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14 records

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DOE OSTI2024

A conservative discontinuous-Galerkin-in-time (DGiT) multirate time integration framework for interface-coupled problems with applications to solid–solid interaction and air–sea models

In this paper we extend the DGiT multirate framework, developed in Connors and Sockwell (2022) for scalar transmission problems, to a solid–solid interaction (SSI) problem involving two coupled elastic solids and a coupled air–sea model with the rotating, thermal shallow water equations. In so doing we aim to demonstrate the broad applicability of the mathematical theory and governing principles established in Connors and Sockwell (2022) to coupled problems characterized by subproblems evolving at different temporal scales. Further, multirate time integration algorithms employing different time steps, optimized for the dynamics of each subproblem, can significantly improve simulation efficiency for such coupled problems. However, development of multirate algorithms is a highly non-trivial task due to the coupling, which can impact accuracy, stability or other desired properties such as preservation of system invariants. DGiT provides a general template for multirate time integration that can achieve these properties. To elucidate the manner in which DGiT accomplishes this task, we fully detail each step in the application of the framework to the SSI and air–sea coupled problems. Numerical examples illustrate key properties of the resulting multirate schemes for both problems.

42 ENGINEERING↗

DOE OSTI2025

Advancing simulations of coupled electron and phonon nonequilibrium dynamics using adaptive and multirate time integration

Electronic structure calculations in the time domain provide a deeper understanding of nonequilibrium dynamics in materials. The real-time Boltzmann equation (rt-BTE), used in conjunction with accurate interactions computed from first principles, has enabled reliable predictions of coupled electron and lattice dynamics. However, the timescales and system sizes accessible with this approach are still limited, with two main challenges being the different timescales of electron and phonon interactions and the cost of computing collision integrals. As a result, only a few examples of these calculations exist, mainly for two-dimensional (2D) materials. Here we leverage adaptive and multirate time integration methods to achieve a major step forward in solving the coupled rt-BTEs for electrons and phonons. Relative to conventional (non-adaptive) time-stepping, our approach achieves a 10x speedup for a target accuracy, or greater accuracy by 3–6 orders of magnitude for the same computational cost, enabling efficient calculations in both 2D and bulk materials. This efficiency is showcased by computing the coupled electron and lattice dynamics in graphene up to ~100 ps, as well as modeling ultrafast lattice dynamics and thermal diffuse scattering maps in bulk materials (silicon and gallium arsenide). In addition to improved efficiency, our adaptive method can resolve the characteristic rates of different physical processes, thus naturally bridging different timescales. This enables simulations of longer timescales and provides a framework for modeling multiscale dynamics of coupled degrees of freedom in matter. Our work opens new opportunities for quantitative studies of nonequilibrium physics in materials, including driven lattice dynamics with phonons coupled to electrons, spin, and other degrees of freedom.

Yao, Jia [California Institute of Technology (CalT↗

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 OSTI2026

Efficient and flexible multirate temporal adaptivity

In this work we present two new families of multirate time step adaptivity controllers, that are designed to work with embedded multirate infinitesimal (MRI) time integration methods for adapting time steps when solving problems with multiple time scales. We compare these controllers against competing approaches on two benchmark problems, showing that the proposed methods offer dramatically improved performance and flexibility. The combination of embedded MRI methods and the proposed controllers enable adaptive simulations of problems with a potentially arbitrary number of time scales, achieving high accuracy while maintaining low computational cost. Additionally, we introduce a new set of embeddings for the family of explicit multirate exponential Runge–Kutta (MERK) methods of orders 2 through 5, resulting in the first-ever fifth-order embedded MRI method. Finally, we compare the performance of a wide range of embedded MRI methods on our benchmark problems to provide guidance on how to select an appropriate MRI method and multirate controller.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Implicit–explicit multirate infinitesimal stage-restart methods

Implicit–Explicit (IMEX) methods are flexible numerical time integration methods which solve an initial-value problem (IVP) that is split into stiff and nonstiff processes with the goal of lower computational costs than a purely implicit or explicit approach. A complementary form of flexible IVP solvers are multirate infinitesimal methods for problems split into fast- and slow-changing dynamics, that solve a multirate IVP by evolving a sequence of “fast” IVPs using any suitably accurate algorithm. This article introduces a new class of high-order implicit–explicit multirate methods that are designed for multirate IVPs in which the slow-changing dynamics are further split in an IMEX fashion. This new class, which we call implicit–explicit multirate infinitesimal stage-restart (IMEX-MRI-SR), both improves upon the previous implicit–explicit multirate infinitesimal generalized-structure additive Runge Kutta (IMEX-MRI-GARK) methods by allowing for far easier creation of new embedded methods, and extends multirate exponential Runge Kutta (MERK) methods by allowing the fast-changing dynamics to be nonlinear and the methods to be implicit. We leverage GARK theory to derive conditions for orders of accuracy up to four, and we provide second- and third-order accurate example methods, which are the first known embedded MRI methods with IMEX structure. We then perform numerical simulations demonstrating convergence rates and computational performance in both fixed-step and adaptive-step settings.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗

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 NTRS1986

Extensions to PIFCGT: Multirate output feedback and optimal disturbance suppression

New control synthesis procedures for digital flight control systems were developed. The theoretical developments are the solution to the problem of optimal disturbance suppression in the presence of windshear. Control synthesis is accomplished using a linear quadratic cost function, the command generator tracker for trajectory following and the proportional-integral-filter control structure for practical implementation. Extensions are made to the optimal output feedback algorithm for computing feedback gains so that the multirate and optimal disturbance control designs are computed and compared for the advanced transport operating system (ATOPS). The performance of the designs is demonstrated by closed-loop poles, frequency domain multiinput sigma and eigenvalue plots and detailed nonlinear 6-DOF aircraft simulations in the terminal area in the presence of windshear.

Broussard, J. R.↗

NASA NTRS2004

Discrete-Time Demodulator Architectures for Free-Space Broadband Optical Pulse-Position Modulation

The objective of this work is to develop discrete-time demodulator architectures for broadband optical pulse-position modulation (PPM) that are capable of processing Nyquist or near-Nyquist data rates. These architectures are motivated by the numerous advantages of realizing communications demodulators in digital very large scale integrated (VLSI) circuits. The architectures are developed within a framework that encompasses a large body of work in optical communications, synchronization, and multirate discrete-time signal processing and are constrained by the limitations of the state of the art in digital hardware. This work attempts to create a bridge between theoretical communication algorithms and analysis for deep-space optical PPM and modern digital VLSI. The primary focus of this work is on the synthesis of discrete-time processing architectures for accomplishing the most fundamental functions required in PPM demodulators, post-detection filtering, synchronization, and decision processing. The architectures derived are capable of closely approximating the theoretical performance of the continuous-time algorithms from which they are derived. The work concludes with an outline of the development path that leads to hardware.

Gray, A. A.↗

NASA NTRS1991

Fault-tolerant multichannel demultiplexer subsystems

Fault tolerance in future processing and switching communication satellites is addressed by showing new methods for detecting hardware failures in the first major subsystem, the multichannel demultiplexer. An efficient method for demultiplexing frequency slotted channels uses multirate filter banks which contain fast Fourier transform processing. All numerical processing is performed at a lower rate commensurate with the small bandwidth of each bandbase channel. The integrity of the demultiplexing operations is protected by using real number convolutional codes to compute comparable parity values which detect errors at the data sample level. High rate, systematic convolutional codes produce parity values at a much reduced rate, and protection is achieved by generating parity values in two ways and comparing them. Parity values corresponding to each output channel are generated in parallel by a subsystem, operating even slower and in parallel with the demultiplexer that is virtually identical to the original structure. These parity calculations may be time shared with the same processing resources because they are so similar.

Redinbo, Robert↗

NASA NTRS1977

Cratering motions and structural deformation in the rim of the Prairie Flat multiring explosion crater

Cratering motions and structural deformation are described for the rim of the Prairie Flat multiring crater, 85.5 m across and 5.3 m deep, which was formed by the detonation of a 500-ton TNT surface-tangent sphere. The terminal displacement and motion data are derived from marker cans and velocity gages emplaced in drill holes in a three-dimensional matrix radial to the crater. The integration of this data with a detailed geologic cross section, mapped from deep trench excavations through the rim, provides a composite view of the general sequence of motions that formed a transiently uplifted rim, overturned flap, inverted stratigraphy, downfolded rim, and deformed strata in the crater walls. Preliminary comparisons with laboratory experimental cratering and with numerical simulations indicate that explosion craters of the Prairie Flat-type generated by surface and near-surface energy sources tend to follow predictable motion sequences and produce comparable structural deformation. More specifically, central uplift and multiring impact craters with morphologies and structures comparable to Prairie Flat are inferred to have experienced similar deformational histories of the rim, such as uplift, overturning, terracing, and downfolding.

Roddy, D. J.↗

DOE OSTI2026

New Time Integrators and Capabilities in SUNDIALS Versions 6.2.0-7.4.0

SUNDIALS is a well-established numerical library that provides robust and efficient time integrators and nonlinear solvers. This article overviews several significant improvements and new features added over the last 3 years to support scientific simulations run on high-performance computing systems. Notably, three new classes of one-step methods have been implemented: low storage Runge–Kutta, symplectic partitioned Runge–Kutta, and operator splitting. In addition, we describe new timestep adaptivity support for multirate methods, adjoint sensitivity analysis capabilities for explicit Runge–Kutta methods, additional options for Anderson acceleration in nonlinear solvers, and improved error handling and logging.

Computer science↗

NASA NTRS1994

Parallel digital modem using multirate digital filter banks

A new class of architectures for an all-digital modem is presented in this report. This architecture, referred to as the parallel receiver (PRX), is based on employing multirate digital filter banks (DFB's) to demodulate, track, and detect the received symbol stream. The resulting architecture is derived, and specifications are outlined for designing the DFB for the PRX. The key feature of this approach is a lower processing rate then either the Nyquist rate or the symbol rate, without any degradation in the symbol error rate. Due to the freedom in choosing the processing rate, the designer is able to arbitrarily select and use digital components, independent of the speed of the integrated circuit technology. PRX architecture is particularly suited for high data rate applications, and due to the modular structure of the parallel signal path, expansion to even higher data rates is accommodated with each. Applications of the PRX would include gigabit satellite channels, multiple spacecraft, optical links, interactive cable-TV, telemedicine, code division multiple access (CDMA) communications, and others.

Sadr, Ramin↗

NASA NTRS2017

Large Impact Features on Icy Galilean Satellites

Impact crater morphology can be a very useful tool for probing planetary interiors, but nowhere in the solar system is a greater variety of crater morphologies observed (Fig. 1) than on the large icy Galilean satellites Ganymede and Callisto [e.g., 1- 3]. As on the rocky terrestrial planets, impact crater morphology becomes more complex with increasing size on these satellites. With increasing size, however, these same craters become less like their counterparts on the rocky planets. Several impact landforms and structures (multiring furrows, palimpsests, and central domes, for example), have no obvious analogs on any other planets. Further, several studies [e.g., 4-6] have drawn attention to impact landforms on Europa which are unusual, even by Galilean satellite standards. These radical differences in morphology suggest that impact into icy lithospheres that are mechanically distinct from silicate lithospheres may be responsible. As such, large impact structures may be important probes of the interiors of these bodies over time [e.g., 7]. The first goal of this work is to integrate and correlate the detailed morphologic and morphometric measurements and observations of craters on icy Galilean satellites [e.g., 4, 8-12] with new detailed mapping of these structures from Galileo high-resolution images. As a result, we put forward a revised crater taxonomy for Ganymede and Callisto in order to simplify the nonuniform impact crater nomenclature cluttering the literature. We develop and present an integrated model for the development of these unusual crater morphologies and their implications for the thermal evolution of these bodies.

crater morphologies↗

NASA NTRS1992

Venusian impact basins and cratered terrains

The consensus regarding interpretation of Magellan radar imagery assigns Venus a young volcanic surface subjected in many areas to moderate crustal shortening. I infer that, on the contrary, ancient densely cratered terrain and large impact basins may be preserved over more than half the planet and that crustal shortening has been much overestimated. I see wind erosion and deposition as far more effective in modifying old structures. Integration with lunar chronology suggests that most of the surface of Venus may be older than 3.0 Ga and much may be older than 3.8 Ga. Broad volcanos, hug volcanic domes, plains preserving lobate flow patterns, and numerous lesser volcanic features, pocked sparsely by impact craters, are indeed obvious on Magellan imagery. Some of these postvolcanic impact craters have been slightly extended, but only a small portion has been flooded by still younger lavas. Relative ages of the young craters are indicated by the varying eolian removal of their forms and ejecta blankets and flow lobes, and the oldest are much subdued. If these young impact craters, maximum diameter 275 km, include all preserved impact structures, then their quantity and distribution indicate that Venus was largely resurfaced by volcanism approx. 0.5 Ga, subsequent eruptions having been at a much reduced rate. Away from the approx. 0.5 Ga volcanic features, much of Venus is, however, dominated by circular and subcircular features, 50-2000 km in diameter, many of them multiring, that may be mostly older impact and impact-melt structures substantially modified by wind action. Eolian erosion scoured to bedrock old ridges and uplands, including those that may be cratered terrains and the rims and outer-ring depressions of large impact basins, and removed all surficial deposits to the limits of resolution of the imagery. The complementary eolian deposits form not only dunes, wind streaks, and small plains, but also broad radar-dark plains, commonly assumed to be volcanic although lacking flow morphology, whose materials appear to be thick because they are smoothly compacted into buried craters.

Hamilton, Warren B.↗