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At least 1,405 records · Page 78
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Fast Quasi-Static Time-Series (QSTS) for yearlong PV impact studies using vector quantization

The rapidly growing penetration levels of distributed photovoltaic (PV) systems requires more comprehensive studies to understand their impact on distribution feeders. IEEE P.1547 highlights the need for Quasi-Static Time Series (QSTS) simulation in conducting distribution impact studies for distributed resource interconnection. Unlike conventional scenario-based simulation, the time series simulation can realistically assess time-dependent impacts such as the operation of various controllable elements (e.g. voltage regulating tap changers) or impacts of power fluctuations. However, QSTS simulations are still not widely used in the industry because of the computational burden associated with running yearlong simulations at a 1-s granularity, which is needed to capture device controller effects responding to PV variability. This study presents a novel algorithm that reduces the number of times that the non-linear 3-phase unbalanced AC power flow must be solved by storing and reassigning power flow solutions as it progresses through the simulation. Each unique power flow solution is defined by a set of factors affecting the solution that can easily be queried. We demonstrate a computational time reduction of 98.9% for a yearlong simulation at 1-s resolution with minimal errors for metrics including: number of tap changes, capacitor actions, highest and lowest voltage on the feeder, line losses, and ANSI voltage violations. Finally, the key contribution of this work is the formulation of an algorithm capable of: (i) drastically reducing the computational time of QSTS simulations, (ii) accurately modeling distribution system voltage-control elements with hysteresis, and (iii) efficiently compressing result time series data for post-simulation analysis.

14 SOLAR ENERGY↗
DOE OSTI2021

Surface Dynamics of Charge Transport in LaAlO 3 /SrTiO 3 with Time-Resolved Kelvin Probe Force Microscopy

Time-resolved Kelvin probe force microscopy (tr-KPFM) was used to map surface potential dynamics in LAO/STO under its critical thickness, where it acts as an insulator, as polarizing and depolarizing electric fields were applied to planar electrodes in ambient conditions. Two time constants, for polarization and relaxation (i.e., depolarization) each, were derived and were shown to be independent of the direction of electrical field, revealing the reproducibility and recovery of the surfaces. Ambient aging or recent electrical history did not change the surface kinetics as determined by tr-KPFM. During polarization, the faster time constant (~3–6 s) is likely associated with the transport of H+ ions through the full length of the channel. The slower time constant (~40–50 s), on the other hand, is observed across only half the channel width near the higher-potential–more positive–electrode, which is likely associated with an electrochemical reaction such as the dissociation of water. This slower time constant drops to ~10–20 s toward the middle of the channel which could represent the transport of OH– ions. Furthermore, during relaxation, the fast time constant is consistent with polarization and is correlated to the same mechanism while the slower time constant is higher than it was during polarization and may represent the reabsorption of moisture from the atmosphere.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Dynamic time-warping correction for shifts in ultrahigh resolving power ion mobility spectrometry and structures for lossless ion manipulations

Detection of arrival time shifts between ion mobility spectrometry (IMS) separations can limit achievable resolving power (Rp), particularly when multiple separations are summed or averaged, as commonly practiced. Such variations are more apparent in higher Rp measurements, and are particularly evident in long path length traveling wave structures for lossless ion manipulations (SLIM) IMS due to their typically much longer separation times. Here we explore the utility of a data processing approaches employing linear alignment (LA) and nonlinear dynamic time warping (DTW) of IMS separations to correct for variations between separations, such as due to pressure fluctuations. For multipass SLIM IMS separations, where narrow mobility range measurements have arrival times that can extend to several seconds, the LA approach effectively corrected for such variations, and significantly improvement Rp for summed separations. However, LA was much less effective for high Rp broad mobility range separations, such as obtained with multilevel SLIM IMS. Changes in IMS arrival times ions were observed to be correlated with small pressure changes, with approximately 0.6% relative arrival time shifts being common, sufficient to result in a loss of Rp for summed separations. Comparison of the approaches showed DTW alignment performed similarly to LA when used over a narrow mobility range, but was significantly better (providing narrower peaks and higher signal intensities) for wide mobility range data. We found the DTW approach increased Rp by as much as 115% for measurements in which 50 IMS separations over 2 seconds were summed, and leading to a large improvement in effective Rp. We conclude that DTW is superior to LA for ultrahigh resolution broad mobility range SLIM IMS separations, correcting for ion arrival time shifts regardless of the cause. Our tool is publicly available for use with universal ion mobility format (.UIMF) and text (.txt) files.

Data alignment, dynamic time warping, ion mobility↗
DOE OSTI2013

Processing optimization and sintering time dependent magnetic and optical behaviors of Aurivillius Bi{sub 5}Ti{sub 3}FeO{sub 15} ceramics

Aurivillius Bi{sub 5}Ti{sub 3}FeO{sub 15} (BTF) ceramics were synthesized using the conventional solid state reaction method by optimizing excess of Bi{sub 2}O{sub 3} and sintering time. Their structures, magnetic, and optical properties were investigated in detail. The optimum process to sinter pure Aurivillius BTF ceramics was confirmed to be 3 wt. % excess Bi{sub 2}O{sub 3} to compensate the Bi volatilization at 1050 Degree-Sign C for 240 min (BTF-240M). The microstructure and crystalline structure of the BTF ceramics had little dependence on the sintering time from the x-ray diffraction (XRD) and scanning electron microscopic data. Nevertheless, the magnetic and optical properties were closely related with the sintering time. The overall magnetic behavior of these BTF ceramics was superparamagnetic (SPM), whereas there were unambiguous clues for the existence of antiferromagnetic (AFM) interactions. However, whether the SPM behavior was intrinsic or arised from a tiny amount of spinel Fe{sub 3}O{sub 4} impurity phase cannot be thoroughly ruled out in the XRD detection limit in the present stage. The AFM interactions were weakened upon extending the sintering time. The effective magnetic moment ({mu}{sub eff}), however, demonstrated different dependency on the sintering time. It increased with the sintering time from 80 min to 240 min, and then dropped with further extending the sintering time. Compared with other BTF ceramics, the BTF-240M ceramic showed the highest values of the refractive index n and real part {epsilon}{sub 1}, as well as the lowest ones of the extinction coefficient k and imagine part {epsilon}{sub 2} in whole photon energy range. Finally, a direct inter-band transition was confirmed for these BTF ceramics and optical energy band gaps were determined to be about 3.08, 3.18, and 3.39 eV for 80 min, 150 min, and 240 min sintered BTF ceramics, respectively, yet abnormal optical behavior was observed in BTF-360M ceramic.

36 MATERIALS SCIENCE↗
DOE OSTI2013

Self-similar space-time evolution of an initial density discontinuity

The space-time evolution of an initial step-like plasma density variation is studied. We give particular attention to formulate the problem in a way that opens for the possibility of realizing the conditions experimentally. After a short transient time interval of the order of the electron plasma period, the solution is self-similar as illustrated by a video where the space-time evolution is reduced to be a function of the ratio x/t. Solutions of this form are usually found for problems without characteristic length and time scales, in our case the quasi-neutral limit. By introducing ion collisions with neutrals into the numerical analysis, we introduce a length scale, the collisional mean free path. We study the breakdown of the self-similarity of the solution as the mean free path is made shorter than the system length. Analytical results are presented for charge exchange collisions, demonstrating a short time collisionless evolution with an ensuing long time diffusive relaxation of the initial perturbation. For large times, we find a diffusion equation as the limiting analytical form for a charge-exchange collisional plasma, with a diffusion coefficient defined as the square of the ion sound speed divided by the (constant) ion collision frequency. The ion-neutral collision frequency acts as a parameter that allows a collisionless result to be obtained in one limit, while the solution of a diffusion equation is recovered in the opposite limit of large collision frequencies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Time-dependent potential-functional embedding theory

We introduce a time-dependent potential-functional embedding theory (TD-PFET), in which atoms are grouped into subsystems. In TD-PFET, subsystems can be propagated by different suitable time-dependent quantum mechanical methods and their interactions can be treated in a seamless, first-principles manner. TD-PFET is formulated based on the time-dependent quantum mechanics variational principle. The action of the total quantum system is written as a functional of the time-dependent embedding potential, i.e., a potential-functional formulation. By exploiting the Runge-Gross theorem, we prove the uniqueness of the time-dependent embedding potential under the constraint that all subsystems share a common embedding potential. We derive the integral equation that such an embedding potential needs to satisfy. As proof-of-principle, we demonstrate TD-PFET for a Na{sub 4} cluster, in which each Na atom is treated as one subsystem and propagated by time-dependent Kohn-Sham density functional theory (TDDFT) using the adiabatic local density approximation (ALDA). Our results agree well with a direct TDDFT calculation on the whole Na{sub 4} cluster using ALDA. We envision that TD-PFET will ultimately be useful for studying ultrafast quantum dynamics in condensed matter, where key regions are solved by highly accurate time-dependent quantum mechanics methods, and unimportant regions are solved by faster, less accurate methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Towards time-dependent current-density-functional theory in the non-linear regime

Time-Dependent Density-Functional Theory (TDDFT) is a well-established theoretical approach to describe and understand irradiation processes in clusters and molecules. However, within the so-called adiabatic local density approximation (ALDA) to the exchange-correlation (xc) potential, TDDFT can show insufficiencies, particularly in violently dynamical processes. This is because within ALDA the xc potential is instantaneous and is a local functional of the density, which means that this approximation neglects memory effects and long-range effects. A way to go beyond ALDA is to use Time-Dependent Current-Density-Functional Theory (TDCDFT), in which the basic quantity is the current density rather than the density as in TDDFT. This has been shown to offer an adequate account of dissipation in the linear domain when the Vignale-Kohn (VK) functional is used. Here, we go beyond the linear regime and we explore this formulation in the time domain. In this case, the equations become very involved making the computation out of reach; we hence propose an approximation to the VK functional which allows us to calculate the dynamics in real time and at the same time to keep most of the physics described by the VK functional. We apply this formulation to the calculation of the time-dependent dipole moment of Ca, Mg and Na{sub 2}. Our results show trends similar to what was previously observed in model systems or within linear response. In the non-linear domain, our results show that relaxation times do not decrease with increasing deposited excitation energy, which sets some limitations to the practical use of TDCDFT in such a domain of excitations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Couplings between hierarchical conformational dynamics from multi-time correlation functions and two-dimensional lifetime spectra: Application to adenylate kinase

An analytical method based on a three-time correlation function and the corresponding two-dimensional (2D) lifetime spectrum is developed to elucidate the time-dependent couplings between the multi-timescale (i.e., hierarchical) conformational dynamics in heterogeneous systems such as proteins. In analogy with 2D NMR, IR, electronic, and fluorescence spectroscopies, the waiting-time dependence of the off-diagonal peaks in the 2D lifetime spectra can provide a quantitative description of the dynamical correlations between the conformational motions with different lifetimes. The present method is applied to intrinsic conformational changes of substrate-free adenylate kinase (AKE) using long-time coarse-grained molecular dynamics simulations. It is found that the hierarchical conformational dynamics arise from the intra-domain structural transitions among conformational substates of AKE by analyzing the one-time correlation functions and one-dimensional lifetime spectra for the donor-acceptor distances corresponding to single-molecule Förster resonance energy transfer experiments with the use of the principal component analysis. In addition, the complicated waiting-time dependence of the off-diagonal peaks in the 2D lifetime spectra for the donor-acceptor distances is attributed to the fact that the time evolution of the couplings between the conformational dynamics depends upon both the spatial and temporal characters of the system. The present method is expected to shed light on the biological relationship among the structure, dynamics, and function.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Time lagged ordinal partition networks for capturing dynamics of continuous dynamical systems

We investigate a generalised version of the recently proposed ordinal partition time series to network transformation algorithm. First, we introduce a fixed time lag for the elements of each partition that is selected using techniques from traditional time delay embedding. The resulting partitions define regions in the embedding phase space that are mapped to nodes in the network space. Edges are allocated between nodes based on temporal succession thus creating a Markov chain representation of the time series. We then apply this new transformation algorithm to time series generated by the Rössler system and find that periodic dynamics translate to ring structures whereas chaotic time series translate to band or tube-like structures—thereby indicating that our algorithm generates networks whose structure is sensitive to system dynamics. Furthermore, we demonstrate that simple network measures including the mean out degree and variance of out degrees can track changes in the dynamical behaviour in a manner comparable to the largest Lyapunov exponent. We also apply the same analysis to experimental time series generated by a diode resonator circuit and show that the network size, mean shortest path length, and network diameter are highly sensitive to the interior crisis captured in this particular data set.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Dynamics of spallation during femtosecond laser ablation studied by time-resolved reflectivity with double pump pulses

The dynamics of photomechanical spallation during femtosecond laser ablation of fused silica was studied by time-resolved reflectivity with double pump pulses. Oscillation of reflectivity was caused by interference between the probe pulses reflected at the sample surface and the spallation layer, and was enhanced when the surface was irradiated with the second pump pulse within a time interval, Δτ, of several picoseconds after the first pump pulse. However, as Δτ was increased, the oscillation amplitude decreased with an exponential decay time of 10 ps. The oscillation disappeared when Δτ exceeded 20 ps. This result suggests that the formation time of the spallation layer is approximately 10 ps. A second pump pulse with Δτ shorter than 10 ps excites the bulk sample. The spallation layer that is photo-excited by the first and second pump pulses is separated afterward. In contrast, a pulse with Δτ longer than the formation time excites and breaks up the spallation layer that has already been separated from the bulk. The formation time of the spallation layer, as determined in this experiment, is attributed to the characteristic time of the mechanical equilibration corresponding to the thickness divided by the sound velocity of the photo-excited layer.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

TIME SERIES ANALYSIS OF GAMMA-RAY BLAZARS AND IMPLICATIONS FOR THE CENTRAL BLACK-HOLE MASS

Radiation from the blazar class of active galactic nuclei (AGNs) exhibits fast time variability which is usually ascribed to instabilities in the emission region near the central supermassive black hole. The variability time scale is generally faster in higher energy region, and data recently provided by the Fermi Gamma-ray Space Telescope in the GeV energy band enable a detailed study of the temporal behavior of AGN. Due to its wide field-of-view in the scanning mode, most sky regions are observed for several hours per day and daily light curves of many AGNs have been accumulated for more than 4 yr. In this paper we investigate the time variability of 15 well-detected AGNs by studying the normalized power spectrum density of their light curves in the GeV energy band. One source, 3C 454.3, shows a specific time scale of 6.8 Multiplication-Sign 10{sup 5} s, and this value suggests, assuming the internal shock model, a mass for the central black hole of (10{sup 8}-10{sup 10}) M{sub Sun} which is consistent with other estimates. It also indicates the typical time interval of ejected blobs is (7-70) times the light crossing time of the Schwarzschild radius.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Characterization of the CMS Endcap Timing Layer readout chip prototype with charge injection

We present the characterization of a readout Application-Specific Integrated Circuit (ASIC) for the CMS Endcap Timing Layer (ETL) of the High-Luminosity LHC upgrade with charge injection. The ASIC, named ETROC and developed in a 65 nm CMOS technology, reads out a 16× 16 pixel matrix of the Low-Gain Avalanche Detector (LGAD). The jitter contribution from ETROC is required to be below 40 ps to achieve the 50 ps overall time resolution per hit. The analog readout circuits in ETROC consist of the preamplifier and the discriminator. The preamplifier handles the LGAD charge signal with the most probable value of around 15 fC. The discriminator generates the digital pulse, which provides the Time-Of-Arrival (TOA, leading edge) and Time-Over-Threshold (TOT, pulse width) information. The prototype of ETROC (ETROC0) that implements a single channel of analog readout circuits has been evaluated with charge injection. The jitter of the analog readout circuits, measured from the discriminator's leading edge, is better than 16 ps for a charge larger than 15 fC with the sensor capacitance. The time walk resulting from different pulse heights can be corrected using the TOT measurement. The time resolution distribution has a standard deviation of 29 ps after the time-walk correction from the charge injection. At room temperature, the preamplifier's power consumption is measured to be 0.74 mW and 1.53 mW per pixel in the low- and high-power mode, respectively. Finally, the measured power consumption of the discriminator is 0.84 mW per pixel. With the ASIC alone or the LGAD sensor, The characterization performances fulfill the ETL's challenging requirements.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

Sample-minimizing co-flow cell for time-resolved pump–probe X-ray solution scattering

A fundamental problem in biological sciences is understanding how macromolecular machines work and how the structural changes of a molecule are connected to its function. Time-resolved techniques are vital in this regard and essential for understanding the structural dynamics of biomolecules. Time-resolved small- and wide-angle X-ray solution scattering has the capability to provide a multitude of information about the kinetics and global structural changes of molecules under their physiological conditions. However, standard protocols for such time-resolved measurements often require significant amounts of sample, which frequently render time-resolved measurements impossible. A cytometry-type sheath co-flow cell, developed at the BioCARS 14-ID beamline at the Advanced Photon Source, USA, allows time-resolved pump–probe X-ray solution scattering measurements to be conducted with sample consumption reduced by more than ten times compared with standard sample cells and protocols. The comparative capabilities of the standard and co-flow experimental setups were demonstrated by studying time-resolved signals in photoactive yellow protein.

36 MATERIALS SCIENCE↗
DOE OSTI2013

Molecular radiotherapy: The NUKFIT software for calculating the time-integrated activity coefficient

Purpose: Calculation of the time-integrated activity coefficient (residence time) is a crucial step in dosimetry for molecular radiotherapy. However, available software is deficient in that it is either not tailored for the use in molecular radiotherapy and/or does not include all required estimation methods. The aim of this work was therefore the development and programming of an algorithm which allows for an objective and reproducible determination of the time-integrated activity coefficient and its standard error.Methods: The algorithm includes the selection of a set of fitting functions from predefined sums of exponentials and the choice of an error model for the used data. To estimate the values of the adjustable parameters an objective function, depending on the data, the parameters of the error model, the fitting function and (if required and available) Bayesian information, is minimized. To increase reproducibility and user-friendliness the starting values are automatically determined using a combination of curve stripping and random search. Visual inspection, the coefficient of determination, the standard error of the fitted parameters, and the correlation matrix are provided to evaluate the quality of the fit. The functions which are most supported by the data are determined using the corrected Akaike information criterion. The time-integrated activity coefficient is estimated by analytically integrating the fitted functions. Its standard error is determined assuming Gaussian error propagation. The software was implemented using MATLAB.Results: To validate the proper implementation of the objective function and the fit functions, the results of NUKFIT and SAAM numerical, a commercially available software tool, were compared. The automatic search for starting values was successfully tested for reproducibility. The quality criteria applied in conjunction with the Akaike information criterion allowed the selection of suitable functions. Function fit parameters and their standard error estimated by using SAAM numerical and NUKFIT showed differences of <1%. The differences for the time-integrated activity coefficients were also <1% (standard error between 0.4% and 3%). In general, the application of the software is user-friendly and the results are mathematically correct and reproducible. An application of NUKFIT is presented for three different clinical examples.Conclusions: The software tool with its underlying methodology can be employed to objectively and reproducibly estimate the time integrated activity coefficient and its standard error for most time activity data in molecular radiotherapy.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2016

Technical Note: High temporal resolution characterization of gating response time

Purpose: Low temporal latency between a gating ON/OFF signal and the LINAC beam ON/OFF during respiratory gating is critical for patient safety. Here the authors describe a novel method to precisely measure gating lag times at high temporal resolutions. Methods: A respiratory gating simulator with an oscillating platform was modified to include a linear potentiometer for position measurement. A photon diode was placed at linear accelerator isocenter for beam output measurement. The output signals of the potentiometer and diode were recorded simultaneously at 2500 Hz with an analog to digital converter for four different commercial respiratory gating systems. The ON and OFF of the beam signal were located and compared to the expected gating window for both phase and position based gating and the temporal lag times extracted. Results: For phase based gating, a real-time position management (RPM) infrared marker tracking system with a single camera and a RPM system with a stereoscopic camera were measured to have mean gate ON/OFF lag times of 98/90 and 86/44 ms, respectively. For position based gating, an AlignRT 3D surface system and a Calypso magnetic fiducial tracking system were measured to have mean gate ON/OFF lag times of 356/529 and 209/60 ms, respectively. Conclusions: Temporal resolution of the method was high enough to allow characterization of individual gate cycles and was primary limited by the sampling speed of the data recording device. Significant variation of mean gate ON/OFF lag time was found between different gating systems. For certain gating devices, individual gating cycle lag times can vary significantly.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

AIR Algebraic Multigrid for a Space-Time Hybridizable Discontinuous Galerkin Discretization of Advection(-Diffusion)

This article investigates the efficiency, robustness, and scalability of approximate ideal restriction (AIR) algebraic multigrid as a preconditioner in the all-at-once solution of a space-time hybridizable discontinuous Galerkin discretization of advection-dominated flows. The motivation for this study is that the time-dependent advection-diffusion equation can be seen as a “steady” advection-diffusion problem in $(d+1)$-dimensions and AIR has been shown to be a robust solver for steady advection-dominated problems. Numerical examples demonstrate the effectiveness of AIR as a preconditioner for advection-diffusion problems on fixed and time-dependent domains, using both slab-by-slab and all-at-once space-time discretizations, and in the context of uniform and space-time adaptive mesh refinement. A closer look at the geometric coarsening structure that arises in AIR also explains why AIR can provide robust, scalable, space-time convergence on advective and hyperbolic problems, while most multilevel parallel-in-time schemes struggle with such problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Adaptive Time Step Control for Multirate Infinitesimal Methods

Multirate methods have been used for decades to temporally evolve initial-value problems in which different components evolve on distinct time scales, and thus use of different step sizes for these components can result in increased computational efficiency. Generally, such methods select these different step sizes based on experimentation or stability considerations. For problems that evolve on a single time scale, adaptivity approaches that strive to control local temporal error are widely used to achieve numerical results of a desired accuracy with minimal computational effort, while alleviating the need for manual experimentation with different time step sizes. However, there is a notable gap in the publication record on the development of adaptive time step controllers for multirate methods. In this paper, we extend the single-rate controller work of Gustafsson [ACM Trans. Math. Software, 20 (1994), pp. 496-517] to the multirate method setting. Specifically, we develop controllers based on polynomial approximations to the principal error functions for both the "fast" and "slow" time scales within multirate infinitesimal (MRI) methods. We additionally investigate a variety of approaches for estimating the errors arising from each time scale within MRI methods. We then numerically evaluate the proposed multirate controllers and error estimation strategies on a range of multirate test problems, comparing their performance against an estimated optimal performance. Through this work, we combine the most performant of these approaches to arrive at a set of multirate adaptive time step controllers that robustly achieve desired solution accuracy with minimal computational effort.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Parallel-in-Time Solution of Scalar Nonlinear Conservation Laws

Here, we consider the parallel-in-time solution of scalar nonlinear conservation laws in one spatial dimension. The equations are discretized in space with a conservative finite-volume method using weighted essentially nonoscillatory (WENO) reconstructions, and in time with high-order explicit Runge–Kutta methods. The solution of the global, discretized space-time problem is sought via a nonlinear iteration that uses a novel linearization strategy in cases of nondifferentiable equations. Under certain choices of discretization and algorithmic parameters, the nonlinear iteration coincides with Newton’s method, although, more generally, it is a preconditioned residual correction scheme. At each nonlinear iteration, the linearized problem takes the form of a certain discretization of a linear conservation law over the space-time domain in question. An approximate parallel-in-time solution of the linearized problem is computed with a single multigrid reduction-in-time (MGRIT) iteration; however, any other effective parallel-in-time method could be used in its place. The MGRIT iteration employs a novel coarse-grid operator that is a modified conservative semi-Lagrangian discretization and generalizes those we have developed previously for nonconservative scalar linear hyperbolic problems. Numerical tests are performed for the inviscid Burgers and Buckley–Leverett equations. For many test problems, the solver converges in just a handful of iterations with a convergence rate independent of mesh resolution, including problems with (interacting) shocks and rarefactions.

97 MATHEMATICS AND COMPUTING↗