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DOE OSTI2024

Performance of explicit and IMEX MRI multirate methods on complex reactive flow problems within modern parallel adaptive structured grid frameworks

Large-scale multiphysics simulations are computationally challenging due to the coupling of multiple processes with widely disparate time scales. The advent of exascale computing systems exacerbates these challenges since these systems enable ever-increasing size and complexity. In recent years, there has been renewed interest in developing multirate methods as a means to handle the large range of time scales, as these methods may afford greater accuracy and efficiency than more traditional approaches of using implicit-explicit (IMEX) and low-order operator splitting schemes. However, to date there have been few performance studies that compare different classes of multirate integrators on complex application problems. In this work, we study the performance of several newly developed multirate infinitesimal (MRI) methods, implemented in the SUNDIALS solver package, on two reacting flow model problems built on structured mesh frameworks. The first model revisits prior work on a compressible reacting flow problem with complex chemistry that is implemented using BoxLib but where we now include comparisons between a new explicit MRI scheme with the multirate spectral deferred correction (SDC) methods in the original paper. The second problem uses the same complex chemistry as the first problem, combined with a simplified flow model, but runs at a large spatial scale where explicit methods become infeasible due to stability constraints. Two recently developed IMEX MRI multirate methods are tested. These methods rely on advanced features of the AMReX framework on which the model is built, such as multilevel grids and multilevel preconditioners. The results from these two problems show that MRI multirate methods can offer significant performance benefits on complex multiphysics application problems and that these methods may be combined with advanced spatial discretization to compound the advantages of both.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Ginkgo - A math library designed to accelerate Exascale Computing Project science applications

Large-scale simulations require efficient computation across the entire computing hierarchy. A challenge of the Exascale Computing Project (ECP) was to reconcile highly heterogeneous hardware with the myriad of applications that were required to run on these supercomputers. Mathematical software forms the backbone of almost all scientific applications, providing efficient abstractions and operations that are crucial to harness the performance of computing systems. Ginkgo is one such mathematical software library, nurtured by ECP, providing high-performance, user-friendly, and performance portable interfaces for applications in ECP and beyond. In this paper, we elaborate on Ginkgo’s philosophy of high-performance software that is sustainable, reproducible, and easy to use. We showcase the wide feature set of solvers and preconditioners available in Ginkgo and the central concepts involved in their design. We elaborate on four different ECP software integrations: MFEM, PeleLM + SUNDIALS, XGC, and ExaSGD that use Ginkgo to accelerate their science runs. Performance studies of different problems from these applications highlight the effectiveness of Ginkgo and the benefits incurred by these ECP applications.

Cojean, Terry↗

DOE OSTI2020

A robust and efficient generalized real cascade model

This paper describes a new separation cascade model that allows for arbitrary cascade connectivity and includes the effects of mixing, material losses and generalized separation element performance. The model also accommodates mixtures with an arbitrary number of component species. The mathematical and numerical framework of this model includes both time-dependent and steady state cascade simulation. Robust numerical approximations of the continuous mathematical model are accomplished using the Sundials suite of nonlinear algebraic and differential-algebraic equation solvers. Verification of the model is accomplished using manufactured solutions while validation is demonstrated by comparison to published experimental results and benchmarks.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Data-driven time-scale separation of ODE right-hand sides using dynamic mode decomposition and time delay embedding

Multi-physics simulation often involves multiple different scales. The ARKODE ODE solver package in the SUNDIALS library addresses multi-scale problems with a multi-rate time-integrator that can work with a right-hand side that has fast scale and slow scale components. In this report, we use dynamic mode decomposition and time delay embedding to extract the fast and slow components of the right-hand sides of a simple ODE from data. We then use the extracted components to solve the ODE with ARKODE. Finally, to move towards a real-world use case, we attempt to extract fast and slow scale dynamics from synthetic seismic modeling data.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Batched Sparse Linear Algebra (Final Report for Subcontract B648960)

This report finalizes design specifications for developing batched kernels for small tensor operations for unassembled matrix-free iterative solvers, batched solvers for partially assembled operators, and batched solvers with support for various sparse formats. The outcome of the project milestones is a set of interfaces to Batched Sparse LA solvers running on hardware accelerators for use in ECP Libraries and Applications. It is part of the development of sparse batched kernels, solvers/preconditioners as well as creating interoperability in xSDK libraries with sparse and dense batched functions to benefit ECP applications. The participants included representatives from ECP libraries (not limited to the xSDK project), applications, and vendors (AMD, Intel, and NVIDIA). Batched sparse linear algebra solvers form the new frontier for algorithmic development and performance engineering. Many applications (ECP and non-ECP alike) require simultaneous solutions of small linear systems of equations that are structurally sparse. To move towards high hardware utilization, it is important to provide these applications with appropriate interfaces to efficient batched sparse solvers running on modern hardware accelerators. We present interface designs in use by HPC software libraries supporting batched sparse linear algebra and the development of sparse batched kernel codes for solvers and preconditioners. We also address the potential interoperability opportunities to keep the software portable between the major hardware accelerators from AMD, Intel, and NVIDIA. The presented interface specifications includes batched band, sparse iterative, and sparse direct solvers. This report summarizes progress in Kokkos Kernels and the xSDK libraries MAGMA, Ginkgo, hypre, SUNDIALS, and SuperLU_dist.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

“Frameworks, Algorithms and Scalable Technologies for Mathematics (FASTMath) SciDAC Institute” (Final Technical Report)

SMU personnel formed a portion of the overall “Time Integration” team within the FASTMath SciDAC-5 Institute, and we interacted very closely with team members from collaborating institutions. The major goals of our team within the FASTMath institute may be categorized into two groups: the development of advanced and application-aware time integration methods and software, and close interactions with DOE application scientists to facilitate their use of these new methods and software. The two goals are intimately linked, since our research and development of novel tools is informed by the needs of our application partners, who in turn benefit from subsequent mathematical and software advances. While the SMU personnel collaborated with the rest of the Time Integration FASTMath team on most of our shared deliverables within the larger FASTMath institute, SMU personnel primarily contributed to the following subset of those goals: ● expanding capabilities for higher-order and solve-decoupled multirate methods, ● enhancing support for temporal adaptivity within multirate methods, and ● adding structure-aware time integration methods. Each of these goals focused both on intellectual contributions through journal articles or research presentations, and on enhancements to the open-source SUNDIALS library of time integrators and nonlinear solvers, of which the SMU PI Reynolds is a core developer.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1988

First-principle and empirical modelling of the global-scale ionosphere

The SUNDIAL program offers a unique opportunity to study ionospheric behavior on a global scale. As part of this program, data pertaining to solar, interplanetary, magnetospheric, ionospheric, and thermospheric conditions are collected simultaneously from a large number of satellite and ground-based sites spread around the world. In the coming years, these data should lead to a major improvement in both empirical and first-principle ionospheric models. As a benchmark against which to compare future progress, the present state of empirical and numerical ionospheric modeling is discussed. The discussion covers the capabilities and limitations of the existing models as well as the direction of future modeling efforts.

Schunk, R. W.↗

NASA NTRS1993

The response of the high-latitude dayside ionosphere to an abrupt northward transition in the IMF

We examine the response of the high-latitude ionosphere in the prenoon sector to a northward turning of the IMF. The event was observed in the 11-13 UT interval on June 1, 1987, in the course of a multiday SUNDIAL campaign. The transition in the IMF was observed by the IMP-8 satellite which was located upstream of the earth at a distance of 36 Re. The ionospheric response in the 70-80 deg invariant latitude interval was monitored by two radars. The preexisting plasma convection observed by the radars exhibited large velocities (500-1000 m/s) and stable longterm trends, consistent with the inertial rotation of the convection pattern expected of the conditions then prevailing, B(z) less than 0, B(y) greater than 0. The plasma flow rapidly abated in response to the IMF transition. The electron density measurements made by radar in the meridional plane showed that the ionosphere had been rich in structure with the active deposition of ionization by particle precipitation. Subsequently it resembled an inactive, unstructured mid-latitude configuration. There was a dramatic decrease in the amount of backscatter observed by the HF radar. We analyze the times of transition in the various data sets and show that the ionosphere began to show the effects of the IMF transition about 2 min after its probable arrival at the magnetopause boundary.

Ruohoniemi, J. M.↗

NASA NTRS1996

Aiming at Targets: The Autobiography of Robert C. Seamans, Jr.

Bob Seamans originally was inspired to write this book for his family and friends. That is a large audience. By his own count his immediate family numbers twenty-four, not counting brothers and cousins and their families. His friends are uncounted but surely run to hundreds. As one of them and as a colleague at NASA, I am pleased and honored that he asked me to write this foreword. While written in Bob's unique and informal style, this autobiography has significance for many readers beyond his large circles of family and friends. Leaders and students of large, complex technological endeavors should be able to learn much from reading how Bob faced the daunting technical and management challenges in his career. As the title of this book implies, Bob has always set high goals for himself and then kept his eyes focused on both the necessary details and the broader picture. His ability to shift smoothly among jobs that required seemingly disparate abilities and skills speaks volumes about his insight, dedication, and enthusiasm for achievement. The book spans a truly remarkable life story. Bob first takes us through his growing up, education, and early professional and family life. Next he focuses on the crucial years when he was the general manager of NASA. Then he moves on to his career in the top jobs at the Air Force, the National Academy of Engineering, and the Energy Research and Development Administration. Finally, he touches on his later leadership activities in the academic and business worlds. Aiming at Targets is a series of fascinating topical vignettes covering his professional life. Taken together, like broad brushstrokes in an impressionist painting, they give a better picture of Bob Seamans and his work than a detailed recitation of facts and dates could hope to do. This is a cheerful account of an interesting and successful career. The book is full of good stories, with many memorable characters. Like the proverbial sundial, it counts the sunny hours. It is a good read. But it has its serious side. Bob's career wasn't all fun. The Apollo 204 fire, which killed three astronauts, was a terrible climax to his time at NASA. As one who lived through those days with him, I can recall the trauma and special sense of responsibility he felt. His account of this period and of the sad deterioration of his relationship with his boss, Jim Webb, is both fair and generous. Those were not happy times, but they should not be allowed to overshadow the fact that in his seven years at NASA, Bob Seamans led the agency to its first successes and laid the groundwork for the great successes that came later.

Seamans, Robert C., Jr.↗

NASA NTRS2007

Flight Qualified Micro Sun Sensor

A prototype small, lightweight micro Sun sensor (MSS) has been flight qualified as part of the attitude-determination system of a spacecraft or for Mars surface operations. The MSS has previously been reported at a very early stage of development in NASA Tech Briefs, Vol. 28, No. 1 (January 2004). An MSS is essentially a miniature multiple-pinhole electronic camera combined with digital processing electronics that functions analogously to a sundial. A micromachined mask containing a number of microscopic pinholes is mounted in front of an active-pixel sensor (APS). Electronic circuits for controlling the operation of the APS, readout from the pixel photodetectors, and analog-to-digital conversion are all integrated onto the same chip along with the APS. The digital processing includes computation of the centroids of the pinhole Sun images on the APS. The spacecraft computer has the task of converting the Sun centroids into Sun angles utilizing a calibration polynomial. The micromachined mask comprises a 500-micron-thick silicon wafer, onto which is deposited a 57-nm-thick chromium adhesion- promotion layer followed by a 200-nm-thick gold light-absorption layer. The pinholes, 50 microns in diameter, are formed in the gold layer by photolithography. The chromium layer is thin enough to be penetrable by an amount of Sunlight adequate to form measurable pinhole images. A spacer frame between the mask and the APS maintains a gap of .1 mm between the pinhole plane and the photodetector plane of the APS. To minimize data volume, mass, and power consumption, the digital processing of the APS readouts takes place in a single field-programmable gate array (FPGA). The particular FPGA is a radiation- tolerant unit that contains .32,000 gates. No external memory is used so the FPGA calculates the centroids in real time as pixels are read off the APS with minimal internal memory. To enable the MSS to fit into a small package, the APS, the FPGA, and other components are mounted on a single two-sided board following chip-on-board design practices

Liebe, Carl Christian↗

NASA NTRS2004

Compact Optoelectronic Compass

A compact optoelectronic sensor unit measures the apparent motion of the Sun across the sky. The data acquired by this chip are processed in an external processor to estimate the relative orientation of the axis of rotation of the Earth. Hence, the combination of this chip and the external processor finds the direction of true North relative to the chip: in other words, the combination acts as a solar compass. If the compass is further combined with a clock, then the combination can be used to establish a threeaxis inertial coordinate system. If, in addition, an auxiliary sensor measures the local vertical direction, then the resulting system can determine the geographic position. This chip and the software used in the processor are based mostly on the same design and operation as those of the unit described in Micro Sun Sensor for Spacecraft (NPO-30867) elsewhere in this issue of NASA Tech Briefs. Like the unit described in that article, this unit includes a small multiple-pinhole camera comprising a micromachined mask containing a rectangular array of microscopic pinholes mounted a short distance in front of an image detector of the active-pixel sensor (APS) type (see figure). Further as in the other unit, the digitized output of the APS in this chip is processed to compute the centroids of the pinhole Sun images on the APS. Then the direction to the Sun, relative to the compass chip, is computed from the positions of the centroids (just like a sundial). In the operation of this chip, one is interested not only in the instantaneous direction to the Sun but also in the apparent path traced out by the direction to the Sun as a result of rotation of the Earth during an observation interval (during which the Sun sensor must remain stationary with respect to the Earth). The apparent path of the Sun across the sky is projected on a sphere. The axis of rotation of the Earth lies at the center of the projected circle on the sphere surface. Hence, true North (not magnetic North), relative to the chip, can be estimated from paths of the Sun images across the APS. In a test, this solar compass has been found to yield a coarse estimate of the North (within tens of degrees) in an observation time of about ten minutes. As expected, the accuracy was found to increase with observation time: after a few hours, the estimated direction of the rotation axis becomes accurate to within a small fraction of a degree.

Christian, Carl↗

DOE OSTI2022

Pele: An Exascale-Ready Suite of Combustion Codes

High fidelity simulations of realistic combustion devices are extremely demanding computationally because of the requirements to capture complex fuel chemical decomposition, its intricate interactions with turbulent, often multiphase, flows, and the wide separation of space and time scales between the thin flame and the device boundaries. Software required to carry out such computations tends to be extremely complex, particularly when designed to exploit hardware accelerators, and can be difficult to port and maintain. We present Pele, a performance portable suite of tools for the simulation of combustion systems, including codes to evolve reactive multiphase configurations in the low Mach number and compressible flow regimes, along with a set of inter-compatible post processing and in situ analysis tools. The Pele suite of tools is built on top of the AMReX framework for block-structured adaptive mesh refinement, which provides efficient data structures and algorithms that enable the development of a wide variety of efficient mesh and particle based PDE integration schemes. A hierarchical MPI+X parallelism scheme supports CPU-only and accelerated architectures, where X can be OpenMP, CUDA, and HIP based approaches for intra-node computational work distribution. The algorithms and data structures underlying the Pele simulation and analysis tools are highly scalable and performant across a wide variety of high-performance computing platforms, including DOEs newest exascale-class machines, Frontier and Aurora. The simulation and analysis tools are fully documented and freely distributed as open source via GitHub. We present key algorithmic and software challenges, solution strategies, performance and resulting set of capabilities.

AMReX↗