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Hybrid eigensolvers for nuclear configuration interaction calculations

We examine and compare several iterative methods for solving large-scale eigenvalue problems arising from nuclear structure calculations. In particular, we discuss the possibility of using block Lanczos method, a Chebyshev filtering based subspace iterations and the residual minimization method accelerated by direct inversion of iterative subspace (RMM-DIIS) and describe how these algorithms compare with the standard Lanczos algorithm and the locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm. Although the RMM-DIIS method does not exhibit rapid convergence when the initial approximations to the desired eigenvectors are not sufficiently accurate, it can be effectively combined with either the block Lanczos or the LOBPCG method to yield a hybrid eigensolver that has several desirable properties. We will describe a few practical issues that need to be addressed to make the hybrid solver efficient and robust.

97 MATHEMATICS AND COMPUTING↗

Influence of silicon infiltration conditions on microstructure and mechanical properties in binder jet 3D printed SiC

Atmosphere, temperature, and hold time were varied for silicon infiltrated binder jet 3D printed SiC preforms. A two-step infiltration process optimized infiltration. The first step at 1450 °C under vacuum facilitated improved wetting. The second step at elevated temperature in argon advanced infiltration while suppressing vaporization. Variation of the second-step temperature (1550–1750 °C) and hold time revealed that 1550 °C for 1 h in argon following initial vacuum treatment yielded the highest silicon uptake ratio (∼96 %) with minimal residual porosity and strengths of 150–180 MPa. Flexural strength was either stable or improved with elevated temperatures up to 1000°C. In contrast, higher temperatures or extended hold times led to increased silicon vaporization and pores. The optimized process was applied to formulations with extra carbon to enhance SiC content and interconnectedness through reaction bonding, which corresponded to increased flexural strength. These findings provide guidance for silicon infiltration in additively manufactured SiC.

Yoon, Bola [ORNL] (ORCID:0000000260875373)↗

Additive manufacturing of AISI M2 tool steel by binder jetting (BJ): Investigation of microstructural and mechanical properties

The presented research demonstrates for the first time the successful processing of AISI M2 tool steel by binder jetting, a promising additive manufacturing technique capable of producing complex shapes with minimal residual stresses and isotropic properties. The optimal printing parameters were explored by varying processing parameters such as the binder saturation (45 %–105 %), binder set time (0 to 10 s), targeted bed temperature (50–60 °C), oscillator (2600–2750 rpm), recoater (20–28 mm/s), and roller speeds (200–300 rpm). Microstructural characterization and evaluation of mechanical properties of binder jetted parts were performed using x-ray diffraction (XRD), scanning electron microscopy (SEM), and energy dispersive spectroscopy (EDS) to study their chemical composition, powder morphology, microstructure, carbide morphologies, relative density, hardness, compressive strength, and ductility. Two powder sizes (5 and 10 μm) were used, and sintering was performed at varying temperatures (1270, 1280, and 1300 °C) and durations (60 and 120 min), followed by a furnace, air, and water cooling. An optimum hardness of ~970 HV was obtained when parts were sintered at 1270 °C for 60 min, followed by water quenching. Impressive compressive strength of ~ 3580 MPa was observed in the sample sintered at 1280 °C for 60 min duration, followed by air cooling. Furnace-cooled parts showed the highest density of ~95 %, whereas the relative density of air- and water-cooled parts varied between ~91 to 93.50 %, respectively. The microstructure of sintered samples revealed the formation of M 6 C stable carbide, M 2 C metastable carbide, MC as a secondary carbide, and a-Fe matrix, which contributed to the observed increase in mechanical properties.

36 MATERIALS SCIENCE↗

Low Peripheral Blood Counts and Elevated Proinflammatory Cytokines Signal a Poor CD19 Chimeric Antigen Receptor T-cell Response in Acute Lymphoblastic Leukemia

CD19 chimeric antigen receptor T-cell (CAR-T) therapy has significantly improved outcomes for patients with relapsed/refractory B-cell acute lymphoblastic leukemia (R/R B-ALL). However, approximately 20% of patients fail to achieve a complete remission (CR), and some develop severe, life-threatening toxicities. Understanding the biological mechanisms underlying both dysfunctional responses and severe toxicity is essential for optimizing patient management and improving therapeutic efficacy. This study aimed to (1) characterize cytokine profiles associated with dysfunctional responses and severe toxicity following CAR-T infusion, (2) examine the timing and trajectory of cytokine changes in relation to treatment outcomes, and evaluate potential strategies for mitigating toxicity and treatment failure. We conducted a comprehensive analysis of serum cytokine profiles in 86 adult and pediatric patients undergoing autologous CD19 CAR-T therapy for B-ALL. Patients were categorized into three groups: (1) Dysfunctional response—Patients who failed to achieve a minimal residual disease-negative CR (MRD-CR) by Day 63 or who experienced recurrence of CD19+ disease in the setting ongoing CAR-T cell detection before Day 63. (2) Functional response with severe cytokine release syndrome (CRS) and/or neurotoxicity (NTX)—Patients with best response of MRD-CR by Day 63 who experienced grade 3 or higher CRS or NTX. (3) Functional response without severe CRS or NTX—Patients with best response of MRD-CR by Day 63 who did not experience grade =3 CRS or NTX. Cytokine levels were measured during the first-week postinfusion and correlated with treatment efficacy, toxicity outcomes, complete blood counts, and CAR-T expansion dynamics. This analysis aimed to better understand how cytokine profiles relate to patient outcomes and immune responses in CAR-T therapy. Patients with dysfunctional response exhibited decreased neutrophils, platelets, and levels of granulocytic cytokines (suggestive of low bone marrow reserve) alongside elevated pro-inflammatory cytokines by Day 1. Functional response with severe toxicity patients showed a progressive rise in proinflammatory cytokines, reaching similar levels to dysfunctional response patients by Day 7. We observed that high cytokines at both the Day 1 and Day 7 time points were associated with poor survival. These findings remained significant when adjusting for high disease burden, a known predictor of severe inflammatory toxicity and lack of response. Early post-CAR-T infusion inflammation is associated with both dysfunctional response and severe toxicity—even after adjusting for disease burden. This suggests that inflammation, in addition to disease burden, plays a role in determining patient outcome. Therefore, strategies aimed at reducing the pro-inflammatory state prior to or early after CAR-T cell infusion may improve outcomes for R/R B-ALL patients.

Serum cytokines↗

Experimental and simulated heating in nanocrystalline diamond charge exchange injection films using an electron beam to mimic SNS conditions

Nanocrystalline diamond (NCD) foils have been in use at the Spallation Neutron Source as primary stripper foils for charge exchange injection since the machine’s inception. NCD’s low atomic number leads to reduced beam scattering while still being easy to handle, as opposed to even lighter elements. NCD foils also have the benefit of being free-standing, and rigid when grown under the right conditions to minimize residual stresses. This study overviews a method to mimic the Spallation Neutron Source (SNS) beam and characterize thermally driven failure of NCD foils. To do this, a foil test stand was developed with in situ diagnostics that tracks signs of foil sublimation and thinning. The foil test stand’s electron beam is equated to the SNS beamline by comparing peak deposited energy densities for both beams. Post-mortem testing is also conducted to help elucidate changes the NCD foils undergo during exposure to the beam. Further, a COMSOL simulation was also developed as a method to assess potential future changes to the NCD film and predict how changes to beam conditions will effect foil temperatures. This method allows for examination of the NCD foil’s thermal limits and can be used to assess future changes to SNS stripper foils.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Iterative methods in GPU-resident linear solvers for nonlinear constrained optimization

Linear solvers are major computational bottlenecks in a wide range of decision support and optimization computations. The challenges become even more pronounced on heterogeneous hardware, where traditional sparse numerical linear algebra methods are often inefficient. For example, methods for solving ill-conditioned linear systems have relied on conditional branching, which degrades performance on hardware accelerators such as graphical processing units (GPUs). To improve the efficiency of solving ill-conditioned systems, our computational strategy separates computations that are efficient on GPUs from those that need to run on traditional central processing units (CPUs). Our strategy maximizes the reuse of expensive CPU computations. Iterative methods, which thus far have not been broadly used for ill-conditioned linear systems, play an important role in our approach. In particular, we extend ideas from Arioli et al., (2007) to implement iterative refinement using inexact LU factors and flexible generalized minimal residual (FGMRES), with the aim of efficient performance on GPUs. In conclusion, we focus on solutions that are effective within broader application contexts, and discuss how early performance tests could be improved to be more predictive of the performance in a realistic environment.

97 MATHEMATICS AND COMPUTING↗

Atomic-scale Imaging of PGM-free Catalyst Active Sites by 30 keV 4D-STEM

Platinum group metal (PGM)-free catalysts have attracted a large amount of attention due to their potential for enabling low-cost, commercially viable hydrogen fuel cells and electrolyzers [1]. Degradation of cell performance remains a significant challenge, however, currently limiting implementation of devices that utilize PGM-free materials [2]. Controlling degradation in these materials requires a better understanding of the atomic structure of active sites, thought to be FeN4 structures within a graphitic carbon lattice, which would enable more accurate prediction of the associated degradation pathways. The exact structural arrangement of active sites in these materials is still debated since a range of structures have been computationally predicted and methods to directly validate these models are still needed [1,3-5].While scanning transmission electron microscopy (STEM) has provided initial glimpses into the nature of the proposed active sites, detailed evaluation of the structure of these sites is challenging since they involve defects, edges, and nitrogen dopants in the graphitic lattice, which are susceptible to beam damage [6,7]. Conventional STEM imaging and spectroscopy methods exacerbate this problem with dose-inefficiency or nonideal contrast characteristics for imaging light and heavy elements simultaneously. A method that minimizes damage while generating dose-efficient, easily-interpretable contrast for both light and heavy elements is therefore needed to facilitate imaging of sensitive active site atomic structure.Here, we demonstrate direct atomic-scale imaging of PGM-free catalyst active sites by low-voltage four-dimensional (4D)-STEM. To accomplish this, we pair a 30 keV aberration-corrected probe, which minimizes knock-on damage, with a fast pixelated detector that has optimal performance at low beam energies [8]. We show how this setup enables relatively simple center-of-mass (CoM) techniques [9,10] to produce images with an increased signal-to-noise ratio (SNR) and light-element contrast over conventional imaging modes, allowing the entire active site structure to be imaged at the atomic scale. Moreover, we show how electron ptychography [11,12] enables images with further improved characteristics to be obtained, for example by minimizing residual aberrations, which provides a more accurate structural representation. The increased understanding that these low-voltage 4D-STEM techniques will provide about the atomic structure of PGM-free active sites and their associated degradation pathways will facilitate rational design of next-generation materials, promoting development of low-cost hydrogen fuel cells, electrolyzers, and other energy conversion devices [13]. References:[1] U Martinez et al., Adv. Mater. 31 (2019), p. 1806545.[2] Y Shao et al., Adv. Mater. 31 (2019), p. 1807615.[3] J Kneebone et al., J. Phys. Chem. C 121, (2017), p.16283.[4] T Mineva et al., ACS Catal. 9 (2019), p. 9359.[5] J Li et al., Nat. Catal. 4 (2021), p. 10.[6] T Susi et al., ACS Nano 6 (2012), p. 8837.[7] P Zelenay and DJ Myers, US Department of Energy Hydrogen and Fuel Cells Program 2017 Annual Merit Review and Peer Evaluation Meeting, Washington, DC (2017).[8] H Ryll et al., J. Inst. 11 (2016), p. P04006.[9] K Müller et al., Nat. Commun. 5 (2014), p. 5653.[10] I Lazic et al., Ultramicroscopy 160 (2016), p. 265.[11] H Yang et al., Nat. Commun. 7 (2016), p. 12532.[12] Y Jiang et al., Nature 559 (2018), p. 343. [13] Research sponsored by the Hydrogen and Fuel Cell Technologies Office, Office of Energy Efficiency and Renewable Energy, US Department of Energy (DOE). Research was conducted at the Center for Nanophase Materials Sciences, which is a DOE Office of Science User Facility.

Zachman, Michael↗

Linearized frequency domain Landau-Lifshitz-Gilbert equation formulation

We present a general finite element linearized Landau-Lifshitz-Gilbert equation (LLGE) solver for magnetic systems under weak time-harmonic excitation field. The linearized LLGE is obtained by assuming a small deviation around the equilibrium state of the magnetic system. Inserting such expansion into LLGE and keeping only first order terms gives the linearized LLGE, which gives a frequency domain solution for the complex magnetization amplitudes under an external time-harmonic applied field of a given frequency. We solve the linear system with an iterative solver using generalized minimal residual method. We construct a preconditioner matrix to effectively solve the linear system. The validity, effectiveness, speed, and scalability of the linear solver are demonstrated via numerical examples.

36 MATERIALS SCIENCE↗

Calibration and simulation of ionization signal and electronics noise in the ICARUS liquid argon time projection chamber

The ICARUS liquid argon time projection chamber (LArTPC) neutrino detector has been taking physics data since 2022 as part of the Short-Baseline Neutrino (SBN) Program. This paper details the equalization of the response to charge in the ICARUS time projection chamber (TPC), as well as data-driven tuning of the simulation of ionization charge signals and electronics noise. The equalization procedure removes non-uniformities in the ICARUS TPC response to charge in space and time. This work leverages the copious number of cosmic ray muons available to ICARUS at the surface. The ionization signal shape simulation applies a novel procedure that tunes the simulation to match what is measured in data. The end result of the equalization procedure and simulation tuning allows for a comparison of charge measurements in ICARUS between Monte Carlo simulation and data, showing good performance with minimal residual bias between the two.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Mixed-precision iterative refinement using tensor cores on GPUs to accelerate solution of linear systems

Double-precision floating-point arithmetic (FP64) has been the de facto standard for engineering and scientific simulations for several decades. Problem complexity and the sheer volume of data coming from various instruments and sensors motivate researchers to mix and match various approaches to optimize compute resources, including different levels of floating-point precision. In recent years, machine learning has motivated hardware support for half-precision floating-point arithmetic. A primary challenge in high-performance computing is to leverage reduced-precision and mixed-precision hardware. We show how the FP16/FP32 Tensor Cores on NVIDIA GPUs can be exploited to accelerate the solution of linear systems of equations Ax = b without sacrificing numerical stability. The techniques we employ include multiprecision LU factorization, the preconditioned generalized minimal residual algorithm (GMRES), and scaling and auto-adaptive rounding to avoid overflow. We also show how to efficiently handle systems with multiple right-hand sides. On the NVIDIA Quadro GV100 (Volta) GPU, we achieve a 4×-5× performance increase and 5× better energy efficiency versus the standard FP64 implementation while maintaining an FP64 level of numerical stability.

GMRES↗

AIVT: Inference of turbulent thermal convection from measured 3D velocity data by physics-informed Kolmogorov-Arnold networks

We propose the artificial intelligence velocimetry-thermometry (AIVT) method to reconstruct a continuous and differentiable representation of the temperature and velocity in turbulent convection from measured three-dimensional (3D) velocity data. AIVT is based on physics-informed Kolmogorov-Arnold networks and trained by optimizing a loss function that minimizes residuals of the velocity data, boundary conditions, and governing equations. We apply AIVT to a set of simultaneously measured 3D temperature and velocity data of Rayleigh-Bénard convection, obtained by combining particle image thermometry and Lagrangian particle tracking. This enables us to directly compare machine learning results to true volumetric, simultaneous temperature and velocity measurements. We demonstrate that AIVT can reconstruct and infer continuous, instantaneous velocity and temperature fields and their gradients from sparse experimental data at a high resolution, providing an additional approach for understanding thermal turbulence.

Science & Technology - Other Topics↗

NCCS High Performance GMRES Mixed Precision

HPG-MxP is a software package that performs a fixed number of multigrid preconditioned (using a Gauss-Seidel smoother) Generalized minimal residual (PGMRES) iterations in order to solve a possibly nonsymmetric large sparse linear system of equations. It is designed to be a benchmark to measure a computer's performance for sparse linear algebra workloads typical in scientific computing while allowing the use of mixed precision methods. The solution is required to have convergence characteristics and accuracy similar to double precision GMRES. It is based on the High Performance Conjugate Gradient Benchmark (HPCG) which restricts all implementations to use only the IEEE double precision format (FP64). The original implementation (https://github.com/hpg-mxp/hpg-mxp) was written by Ichitaro Yamazaki, Jennifer Loe, Christian Glusa, Sivasankaran Rajamanickam, Piotr Luszczek, and Jack Dongarra. Please refer to that repository for documentation on the original implementation. This version is maintained by the National Center for Computational Sciences at Oak Ridge National Laboratory. It is highly scalable and optimized for Oak Ridge Leadership Computing Facility (OLCF) systems, particularly Frontier.

Kashi, Aditya [Oak Ridge National Laboratory (ORNL↗

Fluid-Kinetic Coupling: Advanced Discretizations for Simulations on Emerging Heterogeneous Architectures (LDRD FY20-0643)

Plasma physics simulations are vital for a host of Sandia mission concerns, for fundamental science, and for clean energy in the form of fusion power. Sandia's most mature plasma physics simulation capabilities come in the form of particle-in-cell (PIC) models and magnetohydrodynamics (MHD) models. MHD models for a plasma work well in denser plasma regimes when there is enough material that the plasma approximates a fluid. PIC models, on the other hand, work well in lower-density regimes, in which there is not too much to simulate; error in PIC scales as the square root of the number of particles, making high-accuracy simulations expensive. Real-world applications, however, almost always involve a transition region between the high-density regimes where MHD is appropriate, and the low-density regimes for PIC. In such a transition region, a direct discretization of Vlasov is appropriate. Such discretizations come with their own computational costs, however; the phase-space mesh for Vlasov can involve up to six dimensions (seven if time is included), and to apply appropriate homogeneous boundary conditions in velocity space requires meshing a substantial padding region to ensure that the distribution remains sufficiently close to zero at the velocity boundaries. Moreover, for collisional plasmas, the right-hand side of the Vlasov equation is a collision operator, which is non-local in velocity space, and which may dominate the cost of the Vlasov solver. The present LDRD project endeavors to develop modern, foundational tools for the development of continuum-kinetic Vlasov solvers, using the discontinuous Petrov-Galerkin (DPG) methodology, for discretization of Vlasov, and machine-learning (ML) models to enable efficient evaluation of collision operators. DPG affords several key advantages. First, it has a built-in, robust error indicator, allowing us to adapt the mesh in a very natural way, enabling a coarse velocity-space mesh near the homogeneous boundaries, and a fine mesh where the solution has fine features. Second, it is an inherently high-order, high-intensity method, requiring extra local computations to determine so-called optimal test functions, which makes it particularly suited to modern hardware in which floating-point throughput is increasing at a faster rate than memory bandwidth. Finally, DPG is a residual-minimizing method, which enables high-accuracy computation: in typical cases, the method delivers something very close to the $L^2$ projection of the exact solution. Meanwhile, the ML-based collision model we adopt affords a cost structure that scales as the square root of a standard direct evaluation. Moreover, we design our model to conserve mass, momentum, and energy by construction, and our approach to training is highly flexible, in that it can incorporate not only synthetic data from direct-simulation Monte Carlo (DSMC) codes, but also experimental data. We have developed two DPG formulations for Vlasov-Poisson: a time-marching, backward-Euler discretization and a space-time discretization. We have conducted a number of numerical experiments to verify the approach in a 1D1V setting. In this report, we detail these formulations and experiments. We also summarize some new theoretical results developed as part of this project (published as papers previously): some new analysis of DPG for the convection-reaction problem (of which the Vlasov equation is an instance), a new exponential integrator for DPG, and some numerical exploration of various DPG-based time-marching approaches to the heat equation. As part of this work, we have contributed extensively to the Camellia open-source library; we also describe the new capabilities and their usage. We have also developed a well-documented methodology for single-species collision operators, which we applied to argon and demonstrated with numerical experiments. We summarize those results here, as well as describing at a high level a design extending the methodology to multi-species operators. We have released a new open-source library, MLC, under a BSD license; we include a summary of its capabilities as well.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Design, Fabrication and Concept for the Surface Treatment of the SRF Cavity Prototype for the CLIC Damping Rings

The Compact Linear Collider (CLIC) Damping Rings (DRs) need to generate ultra-low emittance bunches to achieve high luminosity in CLIC. This requires many wiggler magnets with big energy loss which is compensated by the Radio Frequency (RF) system. The resulting strong beam loading transients lead to a challenging design for the RF system. A novel SRF cavity at 2 GHz with an ultra-low R/Q parameter of below 1 Ω is proposed to minimize the transient beam loading effects below acceptable level. The design and fabrication of the bulk Nb prototype based on turning from a single piece of Nb and EB welding is presented. Moreover, conceptual study of the system for cavity surface treatment to achieve the highest surface magnetic field which is the main goal of the prototype cold test is described as well. To enable excellent performance in this cavity, we plan to apply the 75/120C modified low temperature bake in combination with the cold electropolishing process. This surface treatment approach has been shown to consistently deliver high accelerating gradients and improved quality factors in TESLA-shaped 1.3 GHz SRF cavities. By adapting and implementing this process for the 2 GHz ultra-low R/Q design, we aim to maximize the achievable surface magnetic field while minimizing residual resistance and field emission. This treatment strategy will be critical for demonstrating that the cavity can meet the demanding performance requirements of the CLIC damping ring RF system under high beam loading conditions.

Bafia, Daniel P. [Fermilab]↗

Calibration and Performance of the ICARUS Detector at Fermilab

ICARUS is the largest Liquid Argon Time Projection Chamber (LArTPC) in operation and serves as the Far Detector of the Short Baseline Neutrino (SBN) program at Fermilab. Precise detector calibration is essential for reliable energy reconstruction and for maximizing the physics reach of the experiment. In this talk, I will describe the energy and timing calibration procedures developed at ICARUS. Thanks to the abundant flux of cosmic ray muons at the surface, the TPC response to ionization charge has been equalized across the detector, removing non-uniformities and in-transparency effects. A novel data-driven procedure has been used to tune the simulation of ionization signals and electronics noise yielding close agreement between Monte Carlo and data with minimal residual bias in reconstructed charge. In addition, the light detection system has been calibrated to sub-nanosecond timing resolution. This precision enables efficient cosmic background rejection and accurate synchronization of neutrino interactions with the time structure of both the Booster Neutrino Beam (BNB) and Neutrinos at the Main Injector (NuMI) beam. Together, these efforts demonstrate the robust performance of the detector and provide critical experience for future large LArTPCs, such as DUNE.

Vicenzi, Matteo [Brookhaven]↗

Universal dwell time optimization for deterministic optics fabrication

Computer-Controlled Optical Surfacing (CCOS) has been greatly developed and widely used for precision optical fabrication in the past three decades. It relies on robust dwell time solutions to determine how long the polishing tools must dwell at certain points over the surfaces to achieve the expected forms. However, as dwell time calculations are modeled as ill-posed deconvolution, it is always non-trivial to reach a reliable solution that 1) is non-negative, since CCOS systems are not capable of adding materials, 2) minimizes the residual in the clear aperture 3) minimizes the total dwell time to guarantee the stability and efficiency of CCOS processes, 4) can be flexibly adapted to different tool paths, 5) the parameter tuning of the algorithm is simple, and 6) the computational cost is reasonable. In this study, we propose a novel Universal Dwell time Optimization (UDO) model that universally satisfies these criteria. First, the matrix-based discretization of the convolutional polishing model is employed so that dwell time can be flexibly calculated for arbitrary dwell points. Second, UDO simplifies the inverse deconvolution as a forward scalar optimization for the first time, which drastically increases the solution stability and the computational efficiency. Finally, the dwell time solution is improved by a robust iterative refinement and a total dwell time reduction scheme. The superiority and general applicability of the proposed algorithm are verified on the simulations of different CCOS processes. A real application of UDO in improving a synchrotron X-ray mirror using Ion Beam Figuring (IBF) is then demonstrated. The simulation indicates that the estimated residual in the 92.3 mm × 15.7 mm CA can be reduced from 6.32 nm Root Mean Square (RMS) to 0.20 nm RMS in 3.37 min. After one IBF process, the measured residual in the CA converges to 0.19 nm RMS, which coincides with the simulation.

36 MATERIALS SCIENCE↗

Windowed least-squares model reduction for dynamical systems

Here we propose a windowed least-squares (WLS) approach for model reduction of dynamical systems. The proposed approach sequentially minimizes the time-continuous full-order-model residual within a low-dimensional space–time trial subspace over time windows. The approach comprises a generalization of existing model reduction approaches, as particular instances of the methodology recover Galerkin, least-squares Petrov–Galerkin (LSPG), and space–time LSPG projection. In addition, the approach addresses key deficiencies in existing model reduction techniques, e.g., the dependence of LSPG and space–time LSPG projection on the time discretization and the exponential growth in time exhibited by a posteriori error bounds for both Galerkin and LSPG projection. We consider two types of space–time trial subspaces within the proposed approach: one that reduces only the spatial dimension of the full-order model, and one that reduces both the spatial and temporal dimensions of the full-order model. For each type of trial subspace, we consider two different solution techniques: direct (i.e., discretize then optimize) and indirect (i.e., optimize then discretize). Numerical experiments conducted using trial subspaces characterized by spatial dimension reduction demonstrate that the WLS approach can yield more accurate solutions with lower space–time residuals than Galerkin and LSPG projection.

97 MATHEMATICS AND COMPUTING↗

Code for Calculating Regional Seismic Travel Time

The RSTT software computes predictions of the travel time of seismic energy traveling from a source to a receiver through 2.5D models of the seismic velocity distribution within the Earth. The two primary applications for the RSTT library are tomographic inversion studies and seismic event location calculations. In tomographic inversions studies, a seismologist begins with number of source-receiver travel time observations and an initial starting model of the velocity distribution within the Earth. A forward travel time calculator, such as the RSTT library, is used to compute predictions of each observed travel time and all of the residuals (observed minus predicted travel time) are calculated. The Earth model is then modified in some systematic way with the goal of minimizing the residuals. The Earth model obtained in this way is assumed to be a better model than the starting model if it has lower residuals. The other major application for the RSTT library is seismic event location. Given an Earth model, an initial estimate of the location of a seismic event, and some number of observations of seismic travel time thought to have originated from that event, location codes systematically modify the estimate of the location of the event with the goal of minimizing the difference between the observed and predicted travel times. The second application, seismic event location, is routinely implemented by the military as part of its effort to monitor the Earth for nuclear tests conducted by foreign countries.

BALLARD, SANFORD↗