quasi-Newton iteration scheme on the new system, we obtain a three-level iteration scheme that is at least as efficient as commonly used TRT schemes. The new method allows full convergence to the nonlinear backward Euler time-discretized system, increasing accuracy and robustness, while using a similar number of linear iterations as the more common linearized one-step methods Eq. (4).

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Temperature retrievals from TIROS-N

A nonstatistical, nonlinear iterative scheme, has been developed, based on the methods of Chahine (1970), to retrieve surface temperature, vertical temperature profile and cloud distribution from TIROS-N HIRS 2/MSU observations. Fundamental to the technique is the ability to accurately calculate clear column radiances given atmospheric and surface characteristics. The cloud filtering algorithm, making simultaneous use of IR 15 micron channels and microwave channels, allows accurate infrared retrievals in the presence of up to 80 percent cloud cover. Details for the iterative scheme are presented together with preliminary results from analysis of TIROS-N data.

Susskind, J.↗

A Prospective Design Method for Nuclear Power: The Evaluation, Requirements, and Goals Outline for Nuclear (ERGON) Method

Human factors researchers at Idaho National Laboratory (INL) have worked on projects spanning control room modernization, operator support systems, visualization design, and novel system creation. These projects demonstrated the need for an explicit design method for nuclear power. Human factors teams found a high standard in the Human Factors Engineering Program Review Model (NUREG-0711) and needed a design methodology which could be successful in gaining approval. Previous work has been synthesized as the Evaluation, Requirements, and Goals Outline for Nuclear (ERGON) method here. Design tasks are broken into four phases: Context and Orientation, Human Factors Review, Prototyping and Evaluation, Iteration and Improvement. ERGON is intended as a flexible and direct design method for many applications in nuclear power. ERGON has been vetted through collaborative research and development with nuclear utilities and as such, the ERGON method can assist utilities to achieve approval from a NUREG-0711 summative evaluation for HSI implementations.

42 ENGINEERING↗

Ames Optimized TCA Configuration

Configuration design at Ames was carried out with the SYN87-SB (single block) Euler code using a 193 x 49 x 65 C-H grid. The Euler solver is coupled to the constrained (NPSOL) and the unconstrained (QNMDIF) optimization packages. Since the single block grid is able to model only wing-body configurations, the nacelle/diverter effects were included in the optimization process by SYN87's option to superimpose the nacelle/diverter interference pressures on the wing. These interference pressures were calculated using the AIRPLANE code. AIRPLANE is an Euler solver that uses a unstructured tetrahedral mesh and is capable of computations about arbitrary complete configurations. In addition, the buoyancy effects of the nacelle/diverters were also included in the design process by imposing the pressure field obtained during the design process onto the triangulated surfaces of the nacelle/diverter mesh generated by AIRPLANE. The interference pressures and nacelle buoyancy effects are added to the final forces after each flow field calculation. Full details of the (recently enhanced) ghost nacelle capability are given in a related talk. The pseudo nacelle corrections were greatly improved during this design cycle. During the Ref H and Cycle 1 design activities, the nacelles were only translated and pitched. In the cycle 2 design effort the nacelles can translate vertically, and pitch to accommodate the changes in the lower surface geometry. The diverter heights (between their leading and trailing edges) were modified during design as the shape of the lower wing changed, with the drag of the diverter changing accordingly. Both adjoint and finite difference gradients were used during optimization. The adjoint-based gradients were found to give good direction in the design space for configurations near the starting point, but as the design approached a minimum, the finite difference gradients were found to be more accurate. Use of finite difference gradients was limited by the CPU time limit available on the Cray machines. A typical optimization run using finite difference gradients can use only 30 to 40 design variables and one optimization iteration within the 8 hour queue limit for the chosen grid size and convergence level. The efficiency afforded by the adjoint method allowed for 50-120 design variables and 5-10 optimization iterations in the 8 hour queue. Geometric perturbations to the wing and fuselage were made using the Hicks/Henne (HH) shape functions. The HH functions were distributed uniformly along the chords of the wing defining sections and lofted linearly. During single-surface design, constraints on thickness and volume at selected wing stations were imposed. Both fuselage camber and cross-sectional area distributions were permitted to change during design. The major disadvantage to the use of these functions is the inherent surface waviness produced by repeated use of such functions. Many smoothing operations were required following optimization runs to produce a configuration with reasonable smoothness. Wagner functions were also used on the wing sections but were never used on the fuselage. The Wagner functions are a family of increasingly oscillatory functions that have also been used extensively in airfoil design. The leading and trailing edge regions of the wing were designed by use of polynomial and monomial functions respectively. Twist was attempted but was abandoned because of little performance improvement available from changing the baseline twist.

Cliff, Susan E.↗

Streamlined Convergence Acceleration for CFD Codes

Enigma, a simplified interface to the PETSc library, is shown to enable the rapid solution of discrete partial differential equations. Two CFD codes, LAURA and HyperSolve, use Enigma to compute steady solutions of the Navier-Stokes equations. Using PETSc, Enigma is shown to provide a Jacobian-Free Newton-Krylov method (JFNK), globalized with pseudotransient continuation, that improves efficiency over the point-implicit relaxation method traditionally used by LAURA. It is shown that iterative error has a large impact on surface heat transfer predicted by LAURA on an axisymmetric sphere-cone geometry. Also, the convergence rate of HyperSolve simulating subsonic flow over a delta wing geometry with the JFNK method is shown to be more efficient than employing a defect correction method as the nonlinear solver.

Thompson, Kyle B.↗

Effects of nonlinear aerodynamics and static aeroelasticity on mission performance calculations for a fighter aircraft

During conceptual design studies of advanced aircraft, the usual practice is to use linear theory to calculate the aerodynamic characteristics of candidate rigid (nonflexible) geometric external shapes. Recent developments and improvements in computational methods, especially computational fluid dynamics (CFD), provide significantly improved capability to generate detailed analysis data for the use of all disciplines involved in the evaluation of a proposed aircraft design. A multidisciplinary application of such analysis methods to calculate the effects of nonlinear aerodynamics and static aeroelasticity on the mission performance of a fighter aircraft concept is described. The aircraft configuration selected for study was defined in a previous study using linear aerodynamics and rigid geometry. The results from the previous study are used as a basis of comparison for the data generated herein. Aerodynamic characteristics are calculated using two different nonlinear theories, potential flow and rotational (Euler) flow. The aerodynamic calculations are performed in an iterative procedure with an equivalent plate structural analysis method to obtain lift and drag data for a flexible (nonrigid) aircraft. These static aeroelastic data are then used in calculating the combat and mission performance characteristics of the aircraft.

Giles, Gary L.↗

Iterative multi-task learning and inference from seismic images

Seismic interpretation aims to extract quantitative and interpretable attributes from a seismic image produced using some migration method to inform characteristics of a subsurface reservoir or target of interest. Current paradigms for computing seismic attributes mostly rely on single-task algorithms. We develop an iterative, multi-task machine learning method to learn and infer multiple attributes from a seismic image. This method is composed of two stages: a multi-task inference stage and a multi-modal, multi-task refinement stage. The basic mechanism of this method is that we train a multi-task inference neural network (NN) to estimate a set of attributes, including a relative geological time (RGT), a denoised higher-resolution (DHR) seismic image, and multiple fault attributes (including probability, dip, and strike), from a low-resolution, noisy seismic image; then we input the inferred attributes to a multi-task refinement NN to enhance the raw inference results iteratively. The two multi-task NNs are trained separately based on synthetic seismic images and associated attributes generated by a geological modeling algorithm. The software we intend to release is a PyTorch implementation of this multi-task learning method for both 2D and 3D cases along with scripts to run the training/validation. The algorithm and software can be a useful tool for automatic seismic interpretation.

Gao, Kai↗

VIPER Lunar Rover Agile Mission Systems

Agile development methods, which have gone from outlier to mainstream in software development, are poised to expand into all aspects of space mission development. Modern software development operates on a principle of continuous deployment, where progress is verified not with conventional metrics, but with a continuous build, available to key stakeholders, enabling direct examination of the state of the code base, and assessment of progress through demonstration of capability. Delivery times are measured in weeks, not months. Stakeholders are part of the process on an ongoing basis. The cost of change is comparatively low and requirements, which often are not precisely defined at the start of a project, may be iteratively refined in a series of agile development cycles. Agile methods are compatible with traditional system engineering methods and may be tailored to the space operations environment. The low cost of change and iterative development cycles of agile enable requirements to be defined as outcomes and constraints, with design details to be refined during the development cycle. We are now at a point where agile methods may be extended beyond software, to Mission Systems, including the Mission Operations System and the Ground Data System. For NASA’s VIPER Lunar Rover Mission, scheduled to land at a lunar pole in late 2023, we are developing the Mission System using agile methods. As in agile software, where the measure of progress is working code, in agile mission system development, the measure of capability is what we can demonstrate. Demonstrations over presentations. We demonstrate mission system capability using simulations. The concept of operations, from commanding, to driving the rover, to how we downlink images for evaluation for a near-real time command cycle, will be tested and proven in simulation, years before we begin the traditional simulation cycle for training. “Say it then simulate it.” We develop and refine our designs using simulations, with an emphasis on new components of the system that are not well known early. For example, the required duration of a mission planning cycle for a lunar surface asset such as VIPER, that operates twenty-four hours a day, seven days a week, with continuous communications and a unique set of constraints based on the physics of the lunar poles and the line of site to Earth, is a unique problem in mission planning that is unlikely to be solved in a series of meetings. A small number of requirements specifying the outcomes may serve as the jumping off point to an agile development cycle, with demonstration in simulations. We have already demonstrated this process with simulations of rover driver decision time. VIPER is driven using near-real time command and control to waypoints. The driver decision time between waypoints is a fundamental enabling unit of productivity to accomplish the mission timeline. We have validated driver decision time in simulations of rover driving at the lunar South Pole, using the prototype mission tools for driving, command and control. The capability to develop and refine designs using simulations as part of agile Mission System development cycle changes the nature of team interactions, creating a focus on doing, rather than analyzing and documenting. Waterfall development cycles were, in part, a product of the significant cost of change in the early days of spaceflight. When the cost of change is high, it is vital to get your requirements right at the outset, because the system will be built to those specifications, and, when change is expensive, you better get it right early. However, modern technology has greatly lowered the cost of change, enabling iterative, rapid development cycles, in which key operations concepts may be tested and refined during development. Extending agile development to the Mission System for VIPER is a significant step in moving agile development methods for space operations beyond software, to the Mission System.

Agile↗

Metrics for Intercomparison of Remapping Algorithms (MIRA) protocol applied to Earth system models

Abstract. Strongly coupled nonlinear phenomena such as those described by Earth system models (ESMs) are composed of multiple component models with independent mesh topologies and scalable numerical solvers. A common operation in ESMs is to remap or interpolate component solution fields defined on their computational mesh to another mesh with a different combinatorial structure and decomposition, e.g., from the atmosphere to the ocean, during the temporal integration of the coupled system. Several remapping schemes are currently in use or available for ESMs. However, a unified approach to compare the properties of these different schemes has not been attempted previously. We present a rigorous methodology for the evaluation and intercomparison of remapping methods through an independently implemented suite of metrics that measure the ability of a method to adhere to constraints such as grid independence, monotonicity, global conservation, and local extrema or feature preservation. A comprehensive set of numerical evaluations is conducted based on a progression of scalar fields from idealized and smooth to more general climate data with strong discontinuities and strict bounds. We examine four remapping algorithms with distinct design approaches, namely ESMF Regrid (Hill et al., 2004), TempestRemap (Ullrich and Taylor, 2015), generalized moving least squares (GMLS) (Trask and Kuberry, 2020) with post-processing filters, and WLS-ENOR (Li et al., 2020). By repeated iterative application of the high-order remapping methods to the test fields, we verify the accuracy of each scheme in terms of their observed convergence order for smooth data and determine the bounded error propagation using challenging, realistic field data on both uniform and regionally refined mesh cases. In addition to retaining high-order accuracy under idealized conditions, the methods also demonstrate robust remapping performance when dealing with non-smooth data. There is a failure to maintain monotonicity in the traditional L2-minimization approaches used in ESMF and TempestRemap, in contrast to stable recovery through nonlinear filters used in both meshless GMLS and hybrid mesh-based WLS-ENOR schemes. Local feature preservation analysis indicates that high-order methods perform better than low-order dissipative schemes for all test cases. The behavior of these remappers remains consistent when applied on regionally refined meshes, indicating mesh-invariant implementations. The MIRA intercomparison protocol proposed in this paper and the detailed comparison of the four algorithms demonstrate that the new schemes, namely GMLS and WLS-ENOR, are competitive compared to standard conservative minimization methods requiring computation of mesh intersections. The work presented in this paper provides a foundation that can be extended to include complex field definitions, realistic mesh topologies, and spectral element discretizations, thereby allowing for a more complete analysis of production-ready remapping packages.

58 GEOSCIENCES↗

Application of vector-valued rational approximations to the matrix eigenvalue problem and connections with Krylov subspace methods

Let F(z) be a vectored-valued function F: C approaches C sup N, which is analytic at z=0 and meromorphic in a neighborhood of z=0, and let its Maclaurin series be given. We use vector-valued rational approximation procedures for F(z) that are based on its Maclaurin series in conjunction with power iterations to develop bona fide generalizations of the power method for an arbitrary N X N matrix that may be diagonalizable or not. These generalizations can be used to obtain simultaneously several of the largest distinct eigenvalues and the corresponding invariant subspaces, and present a detailed convergence theory for them. In addition, it is shown that the generalized power methods of this work are equivalent to some Krylov subspace methods, among them the methods of Arnoldi and Lanczos. Thus, the theory provides a set of completely new results and constructions for these Krylov subspace methods. This theory suggests at the same time a new mode of usage for these Krylov subspace methods that were observed to possess computational advantages over their common mode of usage.

Sidi, Avram↗

Shattered pellet penetration in low and high energy plasmas on DIII-D

Shattered Pellet Injection (SPI) was previously adopted as the baseline disruption mitigation system for ITER, as the radiative payload penetration into DIII-D plasmas from SPI is superior to those using the Massive Gas Injection (MGI) method. Because of the substantial differences in the energy content of ITER plasma and those in present experiments, reliable 3d MHD modeling, benchmarked against present experiments is needed to project to ITER plasmas. On account of these needs, the depth of SPI fragment penetration in DIII-D plasmas was investigated by injecting SPI into two discharges with vastly different energy content and pedestal height. 400 Torr-L pure Ne fragmented pellets at a velocity of about 200 m s -1 were injected into a 0.2 MJ L-mode discharge and a 2 MJ super H-mode discharge. Results show deep penetration of SPI fragments into low-energy plasmas in DIII-D. SPI fragment penetration is reduced as the plasma energy content increases, with some discharges exhibiting penetration that is confined to the outer regions of the plasma. The injected SPI fragments are also spread out over a distance of about 20 cm, which results in some fragments arriving near the end of or after the thermal quench is over.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗