Mathematical Methods and Modeling in the National Security Sciences
Luttman will be giving this presentation at several colleges and universities at the end of March 2017
97 MATHEMATICS AND COMPUTING↗
SEARCH · Search NASA
Results for “Mathematics of computing”
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Preparing an Incompressible-Flow Fluid Dynamics Code for Exascale-Class Wind Energy Simulations: Preprint
The US Department of Energy has identified Exascale-Class wind farm simulation tools as critical to wind energy scientific discovery. A primary objective of the Exawind project is to build high-performance, predictive Computational Fluid Dynamics tools that satisfy these modeling needs. GPU accelerators will serve as the computational thoroughbreds of next generation, Exascale-Class, platforms. Here, we report on our efforts for preparing the Exawind unstructured mesh solver, Nalu-Wind, for Exascale-Class machines. For computing at this scale, a simple port of the incompressible-flow algorithms to GPUs is not sufficient. One needs novel algorithms that are application aware, memory efficient, and optimized for latest generation GPU devices to get high-performance. The result of our efforts are unstructured mesh simulations of wind turbines that use 1/6 the compute resources of Summit supercomputer at Oak Ridge National Lab. In particular, we demonstrate a first-of-its-kind, simulation using Algebraic Multigrid solvers on over 4000 GPUs.
algebraic multigrid↗
Transforming Energy through Computational Excellence. Exascale Computing: Combustion; Deep Learning for Presumed Probability Density Function (PDF) Models
NREL researchers use advanced machine learning techniques to define improved methods using deep learning models to resolve reacting flows in turbulent combustion flows, reducing the computational burden, increasing computational speed, and improving accuracy. These advancements reduce cost and improve fidelity of rapid-turn-around engineering calculations.
combustion↗
Enabling Combustion Science Simulations for Future Exascale Machines
Reacting flow simulations for combustion applications require extensive computing capabilities. Leveraging the AMReX library, the Pele suite of combustion simulation tools targets the largest supercomputers available and future exascale machines. We introduce PeleC, the compressible solver in the Pele suite, and detail its capabilities, including complex geometry representation, chemistry integration, and discretization. We present a comparison of development efforts using both OpenACC and AMReX's C++ performance portability framework for execution on multiple GPU architectures. We discuss relevant details that have allowed PeleC to achieve high performance and scalability. PeleC's performance characteristics are measured through relevant simulations on multiple supercomputers. The success of PeleC's design for exascale is exhibited through demonstration of a 160 billion cell simulation and weak scaling onto 100\% of Summit, an NVIDIA-based GPU supercomputer at Oak Ridge National Laboratory. Our results provide confidence that PeleC will enable future combustion science simulations with unprecedented fidelity.
combustion↗
Improving the Performance of DGEMM with MoA and Cache-Blocking: Preprint
The goal of this paper is to demonstrate performance enhancements of the high performance dense linear algebra matrix-matrix multiply DGEMM kernel, widely implemented by vendors in the basic linear algebra subroutine BLAS library. The mathematics of arrays (MoA) paradigm due to Mullin (1988) results in contiguous memory accesses in combination with Church-Rosser complete language constructs optimized for target processor architectures [3]. Our performance studies demonstrate that the MoA implementation of DGEMM combined with optimal cache-blocking strategies results in at least a 25% performance gain on both Intel Xeon Skylake and IBM Power-9 processors over the vendor supplied Intel MKL and IBM ESSL basic linear algebra libraries. Results are presented for the NREL Eagle and ORNL Summit supercomputers.
cache-blocking↗
Threaded Multi-Core GEMM with MoA and Cache-Blocking: Preprint
A threaded multi-core implementation of the high performance dense linear algebra matrix-matrix multiply GEMM kernel is described. This kernel is widely implemented by vendors in the basic linear algebra subroutine BLAS library. The mathematics of arrays (MoA) paradigm due to Mullin (1988) results in contiguous memory accesses by employing outer-product forms. Our performance studies demonstrate that the MoA implementation of double precision DGEMM combined with optimal cache-blocking strategies results in at least a 25% performance gain on the Intel Xeon Skylake processor over the vendor supplied Intel MKL basic linear algebra libraries. Results are presented for the NREL Eagle supercomputer. The multi-core DGEMM achieves over 100 GigaFlops/sec with eight openMP threads.
cache-blocking↗
Advanced Computing Annual Report 2021
Advanced computing at the National Renewable Energy Laboratory (NREL) had an exciting 2021. More than 300 projects advanced the U.S. Department of Energy's (DOE's) Office of Energy Efficiency and Renewable Energy (EERE) mission. This annual report highlights capabilities, project highlights, innovations, etc. to showcase the great work conducted within Advanced Computing at NREL.
advanced computing↗
Novel Solver Algorithms for Nearly Singular Linear Systems Arising in Combustion Modelling
Direct Numerical Simulations of realistic combustion devices are extremely challenging due to the wide separation of scales in the simulation, for example an internal combustion (IC) engine chamber, and the flame thickness of a high-pressure flame. The PeleLMeX solver uses adaptive mesh refinement (AMR) to evolve multi-species reacting flows in the low Mach number limit at the Exascale and relies on an embedded boundary (EB) approach to represent complex geometries. In that framework, the EB geometries often give rise to very small cut-cells along the boundary, which translate into extreme ill-conditioning of the pressure-projection, with eigenvalues that span 15-16 orders of magnitude. In this talk, we focus on the case of a typical IC piston bowl geometry for which we present on a novel approach towards solving these nearly singular linear systems with ILU-based, C-AMG smoothers on massively parallel architectures. In particular, we use scaling and equilibration algorithms to handle the non-normality of the upper triangular factors. This enables us to approximate the highly sequential triangular solve algorithm, embedded in the AMG smoothing-solve phase, with Jacobi iterations. This approximation can be written as a convergent Neumann series whose terms are composed of highly parallel sparse matrix vector multiplications. The result is an algorithm that substantially decreases setup and solve time, compared to state-of-the-art, for these challenging linear systems.
combustion modelling↗
Mesoflow: An Open-Source Reacting Flow Solver for Catalysis at Mesoscale
We present the capabilities and software performance metrics of our open-source continuum solver for catalysis, Mesoflow, developed specifically for modeling transport and chemistry at the mesoscale. Our solver utilizes Cartesian block-structured adaptive mesh refinement to resolve complex catalyst surface morphologies directly obtained from X-ray tomography data. An immersed boundary based formulation enables rapid representation of complex geometries prevalent in most mesoporous catalyst interfaces. The solver is developed on top of open-source performance portable library, AMReX, providing parallel execution capabilities on current and upcoming high-performance-computing (HPC) architectures. Our flexible software framework enables integration of complex chemical mechanisms at heterogenous interfaces and time-split algorithms for circumventing highly disparate reaction and flow time-scales. Our current studies indicate a ten-fold performance gain by using graphics-processing-units (GPUs) compared to a single processor for representative problem sizes (2 million cell mesh). We will also present a brief introduction on how to build and use this software for application problems pertaining to catalytic upgrading and gas transport within porous catalyst particles.
adaptive meshing↗
From PeleC to PeleACC, to PeleC++
PeleC is an Exascale Computing Project application for simulating compressible combustion in complex geometries. It has been built on top of the popular AMReX library. In the beginning of the Exascale Computing Project, PeleC was focused on KNL. It uses a mixture of C++, C, and kernels written in Fortran to obtain performance by focusing on vectorization. Recently we have taken two approaches in deciding PeleC's future for obtaining performance on exascale GPU machines. In the first programming model, we decorated the Fortran kernels with OpenACC directives. This expedited our ability to run at large scales on Summit's GPUs, where we achieved a significant speedup over the CPUs on Summit. The second programming model involved rewriting the Fortran kernels in C++ and using AMReX's Kokkos-like lambda abstractions for running on the GPU. This resulted in similar speedups on Summit's GPUs over merely utilizing the CPUs. Both approaches involved AMReX's management of memory transfers between the device and host. In this work, we compare and contrast the benefits and pitfalls to both programming approaches regarding performance, performance portability, and productivity. We also discuss advantages we have found in taking the time to modernize our code and why have chosen a specific pathway to prepare our code for the future DOE exascale machines.
exascale computing↗
ExaWind: Then and Now
The scientific goal of the ExaWind project is to advance our fundamental understanding of the flow physics governing whole wind plant performance, including wake formation, complex terrain impacts, and turbine-turbine-interaction effects. The primary application codes in the ExaWind environment are Nalu-Wind, an unstructured-grid computational fluid dynamics (CFD) code, AMR-Wind, a structured-grid CFD code, and OpenFAST, a whole-turbine simulation code. In this poster we present the current status of the ExaWind software stack in the context of the modeling and simulation capabilities when the project started in 2016.
computational fluid dynamics↗
Advanced Computing Annual Report 2022
National Renewable Energy Laboratory's (NREL) high-performance computing (HPC), efficient data center operation, and state-of-the-art data visualization powered over 300 clean energy projects in Fiscal Year 2022 (FY22). 555 scientists and engineers utilized HPC resources to assess and integrate data into their research. The report highlights the arrival of new HPC Kestrel in 2023, the contributions of the Insight Center, and researchers looking into bias in artificial intelligence, alongside key research collaborations using advanced computing.
advanced computing↗
Mastering HPC Runtime Prediction: From Observing Patterns to a Methodological Approach: Preprint
The continual expansion of high-performance computing (HPC) brings with it an increasing need for efficiency. Heavy investment in energy, hardware, and software infrastructure to support peta- and exascale computing requires the optimization of existing systems and, wherever possible, the discernment and adoption of best-practices towards these goals. Such is the case for runtime prediction. When a job is submitted to an HPC system, an estimate of its runtime is provided by the user in the form of "requested wallclock''. Error in this user-provided estimate can lead to jobs being prematurely killed by the scheduler, increased wait time on the queue, and decreased system utilization. More than fifteen years of research has been directed at mitigating these effects by using data-driven runtime predictions. Codified here is a set of commonalities and insights emerging from this body of work, which we present as recommendations and best practices. These practices are combined into a methodological approach described and evaluated on an 11-million-job dataset from the National Renewable Energy Laboratory's petascale HPC system, Eagle. This dataset and the accompanying codebase have been released to the public domain for the benefit of the wider HPC research community.
high performance computing↗
ExaWind at NREL: Upping the Ante
The objective of the ExaWind component of the Exascale Computing Project is to deliver many-turbine blade-resolved simulations in complex terrain. These simulations bring new challenges to both compute and analysis of the resulting data. In this paper/video, we visually explore the impact of ExaWind on wind simulations through two studies of a small wind farm under two atmospheric conditions. We then turn to analysis and review tools that visualization researchers at NREL use to answer the challenges that ExaWind brings.
collaborative visualization↗
Adaptive Computing and Multi-Fidelity Strategies for Control, Design and Scale-Up of Renewable Energy Applications
We describe our ongoing research in adaptive computing and multi-fidelity modeling strategies. Our goal is to use a combination of low- and high-fidelity simulation models to enable computationally efficient optimization and uncertainty quantification. We develop optimization formulations that take into account the compute resources currently available, which act as a constraint with regards to the fidelity level simulation we can run while maximizing information gain. These strategies are being implemented into a software framework with a generalized API allowing its application to a broad range of applications, from power grid stability and buildings control to material synthesis and biofuels processing. We will discuss a few examples from these applications that can benefit from this approach, especially when considering challenges arising in scaling up experiments and simulations.
adaptive computing↗
Development of a Performance Portable Non-Equilibrium Plasma Fluid Solver on Adaptive Grids
This presentation will describe the numerical techniques, programming paradigms, verification, and performance of a non-equilibrium plasma fluid solver that can effectively utilize current and upcoming central processing and graphics processing unit (CPU+GPU) architectures. Our plasma fluid model solves the conservation equations for self-consistent electrostatic Poisson, electron and heavy species transport, and electron temperature on adaptive Cartesian grids. Our solver is written using performance portable adaptive mesh management library, AMReX (Zhang et al., JOSS, 4 (37) 1370, 2019), and can be built and run on widely available vendor specific GPU architectures (NVIDIA/AMD/Intel). We utilize a non-subcycled second order semi-implicit time-stepping method where all adaptive mesh refinement (AMR) levels are advanced with the same time step. The composite multi-level multigrid solver from within AMReX is used for each of the governing equations that are cast into a Helmholtz equation form. We have also developed a python based chemical mechanism parser framework that uses a similar format as CANTERA (Goodwin et al., Zenodo, 2018) yaml files as input. Our custom parser reads the yaml file and provides C++ files with transport and production rate functions that can be executed on both host (CPU) and device (GPU). We present verification of our solver using method of manufactured solutions that indicate formal second order accuracy with central diffusion and fifth order weighted-essentially-non-oscillatory (WENO) advection scheme. We also verify our solver with published literature on low-pressure capacitive and high-pressure streamer discharges. Our initial performance studies indicate 10X speed-up using 20 NVIDIA GPUs versus 200 CPUs for an atmospheric streamer discharge problem solved on a 512 x 1024 x 512 grid.
graphics processing units↗
Challenges at the Frontiers of Matter and Energy: Transformative Opportunities for Discovery Science
FIVE TRANSFORMATIVE OPPORTUNITIES FOR DISCOVERY SCIENCE As a result of this effort, it has become clear that the progress made to date on the five Grand Challenges has created a springboard for seizing five new Transformative Opportunities that have the potential to further transform key technologies involving matter and energy. These five new Transformative Opportunities and the evidence supporting them are discussed in this new report, “Challenges at the Frontiers of Matter and Energy: Transformative Opportunities for Discovery Science.” Mastering Hierarchical Architectures and Beyond-Equilibrium Matter Complex materials and chemical processes transmute matter and energy, for example from CO2 and water to chemical fuel in photosynthesis, from visible light to electricity in solar cells and from electricity to light in light emitting diodes (LEDs) Such functionality requires complex assemblies of heterogeneous materials in hierarchical architectures that display time-dependent away-from-equilibrium behaviors. Much of the foundation of our understanding of such transformations however, is based on monolithic single- phase materials operating at or near thermodynamic equilibrium. The emergent functionalities enabling next-generation disruptive energy technologies require mastering the design, synthesis, and control of complex hierarchical materials employing dynamic far-from-equilibrium behavior. A key guide in this pursuit is nature, for biological systems prove the power of hierarchical assembly and far- from-equilibrium behavior. The challenges here are many: a description of the functionality of hierarchical assemblies in terms of their constituent parts, a blueprint of atomic and molecular positions for each constituent part, and a synthesis strategy for (a) placing the atoms and molecules in the proper positions for the component parts and (b) arranging the component parts into the required hierarchical structure. Targeted functionality will open the door to significant advances in the harvesting, transforming (e.g., reducing CO2, splitting water, and fixing nitrogen), storing, and use of energy to create new materials, manufacturing processes, and technologies—the lifeblood of human societies and economic growth. Beyond Ideal Materials and Systems: Understanding the Critical Roles of Heterogeneity, Interfaces, and Disorder Real materials, both natural ones and those we engineer, are usually a complex mixture of compositional and structural heterogeneities, interfaces, and disorder across all spatial and temporal scales. It is the fluctuations and disorderly states of these heterogeneities and interfaces that often determine the system’s properties and functionality. Much of our fundamental scientific knowledge is based on “ideal” systems, meaning materials that are observed in “frozen” states or represented by spatially or temporally averaged states. Too often, this approach has yielded overly simplistic models that hide important nuances and do not capture the complex behaviors of materials under realistic conditions. These behaviors drive vital chemical transformations such as catalysis, which initiates most industrial manufacturing processes, and friction and corrosion, the parasitic effects of which cost the U.S. economy billions of dollars annually. Expanding our scientific knowledge from the relative simplicity of ideal, perfectly ordered, or structurally averaged materials to the true complexity of real-world heterogeneities, interfaces, and disorder should enable us to realize enormous benefits in the materials and chemical sciences, which translates to the energy sciences, including solar and nuclear power, hydraulic fracturing, power conversion, airframes, and batteries. Harnessing Coherence in Light and Matter Quantum coherence in light and matter is a measure of the extent to which a wave field vibrates in unison with itself at neighboring points in space and time. Although this phenomenon is expressed at the atomic and electronic scales, it can dominate the macroscopic properties of materials and chemical reactions such as superconductivity and efficient photosynthesis. In recent years, enormous progress has been made in recognizing, manipulating, and exploiting quantum coherence. This progress has already elucidated the role that symmetry plays in protecting coherence in key materials, taught us how to use light to manipulate atoms and molecules, and provided us with increasingly sophisticated techniques for controlling and probing the charges and spins of quantum coherent systems. With the arrival of new sources of coherent light and electron beams, thanks in large part to investments by the U.S. Department of Energy’s Office of Basic Energy Sciences (BES), there is now an opportunity to engineer coherence in heterostructures that incorporate multiple types of materials and to control complex, multistep chemical transformations. This approach will pave the way for quantum information processing and next-generation photovoltaic cells and sensors. Revolutionary Advances in Models, Mathematics, Algorithms, Data, and Computing Science today is benefiting from a convergence of theoretical, mathematical, computational, and experimental capabilities that put us on the brink of greatly accelerating our ability to predict, synthesize, and control new materials and chemical processes, and to understand the complexities of matter across a range of scales. Imagine being able to chart a path through a vast sea of possible new materials to find a select few with desired properties. Instead of the time-honored forward approach, in which materials with desired properties are found through either trial-and-error experiments or lucky accidents, we have the opportunity to inversely design and create new materials that possess the properties we desire. The traditional approach has allowed us to make only a tiny fraction of all the materials that are theoretically possible. The inverse design approach, through the harmonious convergence of theoretical, mathematical, computational, and experimental capabilities, could usher in a virtual cornucopia of new materials with functionalities far beyond what nature can provide. Similarly, enhanced mathematical and computational capabilities significantly enhance our ability to extract physical and chemical insights from vastly larger data streams gathered during multimodal and multidimensional experiments using advanced characterization facilities. Exploiting Transformative Advances in Imaging Capabilities across Multiple Scales Historically, improvements in imaging capabilities have always resulted in improved understanding of scientific phenomena. A prime challenge today is finding ways to reconstruct raw data, obtained by probing and mapping matter across multiple scales, into analyzable images. BES investments in new and improved imaging facilities, most notably synchrotron x-ray sources, free-electron lasers, electron microscopes, and neutron sources, have greatly advanced our powers of observation, as have substantial improvements in laboratory- scale technologies. Furthermore, BES is now planning or actively discussing exciting new capabilities. Taken together, these advances in imaging capabilities provide an opportunity to expand our ability to observe and study matter from the 3D spatial perspectives of today to true “4D” spatially and temporally resolved maps of dynamics that allow quantitative predictions of time-dependent material properties and chemical processes. The knowledge gained will impact data storage, catalyst design, drug delivery, structural materials, and medical implants, to name just a few key technologies. ENABLING SUCCESS Seizing each of these five Transformative Opportunities, as well as accelerating further progress on Grand Challenge research, will require specific, targeted investments from BES in the areas of synthesis, meaning the ability to make the materials and architectures that are envisioned; instrumentation and tools, a category that includes theory and computation; and human capital, the most important asset for advancing the Grand Challenges and Transformative Opportunities. While “Challenges at the Frontiers of Matter and Energy: Transformative Opportunities for Discovery Science” could be viewed as a sequel to the original Grand Challenges report, it breaks much new ground in its assessment of the scientific landscape today versus the scientific landscape just a few years ago. In the original Grand Challenges report, it was noted that if the five Grand Challenges were met, our ability to direct matter and energy would be measured only by the limits of human imagination. This new report shows that, prodded by those challenges, the scientific community is positioned today to seize new opportunities whose impacts promise to be transformative for science and society, as well as dramatically accelerate progress in the pursuit of the original Grand Challenges.
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
ASCR@40: Four Decades of Department of Energy Leadership in Advanced Scientific Computing Research
Throughout its long history, the Office of Advanced Scientific Computing Research (ASCR) has built the critical technologies to ensure U.S. leadership in energy science and national security. It has made its parent agency, the Department of Energy (DOE) and its Office of Science, the world’s recognized leader in computational science. ASCR’s stated mission is “to discover, develop, and deploy computational and networking capabilities to analyze, model, simulate, and predict complex phenomena important to the DOE.” To accomplish this goal, ASCR oversees a large complex of computing and networking facilities and is responsible for procuring, deploying and operating high-performance computing (HPC), networking and storage resources; conducting basic research in mathematics and computer science; developing and sustaining a large body of software; and collaborating with other Office of Science programs, academia and industry. ASCR’s computational science leadership has a long history, predating even DOE’s inception. Applied mathematics and advanced computing were both elements of the Manhattan Project’s Theoretical Division. In the 1950s, DOE’s predecessor, the Atomic Energy Commission, created a mathematics program to develop and apply digital computing by supporting researchers at universities and AEC laboratories. Several organizational and name changes later, this program would grow and become ASCR.
97 MATHEMATICS AND COMPUTING↗