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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records

Computational Math Problems for a Clean Energy Future

Cutting edge computational mathematics are ubiquitous in renewable energy research. Problems in resilient and reliable electric grid operations, infrastructure planning, wind farm yaw control, and more demand sophisticated and scalable computational tools that enable the transition of renewable energy technologies from proof of concept to deployment into our energy system. The mission of the Computational Science Center at NREL is to lead the lab's efforts to solve energy challenges using high-performance computing (HPC), computational science, applied mathematics, scientific data management, visualization, and informatics. In this poster, we provide a short overview of three areas of computational mathematics research at NREL: wind power scenario generation for stochastic grid operations and infrastructure planning, improved rational function approximations for electromagnetic transients codes, and wind farm yaw control using a combination of the Alternating Direction Method of Multipliers (ADMM) and reinforcement learning (RL). Increasing penetrations of renewable energy into power grids motivate the investigation of new approaches to characterizing uncertainty for five-minute economic dispatch problems. Similarly, as the penetration of distributed energy resources on power grids increases, it becomes important to revisit our methods of modelling transient phenomena, i.e. electromagnetic transients programs. Finally, the combination of ADMM and RL for wind farm yaw control presented here can potentially increase the efficiency of the deployed distributed controllers by orders of magnitude.

ADMM↗

Verification of post permanently manned configuration Space Station elements

An account is given of the techniques and ground systems designed to fulfill post permanently manned configuration (PMC) Space Station verification tasks. Consideration is given to analysis using computer math models and computer-aided interface verification systems, testing using simulators and interface mixtures, and special inspection. It is noted that an initial Space Station design that accommodates and facilitates verification is crucial to an effective verification program as well as proper instrumentation, built-in test capability, and a precise configuration management, control and record system. It is concluded that post PMC verification should be accounted for both in the initial Space Station design and in the subsequent development of initial assembly flight verification techniques and capabilities.

Scully, E. J.↗

Scalable DPG multigrid solver for Helmholtz problems: A study on convergence

This paper presents a scalable multigrid preconditioner targeting large-scale systems arising from discontinuous Petrov–Galerkin (DPG) discretizations of high-frequency wave operators. This work is built on previously developed multigrid preconditioning techniques of Petrides and Demkowicz (Comput. Math. Appl. 87 (2021) pp. 12–26) and extends the convergence results from $\mathscr{O}$(10 7 ) degrees of freedom (DOFs) to $\mathscr{O}$(10 9 ) DOFs using a new scalable parallel MPI/OpenMP implementation. Novel contributions of this paper include an alternative definition of coarse-grid systems based on restriction of fine-grid operators, yielding superior convergence results. In the uniform refinement setting, a detailed convergence study is provided, demonstrating h and p robust convergence and linear scaling with respect to the wave frequency. Finally, the paper concludes with numerical results on hp -adaptive simulations including a large-scale seismic modeling benchmark problem with high material contrast.

97 MATHEMATICS AND COMPUTING↗

An analytical investigation of the free-tip rotor for helicopters

A rotor configuration called the free-tip rotor was analytically investigated for its potential to improve helicopter forward-flight performance characteristics. This rotor differs from a conventional rotor only in the blade tip region. In this configuration, the tip is self-adjusting in pitch with respect to the rest of the blade, in accordance with a moment balance about its pitch axis. With this self-adjusting capability, the resulting pitch motion generates a more uniform airload distribution around the azimuth. Computer math models were used to compare performance characteristics of the free tip rotor with those of a conventional rotor operation at flight speeds from 130 to 160 knots. The results of this analysis indicate that the free-tip rotor improves cruise lift-drag ratio by at least 22%.

Stroub, R. H.↗

Performance improvements with the free-tip rotor

A new rotor configuration called the free-tip rotor was investigated for its potential to improve helicopter forward-flight performance characteristics. This rotor differs from a conventional rotor only in the blade tip region. Free tip is self-adjusting in pitch with respect to the rest of the blade. With this capability, the resulting pitch motion generated a more uniform airload distribution around the azimuth. Computer math models were used to compare performance characteristics of the free-tip rotor with those of a conventional rotor operating at flight speeds from 130 to 160 knots. The free-tip rotor is shown to improve cruise L/DE by at least 22%.

Stroub, R. H.↗

Second Target Station Computer Science and Math Workshop Report

Discovery science drives innovation and underpins the technological advances that will solve some of society’s most challenging issues, including clean energy technologies, better medicines, safe potable water, and addressing aging infrastructures, including transportation. Many of these advances will result from basic research into new materials and new ways to optimize our use of existing materials. Oak Ridge National Laboratory’s neutron sources provide cutting-edge scientific tools to probe the structure and dynamics of matter in unique ways. This insight is fundamental to advancing our ability to discover, design, control, and use new materials to address society’s most pressing needs.

97 MATHEMATICS AND COMPUTING↗

Math modeling and computer mechanization for real time simulation of rotary-wing aircraft

Mathematical modeling and computer mechanization for real time simulation of rotary wing aircraft is discussed. Error analysis in the digital simulation of dynamic systems, such as rotary wing aircraft is described. The method for digital simulation of nonlinearities with discontinuities, such as exist in typical flight control systems and rotor blade hinges, is discussed.

Howe, R. M.↗

Finding New Math Identities by Computer

Recently a number of interesting new mathematical identities have been discovered by means of numerical searches on high performance computers, using some newly discovered algorithms. These include the following: pi = ((sup oo)(sub k=0))(Sigma) (1 / 16) (sup k) ((4 / 8k+1) - (2 / 8k+4) - (1 / 8k+5) - (1 / 8k+6)) and ((17 pi(exp 4)) / 360) = ((sup oo)(sub k=1))(Sigma) (1 + (1/2) + (1/3) + ... + (1/k))(exp 2) k(exp -2), zeta(3, 1, 3, 1, ..., 3, 1) = (2 pi(exp 4m) / (4m+2)! where m = number of (3,1) pairs. and where zeta(n1,n2,...,nr) = (sub k1 (is greater than) k2 (is greater than) ... (is greater than) kr)(Sigma) (1 / (k1 (sup n1) k2 (sup n2) ... kr (sup nr). The first identity is remarkable in that it permits one to compute the n-th binary or hexadecimal digit of pu directly, without computing any of the previous digits, and without using multiple precision arithmetic. Recently the ten billionth hexadecimal digit of pi was computed using this formula. The third identity has connections to quantum field theory. (The first and second of these been formally established; the third is affirmed by numerical evidence only.) The background and results of this work will be described, including an overview of the algorithms and computer techniques used in these studies.

Bailey, David H.↗

Software Accelerates Computing Time for Complex Math

Ames Research Center awarded Newark, Delaware-based EM Photonics Inc. SBIR funding to utilize graphic processing unit (GPU) technology- traditionally used for computer video games-to develop high-computing software called CULA. The software gives users the ability to run complex algorithms on personal computers with greater speed. As a result of the NASA collaboration, the number of employees at the company has increased 10 percent.

Source record↗

A posteriori superlinear convergence bounds for block conjugate gradient

In this paper, we extend to the block case the a posteriori bound showing superlinear convergence of the conjugate gradient method developed by van der Vorst and Vuik in [J. Comput. Applied Math., 48 (1993), pp. 327–341]. That is, we obtain similar bounds but now for the block conjugate gradient method. We also present a series of computational experiments, illustrating the validity of the bound developed here as well as the bound by Simoncini and Szyld from [SIAM Review, 47 (2005), pp. 247–272] using angles between subspaces. Using these bounds, we make some observations on the onset of superlinearity and how this onset depends on the eigenvalue distribution and the block size.

97 MATHEMATICS AND COMPUTING↗

Regional-scale fault-to-structure earthquake simulations with the EQSIM framework: Workflow maturation and computational performance on GPU-accelerated exascale platforms

Continuous advancements in scientific and engineering understanding of earthquake phenomena, combined with the associated development of representative physics-based models, is providing a foundation for high-performance, fault-to-structure earthquake simulations. However, regional-scale applications of high-performance models have been challenged by the computational requirements at the resolutions required for engineering risk assessments. The EarthQuake SIMulation (EQSIM) framework, a software application development under the US Department of Energy (DOE) Exascale Computing Project, is focused on overcoming the existing computational barriers and enabling routine regional-scale simulations at resolutions relevant to a breadth of engineered systems. This multidisciplinary software development—drawing upon expertise in geophysics, engineering, applied math and computer science—is preparing the advanced computational workflow necessary to fully exploit the DOE’s exaflop computer platforms coming online in the 2023 to 2024 timeframe. Achievement of the computational performance required for high-resolution regional models containing upward of hundreds of billions to trillions of model grid points requires numerical efficiency in every phase of a regional simulation. This includes run time start-up and regional model generation, effective distribution of the computational workload across thousands of computer nodes, efficient coupling of regional geophysics and local engineering models, and application-tailored highly efficient transfer, storage, and interrogation of very large volumes of simulation data. This article summarizes the most recent advancements and refinements incorporated in the workflow design for the EQSIM integrated fault-to-structure framework, which are based on extensive numerical testing across multiple graphics processing unit (GPU)-accelerated platforms, and demonstrates the computational performance achieved on the world’s first exaflop computer platform through representative regional-scale earthquake simulations for the San Francisco Bay Area in California, USA.

58 GEOSCIENCES↗

Mojo: MLIR-based Performance-Portable HPC Science Kernels on GPUs for the Python Ecosystem

We explore the performance and portability of the novel Mojo language for scientific computing workloads on GPUs. As the first language based on the LLVM’s Multi-Level Intermediate Representation (MLIR) compiler infrastructure, Mojo aims to close performance and productivity gaps by combining Python’s interoperability and CUDA-like syntax for compile-time portable GPU programming. We target four scientific workloads: a seven-point stencil (memory-bound), BabelStream (memory-bound), miniBUDE (compute-bound), and Hartree–Fock (compute-bound with atomic operations); and compare their performance against vendor baselines on NVIDIA H100 and AMD MI300A GPUs. We show that Mojo’s performance is competitive with CUDA and HIP for memory-bound kernels, whereas gaps exist on AMD GPUs for atomic operations and for fast-math compute-bound kernels on both AMD and NVIDIA GPUs. Although the learning curve and programming requirements are still fairly low-level, Mojo can close significant gaps in the fragmented Python ecosystem in the convergence of scientific computing and AI.

Godoy, William [ORNL] (ORCID:0000000225905178)↗

ADROC: An Emulation Experimentation Platform for Advancing Resilience of Control Systems

Cyberattacks against industrial control systems have increased over the last decade, making it more critical than ever for system owners to have the tools necessary to understand the cyber resilience of their systems. However, existing tools are often qualitative, subject matter expertise-driven, or highly generic, making thorough, data-driven cyber resilience analysis challenging. The ADROC project proposed to develop a platform to enable efficient, repeatable, data-driven cyber resilience analysis for cyber-physical systems. The approach consists of two phases of modeling: computationally efficient math modeling and high-fidelity emulations. The first phase allows for scenarios of low concern to be quickly filtered out, conserving resources available for analysis. The second phase supports more detailed scenario analysis, which is more predictive of real-world systems. Data extracted from experiments is used to calculate cyber resilience metrics. ADROC then ranks scenarios based on these metrics, enabling prioritization of system resources to improve cyber resilience.

97 MATHEMATICS AND COMPUTING↗

RFI Math Model programs for predicting intermodulation interference

Receivers operating on a space vehicle or an aircraft having many on-board transmitters are subject to intermodulation interference from mixing in the transmitting antenna systems, the external environment, or the receiver front-ends. This paper presents the techniques utilized in RFI Math Model computer programs that were developed to aid in the prevention of interference by predicting problem areas prior to occurrence. Frequencies and amplitudes of possible intermodulation products generated in the external environment are calculated and compared to receiver sensitivities. Intermodulation products generated in receivers are evaluated to determine the adequacy of preselector ejection.

Stafford, J. M.↗

Development of flat-plate solar collectors for the heating and cooling of buildings

The relevant design parameters in the fabrication of a solar collector for heating liquids were examined. The objective was to design, fabricate, and test a low-cost, flat-plate solar collector with high collection efficiency, high durability, and requiring little maintenance. Computer-aided math models of the heat transfer processes in the collector assisted in the design. The preferred physical design parameters were determined from a heat transfer standpoint and the absorber panel configuration, the surface treatment of the absorber panel, the type and thickness of insulation, and the number, spacing and material of the covers were defined. Variations of this configuration were identified, prototypes built, and performance tests performed using a solar simulator. Simulated operation of the baseline collector configuration was combined with insolation data for a number of locations and compared with a predicted load to determine the degree of solar utilization.

Ramsey, J. W.↗