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At least 793 records · Page 44
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Lax-Oleinik-Type Formulas and Efficient Algorithms for Certain High-Dimensional Optimal Control Problems

Two of the main challenges in optimal control are solving problems with state-dependent running costs and developing efficient numerical solvers that are computationally tractable in high dimension. In this paper, we provide analytical solutions to certain optimal control problems whose running cost depends on the state variable and with constraints on the control. We also provide Lax-Oleinik-type representation formulas for the corresponding Hamilton-Jacobi partial differential equations with state-dependent Hamiltonians. Additionally, we present an efficient, grid-free numerical solver based on our representation formulas, which is shown to scale linearly with the state dimension, and thus, to overcome the curse of dimensionality. Using existing optimization methods and the min-plus technique, we extend our numerical solvers to address more general classes of convex and nonconvex initial costs. We demonstrate the capabilities of our numerical solvers using implementations on a central processing unit (CPU) and a field-programmable gate array (FPGA). In several cases, our FPGA implementation obtains over a 10 times speedup compared to the CPU, which demonstrates the promising performance boosts FPGAs can achieve. Furthermore, our numerical results show that our solvers have the potential to serve as a building block for solving broader classes of high-dimensional optimal control problems in real-time.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Search for interacting galaxy clusters from SDSS DR-17 employing optimized friends-of-friends algorithm and multimessenger tracers

ABSTRACT In the theoretical framework of hierarchical structure formation, galaxy clusters evolve through continuous accretion and mergers of substructures. Cosmological simulations have revealed the best picture of the universe as a 3D filamentary network of dark-matter distribution called the cosmic web. Galaxy clusters are found to form at the nodes of this network and are the regions of high merging activity. Such mergers being highly energetic, contain a wealth of information about the dynamical evolution of structures in the Universe. Observational validation of this scenario needs a colossal effort to identify numerous events from all-sky surveys. Therefore, such efforts are sparse in literature and tend to focus on individual systems. In this work, we present an improved search algorithm for identifying interacting galaxy clusters and have successfully produced a comprehensive list of systems from SDSS DR-17. By proposing a set of physically motivated criteria, we classified these interacting clusters into two broad classes, ‘merging’ and ‘pre-merging/postmerging’ systems. Interestingly, as predicted by simulations, we found that most cases show cluster interaction along the prominent cosmic filaments of galaxy distribution (i.e. the proxy for dark matter filaments), with the most violent ones at their nodes. Moreover, we traced the imprint of interactions through multiband signatures, such as diffuse cluster emissions in radio or X-rays. Although we could not find direct evidence of diffuse emission from connecting filaments and ridges; our catalogue of interacting clusters will ease locating such faintest emissions as data from sensitive telescopes such as eROSITA or SKA, becomes accessible.

Oak, Tejas↗
DOE OSTI2023

Encoding trade-offs and design toolkits in quantum algorithms for discrete optimization: coloring, routing, scheduling, and other problems

Challenging combinatorial optimization problems are ubiquitous in science and engineering. Several quantum methods for optimization have recently been developed, in different settings including both exact and approximate solvers. Addressing this field of research, this manuscript has three distinct purposes. First, we present an intuitive method for synthesizing and analyzing discrete (i.e., integer-based) optimization problems, wherein the problem and corresponding algorithmic primitives are expressed using a discrete quantum intermediate representation (DQIR) that is encoding-independent. This compact representation often allows for more efficient problem compilation, automated analyses of different encoding choices, easier interpretability, more complex runtime procedures, and richer programmability, as compared to previous approaches, which we demonstrate with a number of examples. Second, we perform numerical studies comparing several qubit encodings; the results exhibit a number of preliminary trends that help guide the choice of encoding for a particular set of hardware and a particular problem and algorithm. Our study includes problems related to graph coloring, the traveling salesperson problem, factory/machine scheduling, financial portfolio rebalancing, and integer linear programming. Third, we design low-depth graph-derived partial mixers (GDPMs) up to 16-level quantum variables, demonstrating that compact (binary) encodings are more amenable to QAOA than previously understood. We expect this toolkit of programming abstractions and low-level building blocks to aid in designing quantum algorithms for discrete combinatorial problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

CG-Kit: Code Generation Toolkit for performant and maintainable variants of source code applied to Flash-X hydrodynamics simulations

CG-Kit is a new Code Generation tool-Kit that we have developed as a part of the solution for portability and maintainability for multiphysics computing applications. The development of CG-Kit is rooted in the urgent need created by the shifting landscape of high-performance computing platforms and the algorithmic complexities of a particular large-scale multiphysics application: Flash-X. To efficiently use computing resources on a heterogeneous node, an application must have a map of computation to resources and a mechanism to move the data and computation to the resources according to the map. Most existing performance portability solutions are focussed on abstracting the expression of computations so that a unified source code can be specialized to run on different resources. However, such an approach is insufficient for a code like Flash-X, which has a multitude of code components that can be assembled in various permutations and combinations to form different instances of applications. Similar challenges apply to any code that has composability, where a single specified way of apportioning work among devices may not be optimal. Additionally, use cases arise where the optimal control flow of computation may differ for different devices while the underlying numerics remain identical. This combination leads to unique challenges including handling an existing large code base in Fortran and/or C/C++, subdivision of code into a great variety of units supporting a wide range of physics and numerical methods, different parallelization techniques for distributed and shared memory systems and accelerator devices, and heterogeneity of computing platforms requiring coexisting variants of parallel algorithms. All of these challenges demand that scientific software developers apply existing knowledge about domain applications, algorithms, and computing platforms to determine custom abstractions and granularity for code generation. There is a critical lack of tools to tackle those problems. CG-Kit is designed to fill this gap by providing a user with the ability to express their desired control flow and computation-to-resource map in the form a pseudocode-like recipe. It consists of standalone tools that can be combined into highly specific and, we argue, highly effective portability and maintainability toolchains. Here we present the design of our new tools: parametrized source trees, control flow graphs, and recipes. The tools are implemented in Python. They are agnostic to the programming language of the source code targeted for code generation. In conclusion, we demonstrate the capabilities of the toolkit with two examples, first, multithreaded variants of the basic AXPY operation, and second, variants of parallel algorithms within a hydrodynamics solver, called Spark, from Flash-X that operates on block-structured adaptive meshes.

Algorithmic portability↗
DOE OSTI2022

A coupled DEM-IMB-LBM model for simulating methane hydrate exploitation involving particle dissolution

The coupled discrete element and lattice Boltzmann method using an immersed moving boundary scheme was extended to simulate methane hydrate exploitation involving mass transport and particle dissolution. In this coupled DEM-IMB-LBM model, a new Dirichlet-type thermal boundary condition is extended to simulate moving curved boundaries with constant concentration. A novel periodic boundary including an efficient searching algorithm for particle contact is proposed to reduce the computational cost and boundary effect. So, this model is validated by two numerical examples: a circular particle with concentration convection-diffusion moving in a horizontal channel and mass transport from a cylinder particle in a simple shear flow. The numerical results obtained from the proposed model agree well with previous studies. To further demonstrate the capacity of the proposed model, simulations of methane hydrate exploitation including two formations in marine sediments are carried out. The numerical results indicate that the coupled DEM-IMB-LBM is not only capable of simulating the dissolution of hydrate particles at the grain level, but also recover the sand erosion and migration process in a fundamental perspective during the methane hydrate exploitation process.

42 ENGINEERING↗
DOE OSTI2022

Toward control co-design of utility-scale wind turbines: Collective vs. individual blade pitch control

A large-eddy simulation framework has been coupled with controller modules to systematically investigate the impacts of collective (CPC) and individual (IPC) pitch control strategies on utility-scale wind turbine energy production and fatigue loads. Wind turbine components were parameterized using an actuator surface model to simulate the rotor blades and the turbine nacelle. The baseline CPC and IPC algorithms, consisting of single-input single-output proportional–integral controllers and two integral controllers, respectively, were incorporated into the numerical framework. A series of simulations were carried out to investigate the relative performance of the two controllers under various turbulent inflow conditions, spanning hub-height velocities of 7 to 14 m/s. The numerical simulation results of this study showed that, in comparison to the CPC, the IPC controller could successfully reduce the damage equivalent loads of utility-scale turbines at regions 2 and 3 of turbine operation by about 3% and 40%, respectively, without any penalty on the power production of the turbine. It was also shown that, despite its minor impact on the turbulence kinetic energy of the wake, the IPC controller did not influence the recovery of the turbine wake.

17 WIND ENERGY↗
DOE OSTI2021

Landmark-embedded Gaussian process with applications for functional data modeling

In practice, we often need to infer the value of a target variable from functional observation data. A challenge in this task is that the relationship between the functional data and the target variable is very complex: the target variable not only influences the shape but also the location of the functional data. In addition, due to the uncertainties in the environment, the relationship is probabilistic, that is, for a given fixed target variable value, we still see variations in the shape and location of the functional data. To address this challenge, we present a landmark-embedded Gaussian process model that describes the relationship between the functional data and the target variable. A unique feature of the model is that landmark information is embedded in the Gaussian process model so that both the shape and location information of the functional data are considered simultaneously in a unified manner. Gibbs-Metropolis-Hasting algorithm is used for model parameters estimation and target variable inference. The performance of the proposed framework is evaluated by extensive numerical studies and a case study of nano-sensor calibration.

42 ENGINEERING↗
DOE OSTI2024

Single-ancilla ground state preparation via Lindbladians

We design a quantum algorithm for ground state preparation in the early fault tolerant regime. As a Monte Carlo style quantum algorithm, our method features a Lindbladian where the target state is stationary. The construction of this Lindbladian is algorithmic and should not be seen as a specific approximation to some weakly coupled system-bath dynamics in nature. Our algorithm can be implemented using just one ancilla qubit and efficiently simulated on a quantum computer. It can prepare the ground state even when the initial state has zero overlap with the ground state, bypassing the most significant limitation of methods like quantum phase estimation. As a variant, we also propose a discrete-time algorithm, demonstrating even better efficiency and providing a near-optimal simulation cost depending on the desired evolution time and precision. Numerical simulations using Ising and Hubbard models demonstrate the efficacy and applicability of our method. Published by the American Physical Society 2024

Ding, Zhiyan (ORCID:000000018863403X)↗
DOE OSTI2021

Restoration Strategy for Active Distribution Systems Considering Endogenous Uncertainty in Cold Load Pickup

Cold load pickup (CLPU) phenomenon is identified as the persistent power inrush upon a sudden load pickup after an outage. Under the active distribution system (ADS) paradigm, where distributed energy resources (DERs) are extensively installed, the decreased outage duration can induce a strong interdependence between CLPU pattern and load pickup decisions. In this paper, we propose a novel modelling technique to tractably capture the decision-dependent uncertainty (DDU) inherent in the CLPU process. Subsequently, a two-stage stochastic decision-dependent service restoration (SDDSR) model is constructed, where first stage searches for the optimal switching sequences to decide step-wise network topology, and the second stage optimizes the detailed generation schedule of DERs as well as the energization of switchable loads. Further, to tackle the computational burdens introduced by mixed-integer recourse, the progressive hedging algorithm (PHA) is utilized to decompose the original model into scenario-wise subproblems that can be solved in parallel. The numerical test on modified IEEE 123-node test feeders has verified the efficiency of our proposed SDDSR model and provided fresh insights into the monetary and secure values of DDU quantification.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Decomposable Formulation of Transmission Constraints for Decentralized Power Systems Optimization

One of the most complicating factors in decentralized solution methods for a broad range of power system optimization problems is the modeling of power flow equations. Existing formulations for direct current power flows either have limited scalability or are very dense and unstructured, making them unsuitable for large-scale decentralized studies. Here, in this work, we present a novel sparsified variant of the injection shift factors formulation, which has a decomposable block-diagonal structure and scales well for large systems. We also propose a decentralized solution method, based on the alternating direction multiplier method, that efficiently handles transmission line outages in N-1 security requirements. Benchmarks on multizonal security-constrained unit commitment problems show that the proposed formulation and algorithm can reliably and efficiently solve interconnection-level test systems with up to 6,515 buses with no convergence or numerical issues.

Alternating-method of multipliers (ADMM)↗
DOE OSTI2025

Cardinal: Seismic and Geoacoustic Array Processing

Data collected via seismic and infrasound array deployments are leveraged in the geosciences to detect and characterize a myriad of natural and anthropogenic sources. These deployments consist of numerous sensors placed in a predetermined configuration to amplify signal strength and improve the efficacy of array processing techniques used to measure signal directionality and waveform coherence. High‐fidelity feature extraction is often predicated on interstation distance as well as the frequency content and wavelength of an incident signal. Numerous array processing softwares analyze data in sequential frequency bands to obtain a more detailed characterization of a signal. However, current algorithms are limited in their ability to determine optimal array configuration for each band. We introduce an open‐source Python code, called Cardinal, to process seismic and infrasound array data in discretized time–frequency space with the option of applying an adaptive array design to determine optimal subarray configuration for each frequency band. To reduce computational time, the array processing step can be run in parallel using multithreading. Furthermore, the software has the capability to aggregate array processing results from different time–frequency pixels to produce separate sets of detections, or families, with added utility via the application of an adaptive semblance threshold, which aids in isolating signals‐of‐interest from coherent background noise. Upon appropriate configuration, Cardinal exhibits the potential to combine distinct seismic and infrasound phases into separate families.

Adaptive Array↗
DOE OSTI2020

RELAP-7 Application and Enhancement for FLEX Strategies and ATF Behavior under Extended Loss of AC Power Conditions

This report summarizes the results of a three-year research project sponsored by the U.S. Department of Energy (DOE) Nuclear Energy University Program (NEUP) to enhance and apply the RELAP-7 code by adding and improving several important components (e.g., a mechanistic Reactor Core Isolation Cooling (RCIC) system model) for thermal hydraulic studies of LWRs under ELAP conditions and evaluating the time available for transition to portable FLEX equipment. The project team included University of Massachusetts–Lowell, The Ohio State University, Texas A&M University, Idaho National Laboratory and Oak Ridge National Laboratory. In the Fukushima accident, it was found that the RCIC system played a crucial role in delaying core meltdown by almost three days in Fukushima Daiichi Unit 2, because of self-regulated operation of the steam driven RCIC turbine-pump injection system. Steam flow in the convergent-divergent nozzles of the RCIC Terry turbine is two-phase non-equilibrium transonic flow with homogenous nucleation condensation. To more accurately predict the dynamic process and behavior of the transonic compressible steam flow, a one-dimensional transient two-phase analytical model is presented. A simplified four-fluid model was employed in the present work with the consideration of four separate fluid fields: vapor, liquid film, entrained droplets and condensed droplets. The mass, momentum and energy interactions between the fluids were considered and modeled. An extended seven-equation non-equilibrium critical flow model was developed to obtain the critical pressure and velocities of each phase at the nozzle throat. To predict the wetness in the divergent section, a mechanistic nucleation condensation model was integrated in the nozzle analysis model, considering the generation and consequent growth of droplets. The governing differential equations on a staggered grid were discretized using the second-order Lax-Wendroff scheme with a flux limiter, and the Semi-Implicit Method for Pressure-Linked Equation (SIMPLE) algorithm was employed to solve the discrete linear system. To demonstrate the predictability and reliability of the physical models and the numerical method proposed in the present work, three representative nozzles were modeled and simulated. The results show good agreement with the available experimental data, even for condensation shock. Then, the 1D nozzle model was employed to obtain nozzle flow tables of the Terry turbine nozzle for different working pressures which can cover the operation pressure range of the RCIC system. A mechanistic RCIC turbine-pump system model was developed and implemented in the system code TRACE to simulate dynamic responses of the RCIC system under Beyond Design Basis Accident (BDBA) conditions. The turbine-pump governing equations are based on the control volume approach of the angular momentum balance. The physics based mechanistic RCIC model was developed using the TRACE control system components (i.e., signal variables, control blocks, and tables), and incorporated into a TRACE boiling water reactor (BWR) model. The TRACE model in this report has a detailed nodalization of the reactor pressure vessel (RPV), and all of the major flow paths and system components, including the safety relief valves (SRVs) and the containment suppression pool and drywell. Based on the nozzle flow tables generated from the 1D nozzle model developed, the turbine drive torque can be calculated from table lookup. Since the detailed specifications of the RCIC pump are unavailable, the homologous curves for a Bingham pump were used in the current pump component. A station black-out (SBO) accident test problem was selected to demonstrate the TRACE RCIC model. The short-term SBO simulations were performed for two cladding materials: Zircaloy and FeCrAl, to demonstrate the effect of the accident tolerant fuel cladding on fuel heat-up under BDBA accident conditions. The wetwell plays a vital safety role in SBO and other BWR accident scenarios in that it can reduce containment pressure and supply additional core make-up water. The suppression pool temperature distribution has a very large impact on both RPV and containment pressure. Thus, another novel contribution of the project comes mainly from an improved, systems-level wetwell model which can capture buoyancy-induced thermal stratification effects due to steam injection and condensation. A two-zone stratified wetwell model has been implemented in RELAP-7 and some results from that model are presented. This wetwell model is capable of simulating thermal stratification due to a low steam mass injection rate. With a low mass flow rate, the model assumes that all the steam condenses within the pipe and the resulting plume can be approximated with a purely buoyant, heat-source driven model. The wetwell model developed with these assumptions is adequate to simulate slow transients such as extended SBO transients.

42 ENGINEERING↗
DOE OSTI2022

Introducing the 9500 Node Distribution Test System to Support Advanced Power Applications: An Operations-Focused Approach

The 9500 Node Test System is a representative section of distribution power system model developed as a part of the GridAPPS-D™ project, an effort funded by DOE as a part of the Grid Modernization Lab Consortium (GMLC) program. The test system was developed to fulfill a growing need to represent the rapidly evolving state of electric distribution systems by combining elements of legacy infrastructure systems, modern feeder topologies, and an anticipated future with smart grid technologies. It also provides a network model capable of supporting the simulation of operational scenarios such as the ones in a utility distribution control center. This test system allows the evaluation of the performance of advanced power applications in real-time, such as one that simulates the operations of an Advanced Distribution Management Systems (ADMS), Distributed Energy Resource Management Systems (DERMS), etc. in a Distribution control center. This model is an extension of the widely used IEEE 8500 Node Test Feeder and is currently being validated to become an IEEE test case to help increase adoption and widespread usage among both academia and industry. It is a full-size model representative of a section of a utility’s distribution system with multiple feeders fed from different substations. The model includes multiple distribution circuits, a sub-transmission system, multiple substations, behind the meter customer rooftop photovoltaics (PV), and multiple utility-scale distributed energy resources. To enable accurate simulations of operational scenarios, the 9500 Node Test System is designed to support procedure-based operations, with the ability to realistically demonstrate switching operations, feeder reconfiguration, adjustment of volt-var control equipment, dispatch of distributed generation, and response to planned and unplanned outages. The 9500 Node Test System includes three radial distribution feeders with 12.3 MVA of average load, consisting of both medium voltage and low voltage equipment each supplied by a different distribution substation. The three distribution feeders are connected to each other through Normally-Open switches which can be closed when needed to simulate restoration scenarios due to a fault. One feeder represents today’s grid with low penetration of customer-side renewables. The second represents a potential future grid with microgrids and 100% renewable penetration. The third has no customer generation resources, a district steam plant, and a utility-scale solar farm. The three diverse circuits were created to allow the simulation of both today’s situation as well as potential future scenarios. All three feeders have customers connected by low-voltage secondary triplex lines. This test system meets all requirements outlined in the report for creating a simulation environment that would enable discussion between key technical stakeholders as well as having the potential to accelerate operational application development and their subsequent testing and integration. The new model is a possible representation of what we believe the distribution grid may look like in the future: a high penetration of renewables, reconfigurable radial and mesh topology, numerous DERs, islanded microgrids, and significantly increased data and measurement density. The system supports both the solution of existing and newer algorithms but also enables the evaluation of applications in a realistic operational environment defined by task oriented procedural steps that represent the interaction between the control center operator and field personnel.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Single-shot Quantum Signal Processing Interferometry

Quantum systems of infinite dimension, such as bosonic oscillators, provide vast resources for quantum sensing. Yet, a general theory on how to manipulate such bosonic modes for sensing beyond parameter estimation is unknown. We present a general algorithmic framework, quantum signal processing interferometry (QSPI), for quantum sensing at the fundamental limits of quantum mechanics by generalizing Ramsey-type interferometry. Our QSPI sensing protocol relies on performing nonlinear polynomial transformations on the oscillator's quadrature operators by generalizing quantum signal processing (QSP) from qubits to hybrid qubit-oscillator systems. We use our QSPI sensing framework to make efficient binary decisions on a displacement channel in the single-shot limit. Theoretical analysis suggests the sensing accuracy, given a single-shot qubit measurement, scales inversely with the sensing time or circuit depth of the algorithm. We further concatenate a series of such binary decisions to perform parameter estimation in a bit-by-bit fashion. Numerical simulations are performed to support these statements. Our QSPI protocol offers a unified framework for quantum sensing using continuous-variable bosonic systems beyond parameter estimation and establishes a promising avenue toward efficient and scalable quantum control and quantum sensing schemes beyond the NISQ era.

Physics↗
DOE OSTI2022

A backward SDE method for uncertainty quantification in deep learning

Here, we develop a backward stochastic differential equation based probabilistic machine learning method, which formulates a class of stochastic neural networks as a stochastic optimal control problem. An efficient stochastic gradient descent algorithm is introduced with the gradient computed through a backward stochastic differential equation. Convergence analysis for stochastic gradient descent optimization and numerical experiments for applications of stochastic neural networks are carried out to validate our methodology in both theory and performance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Fast truncated SVD of sparse and dense matrices on graphics processors

We investigate the solution of low-rank matrix approximation problems using the truncated singular value decomposition (SVD). For this purpose, we develop and optimize graphics processing unit (GPU) implementations for the randomized SVD and a blocked variant of the Lanczos approach. Our work takes advantage of the fact that the two methods are composed of very similar linear algebra building blocks, which can be assembled using numerical kernels from existing high-performance linear algebra libraries. Furthermore, the experiments with several sparse matrices arising in representative real-world applications and synthetic dense test matrices reveal a performance advantage of the block Lanczos algorithm when targeting the same approximation accuracy.

Computer Science↗
DOE OSTI2020

Sampling and resolution characteristics in reduced order models of shallow water equations: Intrusive vs nonintrusive

We investigate the sensitivity of reduced order models (ROMs) to training data spatial resolution as well as sampling rate. In particular, we consider proper orthogonal decomposition (POD), coupled with Galerkin projection (POD-GP), as an intrusive reduced order modeling technique. For non-intrusive ROMs, we consider two frameworks. The first is using dynamic mode decomposition (DMD), and the second is based on artificial neural networks (ANNs). For ANN, we utilized a residual deep neural network, and for DMD we have studied two versions of DMD approaches; one with hard thresholding and the other with sorted bases selection. Also, we highlight the differences between mean-subtracting the data (centering) and using the data without mean-subtraction. We tested these ROMs using a system of 2D shallow water equations for four different numerical experiments, adopting combinations of sampling rates and spatial resolutions. For these cases, we found that the DMD basis obtained with hard threshodling is sensitive to sampling rate. The sorted DMD algorithm helps to mitigate this problem and yields more stabilized and converging solution. Furthermore, we demonstrate that both DMD approaches without mean subtraction provide significantly more accurate results than DMD with mean-subtracting the data. On the other hand, POD is relatively insensitive to sampling rate and yields better representation of the flow field. Meanwhile, spatial resolution has little effect on both POD and DMD performances. Here, the numerical results reveal that an ANN on POD subspace (POD-ANN) performs remarkably better than POD-GP and DMD in capturing system dynamics, even with a small number of modes.

42 ENGINEERING↗
DOE OSTI2025

A scalable multidimensional fully implicit solver for Hall magnetohydrodynamics

We propose an optimally performant fully implicit algorithm for the Hall magnetohydrodynamics (HMHD) equations based on multigrid-preconditioned Jacobian-free Newton-Krylov methods. HMHD is a challenging system to solve numerically because it supports stiff fast dispersive waves. The preconditioner is formulated using an operator-split approximate block factorization (Schur complement), informed by physics insight. We use a vector-potential formulation (instead of a magnetic field one) to allow a clean segregation of the problematic $\nabla$ x $\nabla$ x operator in the electron Ohm's law subsystem. This segregation allows the formulation of an effective damped block-Jacobi smoother for multigrid. We demonstrate by analysis that our proposed block-Jacobi iteration is convergent and has the smoothing property. The resulting HMHD solver is verified linearly with wave propagation examples, and nonlinearly with the GEM challenge reconnection problem by comparison against another HMHD code. We demonstrate the excellent algorithmic and parallel performance of the algorithm up to 16384 MPI tasks in two dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗