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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↗

NASA NTRS1994

Digital Modem Design Based on Multirate Filter Banks

A new approach for the architecture of an all digital modem design is presented. The key feature is a lower processing rate than that of the Nyquist rate (the input sampling rate) and even the symbol rate. The lower processing rate is achieved by the use of a parallel structure, based on multirate filter banks concepts. In this proposed scheme, matched filtering is implemented in the subbands of an analysis/synthesis filter bank.

digital modem design↗

DOE OSTI2021

Implicit Multirate GARK Methods

This article considers multirate generalized-structure additively partitioned Runge–Kutta methods for solving stiff systems of ordinary differential equations with multiple time scales. These methods treat different partitions of the system with different timesteps for a more targeted and efficient solution compared to monolithic single rate approaches. With implicit methods used across all partitions, methods must find a balance between stability and the cost of solving nonlinear equations for the stages. In order to characterize this important trade-off, we explore multirate coupling strategies, problems for assessing linear stability, and techniques to efficiently implement Newton iterations for stage equations. Unlike much of the existing multirate stability analysis which is limited in scope to particular methods, we present general statements on stability and describe fundamental limitations for certain types of multirate schemes. New implicit multirate methods up to fourth order are derived, and their accuracy and efficiency properties are verified with numerical tests.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1997

Original Size and Shape of the Sudbury Structure

This paper presents new evidence bearing on the original size and shape of the Sudbury impact structure. Current opinion is almost unanimous that the structure is a multiring basin with an original diameter of about 200 km and a circular shape that has since been shortened in a northwest-southeast direction by Penokean deformation Evidence for this interpretation, collected chiefly from north of the Sudbury Igneous Complex (SIC), includes supposed outer rings on Landsat imagery, distant occurrences of "Sudbury breccia" (generally defined as pseudotachylite), shatter cone occurrences, and outliers of Huronian sedimentary rock thought to be down-faulted rings. New data from imaging radar and field work north of the SIC, however, contradict this evidence. Radar imagery shows no signs of the supposed outer rings mapped by earlier workers on Landsat images. The most prominent ring has been found to be a chance alignment of two independent fracture sets. Radar imagery from the CCRS Convair 580, with look direction almost normal to the north rim of the SIC, shows no evidence of the rings despite strong look azimuth highlighting. Radar imagery has shown many unmapped diabase dikes north of the SIC. Several exposures of supposed Sudbury breccia are associated with these dikes or with Nipissing diabase intrusions, in some cases actually inside the dikes or directly continuous with them. They appear to be igneous intrusion breccias with no relation to impact. Shock-wave interaction at lithologic contacts cannot be invoked for most of these, because they are part of a northwest trending swarm cutting the SIC in the North Range, and hence too young for an impact origin. Similar diabase-related breccias and pseudotachylite-like veins have been found far outside the Sudbury area between Chapleau and Thessalon. Shatter cones north of the SIC are few and poorly developed, perhaps due to the coarse-grained Footwall rock, and cannot be considered a continuous zone analogous to their occurrence on the South Range in Huronian rocks. Supposed down-faulted outliers of Huronian rocks north of the SIC show no consistent relation to faulting, and the Huronian/Archean contact is locally erosional. Radar imagery and field-checking confirm Rousell's conclusion that the North Range has undergone little or no Penokean deformation. T'his implies that the plan view outline of the crater (floor of the SIC) is original. Extrapolation of the North Range as part of a circular arc leads to an impossibly great diameter. It is concluded that although Penokean deformation largely accounts for the structure's shape, the original crater was not circular and was much smaller than 200 km across.

Lowman, P. D., Jr.↗

DOE OSTI2022

A Fast Time-Stepping Strategy for Dynamical Systems Equipped with a Surrogate Model

Simulation of complex dynamical systems arising in many applications is computationally challenging due to their size and complexity. Model order reduction, machine learning, and other types of surrogate modeling techniques offer cheaper and simpler ways to describe the dynamics of these systems but are inexact and introduce additional approximation errors. In order to overcome the computational difficulties of the full complex models, on one hand, and the limitations of surrogate models, on the other, this work proposes a new accelerated time-stepping strategy that combines information from both. This approach is based on the multirate infinitesimal general-structure additive Runge--Kutta framework. The inexpensive surrogate model is integrated with a small time step to guide the solution trajectory, and the full model is treated with a large time step to occasionally correct for the surrogate model error and ensure convergence. Here, we provide a theoretical error analysis, and several numerical experiments, to show that this approach can be significantly more efficient than using only the full or only the surrogate model for the integration.

Surrogate models↗

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 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 OSTI2021

Implicit-Explicit Multirate Infinitesimal GARK Methods

This work focuses on the development of a new class of high-order accurate methods for multirate time integration of systems of ordinary differential equations. Unlike other recent work in this area, the proposed methods support mixed implicit-explicit (IMEX) treatment of the slow time scale. In addition to allowing this slow time scale flexibility, the proposed methods utilize a so-called infinitesimal formulation for the fast time scale through definition of a sequence of modified “fast" initial-value problems that may be solved using any viable algorithm. We name the proposed class as implicit-explicit multirate infinitesimal generalized-structure additive Runge--Kutta (IMEX-MRI-GARK) methods. In addition to defining these methods, we prove that they may be viewed as specific instances of GARK methods and derive a set of order conditions on the IMEX-MRI-GARK coefficients to guarantee both third and fourth order accuracy for the overall multirate method. Additionally, we provide three specific IMEX-MRI-GARK methods, two of order three and one of order four. We conclude with numerical simulations on two multirate test problems, demonstrating the methods' predicted convergence rates and comparing their efficiency against both legacy IMEX multirate schemes and recent third and fourth order implicit MRI-GARK methods.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1985

Some morphologic systematics of complex impact structures

Current measurements of the horizontal dimensions of complex meteorite structures are summarized. The measurements were used in a least squares analysis of correlations among the dimensions of the crater rings and central peaks of compact meteorites. Some geometric similarities between terrestrial complex impact structures and the large multiring basin of the planets are demonstrated, and the possible physical constraints on ring formation are discussed.

Pike, R. J.↗

NASA NTRS1990

Multirate sampled-data yaw-damper and modal suppression system design

A multirate control law synthesized algorithm based on an infinite-time quadratic cost function, was developed along with a method for analyzing the robustness of multirate systems. A generalized multirate sampled-data control law structure (GMCLS) was introduced. A new infinite-time-based parameter optimization multirate sampled-data control law synthesis method and solution algorithm were developed. A singular-value-based method for determining gain and phase margins for multirate systems was also developed. The finite-time-based parameter optimization multirate sampled-data control law synthesis algorithm originally intended to be applied to the aircraft problem was instead demonstrated by application to a simpler problem involving the control of the tip position of a two-link robot arm. The GMCLS, the infinite-time-based parameter optimization multirate control law synthesis method and solution algorithm, and the singular-value based method for determining gain and phase margins were all demonstrated by application to the aircraft control problem originally proposed for this project.

Berg, Martin C.↗

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 NTRS1997

Large-Scale Impact Cratering and Early Earth Evolution

The surface of the Moon attests to the importance of large-scale impact in its early crustal evolution. Previous models of the effects of a massive bombardment on terrestrial crustal evolution have relied on analogies with the Moon, with allowances for the presence of water and a thinner lithosphere. It is now apparent that strict lunar-terrestrial analogies are incorrect because of the "differential scaling" of crater dimensions and melt volumes with event size and planetary gravity. Impact melt volumes and "ancient cavity dimensions for specific impacts were modeled according to previous procedures. In the terrestrial case, the melt volume (V(sub m)) exceeds that of the transient cavity (V(sub tc)) at diameters > or = 400 km. This condition is reached on the Moon only with transient cavity diameters > or = 3000 km, equivalent to whole Moon melting. The melt volumes in these large impact events are minimum estimates, since, at these sizes, the higher temperature of the target rocks at depth will increase melt production. Using the modification-scaling relation of Croft, a transient cavity diameter of about 400 km in the terrestrial environment corresponds to an expected final impact "basin" diameter of about 900 km. Such a "basin" would be comparable in dimensions to the lunar basin Orientale. This 900-km "basin" on the early Earth, however, would not have had the appearance of Orientale. It would have been essentially a melt pool, and, morphologically, would have had more in common with the palimpsests structures on Callisto and Ganymede. With the terrestrial equivalents to the large multiring basins of the Moon being manifested as muted palimpsest-like structures filled with impact melt, it is unlikely they played a role in establishing the freeboard on the early Earth. The composition of the massive impact melt sheets (> 10 (exp 7) cu km) produced in "basin-forming" events on the early Earth would have most likely ranged from basaltic to more mafic for the largest impacts, where the melt volume would have reached well into the mantle. Any contribution from adiabatic melting or shock heating of the asthenosphere would have had similar mafic compositions. The depth of the melt sheets is unknown but would have been in the multilkilometer range. Bodies of basaltic melt > or = 300 m thick differentiate in the terrestrial environment, with the degree of differentiation being a function of the thickness of the body. We therefore expect that these thick, closed-system melt pools would have differentiated into an ultramafic-mafic base and felsic top. If only 10% of the impact melt produced in a single event creating a 400-km diameter transient cavity evolved into felsic differentiates, they would be comparable in volume to the Columbia River basalts. It has been estimated that at least 200 impact events of this size or larger occurred on the early Earth during a period of heavy bombardment. We speculate that these massive differentiated melt sheets may have had a role in the formation of the initial felsic component of the Earth's crust. Additional information is contained in the original.

Grieve, R. A. F.↗

DOE OSTI2024

Haasttse‐baad Tessera Ring Complex: A Valhalla‐Type Impact Structure on Venus?

Abstract Venus preserves ∼1,000 impact craters, yet to date no impact basins larger than 300 km in diameter—common in the oldest terrains on Mercury, Mars and the Moon—are recognized on Venus. The tessera terrain is Venus' oldest recognized terrain. We describe a ∼1,500 km‐diameter concentric ring‐graben complex preserved on Haasttse‐baad Tessera, Venus that we identify as the Haasttse‐baad Tessera Ring Complex (HTRC). Based on geologic relations and numerical modeling, we propose that the HTRC may represent a Valhalla‐type multiring impact basin formed late during the evolution of its host ribbon‐tessera terrain (rtt). Formation of Valhalla‐type impact basins could involve a unique three‐layer target rheology with a thin elastic layer above a low viscosity layer above a deep strong layer. This multi‐layer rheological sandwich is consistent with crustal rheology previously proposed for the formation of Venus' rtt. If the HTRC is a Valhalla‐type impact basin, it would be Venus' oldest, and currently largest, impact structure, providing a rare window into Venus' ancient past and with implications for early crustal processes on Venus.

58 GEOSCIENCES↗

NASA NTRS1985

The scaling of complex craters

The empirical relation between the transient crater diameter (Dg) and final crater diameter (Dr) of complex craters and basins is estimated using cumulative terrace widths, central uplift diameters, continuous ejecta radii, and transient crater reconstructions determined from lunar and terrestrial impact structures. The ratio Dg/Dr is a power law function of Dr, decreasing uniformly from unity at the diameter of the simple-complex crater morphology transition to about 0.5 for large multiring basins like Imbrium on the moon. The empirical constants in the Dg/Dr relation are interpreted physically to mean that the position of the final rim relative to the transient crater, and hence the extent of collapse, is controlled or greatly influenced by the properties of the zone of dissociated material produced by the impact shock. The continuity of the Dg/Dr relation over the entire spectrum of morphologic types from complex craters to multiring basins implies that the rims of all these structures form in the same tectonic environment despite morphologic differences.

Croft, S. K.↗

NASA NTRS1976

High-explosive cratering analogs for bowl-shaped, central uplift, and multiring impact craters

The paper describes six experimental explosion craters in terms of their basic morphology, subsurface structural deformation, and surrounding ejecta blanket. These craters exhibit one or more of the following features: bowl shapes with underlying breccia lens, central uplifts, multirings, terraced walls, rim strata, zones of concentric rim deformation, inner continuous ground cover of ejecta blankets formed by overturned flaps, secondary cratering, and fused alluvium. These craters were formed by large shock wave energy transfers at or near zero heights-of-burst, and it is possible that impact craters with analogous morphologic and structural features may have formed under similar surface energy transfer conditions.

Roddy, D. J.↗

NASA NTRS1993

Chicxulub multiring impact basin - Size and other characteristics derived from gravity analysis

The buried Chicxulub impact structure in Mexico, which is linked to the Cretaceous-Tertiary (K-T) boundary layer, may be significantly larger than previously suspected. Reprocessed gravity data over Northern Yucatan reveal three major rings and parts of a fourth ring, spaced similarly to those observed at multiring impact basins on other planets. The outer ring, probably corresponding to the basin's topographic rim, is almost 300 kilometers in diameter, indicating that Chicxulub may be one of the largest impact structures produced in the inner solar system since the period of early bombardment ended nearly 4 billion years ago.

Sharpton, Virgil L.↗

NASA NTRS1992

Sudbury project (University of Muenster-Ontario Geological Survey): New investigations on Sudbury breccia

Sudbury breccias occur as discordant dike breccias within the footwall rocks of the Sudbury structure, which is regarded as the possible remnant of a multiring basin. Exposures of Sudbury breccias in the North Range are known up to a radial distance of 60-80 km from the Sudbury Igneous Complex (SIC). The breccias appear more frequent within a zone of 10 km adjacent to the SIC and a further zone located about 20-33 km north of the structure. From differences in the structure of the breccias, as for example the size of the breccia dikes, contact relationships between breccia and country rock as well as between different breccia dikes, fragment content, and fabric of the ground mass, as seen in this section, the Sudbury Breccias have been classified into four different types. (1) Early breccias with a clastic/crystalline matrix comprise small dikes ranging in size from approx. 1 cm to max. 20 cm. (2) Polymict breccias with a clastic matrix represent the most common type of Sudbury breccia. The thickness of the dikes varies from several tens of centimeters to a few meters but can also extend to more than 100 m in the case of the largest known breccia dike. Contacts with country rock are sharp or gradational. Heterogenous matrix consisting of a fine-grained rock flour displays nonoriented textures as well as extreme flow lines. Chemical analysis substantiates at least some mixing with allochthonous material. (3) Breccias with a crystalline matrix are a subordinate type of Sudbury breccia. According to petrographical and chemical differences, three subtypes have been separated. (4) Late breccias with a clastic matrix are believed to represent the latest phase of brecciation. Two subtypes have been distinguished due to differences in the fragment content.

Mueller-Mohr, V.↗

NASA NTRS1977

Large-scale impact and explosion craters - Comparisons of morphological and structural analogs

Crater studies indicate now that there are a broad set of morphological and structural analogs which occur in both impact and explosion craters. A description is presented of impact and explosion analogs for three basic crater types, including bowl-shaped craters, flat-floored craters with central uplift, and flat-floored craters with multirings. A systematic documentation is provided of the more critical morphological and structural analogs common between large natural bowl-shaped impact and explosion craters, between central uplift impact and explosion craters, and between multiring impact and explosion craters. The data presented consist of a set of published and unpublished cratering studies assembled into a single ordered outline with each crater described in the same format and graphic style.

Roddy, D. J.↗