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At least 1,261 records · Page 70
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Phase transitions of α-quartz at elevated temperatures under dynamic compression using a membrane-driven diamond anvil cell: Clues to impact cratering?

Coesite and stishovite are high-pressure silica polymorphs known to have been formed at several terrestrial impact structures. They have been used to assess pressure and temperature conditions that deviate from equilibrium formation conditions. Here in this paper, we investigate the effects of nonhydrostatic, dynamic stresses on the formation of high-pressure polymorphs and the amorphization of α-quartz at elevated temperatures. The obtained disequilibrium states are compared with those predicted by phase diagrams derived from static experiments under equilibrium conditions. We analyzed phase transformations starting with α-quartz in situ under dynamic loading utilizing a membrane-driven diamond anvil cell. Using synchrotron powder X-ray diffraction, the phase transitions of SiO 2 are identified up to 77.2 GPa and temperatures of 1160 K at compression rates ranging between 0.10 and 0.37 GPa s -1 . Coesite starts forming above 760 K in the pressure range between 2 and 11 GPa. At 1000 K, coesite starts to transform to stishovite. This phase transition is not completed at 1160 K in the same pressure range. Therefore, the temperature initiates the phase transition from α-quartz to coesite, and the transition from coesite to stishovite. Below 1000 K and during compression, α-quartz becomes amorphous and partially converts to stishovite. This phase transition occurs between 25 and 35 GPa. Above 1000 K, no amorphization of α-quartz is observed. High temperature experiments reveal the strong thermal dependence of the formation of coesite and stishovite under nonhydrostatic and disequilibrium conditions.

58 GEOSCIENCES↗
DOE OSTI2020

A Resonant Metamaterial Line Array for Ultrasound Compressive Imaging

Abstract Acoustic metamaterials have been proposed for numerous applications including subwavelength imaging, impedance matching, and lensing. Yet, their application in compressive sensing and imaging has not been fully investigated. When metamaterials are used as resonators at certain frequencies, they can generate random radiation patterns in the transmitted waves from the transducers and received waves from a target. Compressive sensing favors such randomness inasmuch as it can increase incoherence by decreasing the amount of mutual information between any two different measurements. This study aims at assessing whether the use of resonating metamaterial unit cells in a single-layered non-optimized array between a number of ultrasound transceivers and targets can improve the sensing capacity, point-spread function of the sensing array (their beam focusing ability), and imaging performance in point-like target detection. The theoretical results are promising and can open the way for more efficient metamaterial designs with the aim of enhancing ultrasound imaging with lower number of transceivers compared to the regular systems.

Acoustics↗
DOE OSTI2021

Gasoline Compression Ignition on a Light-Duty Multi-Cylinder Engine Using a Wide Range of Fuel Reactivities and Heavy Fuel Stratification

Many research studies have focused on utilizing gasoline in modern compression ignition engines to reduce emissions and improve efficiency. Collectively, this combustion mode has become kn+own as gasoline compression ignition (GCI). One of the biggest challenges with GCI operation is maintaining control over the combustion process through the fuel injection strategy, such that the engine can be controlled on a cycle-by-cycle basis. Research studies have investigated a wide variety of GCI injection strategies (i.e., fuel stratification levels) to maintain control over the heat release rate while achieving low-temperature combustion (LTC). This work shows that at loads relevant to light-duty engines, partial fuel stratification (PFS) with gasoline provides very little controllability over the timing of combustion. On the contrary, heavy fuel stratification (HFS) provides very linear and pronounced control over the timing of combustion. However, the HFS strategy has challenges achieving LTC operation due to the air handling burdens associated with the high exhaust gas recirculation (EGR) rates that are required to reduce NOx emissions to near zero levels. In this work, a wide variety of gasoline fuel reactivities (octane numbers ranging from <40 to 87) were investigated to understand the engine performance and emissions of HFS-GCI operation on a multi-cylinder light-duty engine. Overall, the results indicate that over an EGR sweep at 4 bar brake mean effective pressure (BMEP), the gasoline fuels can achieve LTC operation with ultra-low NO x and soot emissions, while conventional diesel combustion (CDC) is unable to simultaneously achieve low NO x and soot. At 10 bar BMEP, all the gasoline fuels were compared to diesel, but using mixing controlled combustion and not LTC.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2022

Initial Results on a New Light-Duty 2.7-L Opposed-Piston Gasoline Compression Ignition Multi-Cylinder Engine

Abstract Gasoline compression ignition (GCI) is a cost-effective approach to achieving diesel-like efficiencies with low emissions. The fundamental architecture of the two-stroke Achates Power Opposed-Piston (OP) Engine enables GCI by decoupling piston motion from cylinder scavenging, allowing for flexible and independent control of cylinder residual fraction and temperature leading to improved low-load combustion. In addition, the high peak cylinder pressure and noise challenges at high-load operation are mitigated by the lower brake mean effective pressure (BMEP) operation and faster heat release for the same pressure rise rate of the OP Engine. These advantages further solidify the performance benefits of the OP Engine and demonstrate the near-term feasibility of advanced combustion technologies, enabled by the opposed-piston architecture. This paper presents initial results from steady-state testing on a brand new 2.7-L OP GCI multi-cylinder engine (MCE) designed for light-duty truck applications. Successful GCI operation calls for a high compression ratio (CR), leading to higher combustion stability at low loads, higher efficiencies, and lower cycle HC + NOX emissions. Initial results show a cycle average brake thermal efficiency (BTE) of 31.7%, which is already greater than 11% conventional engines, after only ten weeks of testing. Emissions results suggest that Tier 3 Bin 160 levels can be achieved using a traditional diesel after-treatment system. Combustion noise was well controlled at or below the United States Council for Automotive Research limits. In addition, initial results on catalyst light-off mode with GCI are also presented.

Energy & Fuels↗
DOE OSTI2022

A Double-Wiebe Function for Reactivity Controlled Compression Ignition Combustion Using Reformate Diesel

Abstract Reactivity controlled compression ignition (RCCI) combustion has previously been proposed as a method to achieve high fuel conversion efficiency and reduce engine emissions. A single-fuel RCCI combustion strategy can have decreased fuel system complexity by using a reformate fuel for port fuel injection and the parent fuel (diesel) for direct injection. This paper presents a one-dimensional computational model of a compression ignition engine with single-fuel RCCI. A Wiebe function is used to predict the combustion process by representing the mass fraction burned (MFB) on a crank angle resolved basis. One single-Wiebe function (SWF) and two double-Wiebe functions(DWFs) were fitted to experimentally derive MFB data using the least-square method. The fitted results were compared with MFBs calculated from experimental data to verify the accuracy. The SWF did not fully capture the MFB curve with high fidelity while the detailed DWF captured the MFB curve within a root mean square error of 1.4%. The reduced double-Wiebe function (RDWF) also resulted in a predicted combustion profile with similar accuracy. Hence, the RDWF was used in a GT-power thermodynamic study to understand the effects of the low-temperature heat release (LTHR) fraction and combustion phasing on combustion characteristics. At optimum phasing of 5–10 crank angle degree after the top dead center, increasing the LTHR fraction from 20% to 60% resulted in the fuel conversion efficiency increasing from 39.5% to 41.1%, thus suggesting that the reformate fuel-based RCCI strategy is viable to unlock improved combustion performance.

Energy & Fuels↗
DOE OSTI2020

Gasoline Compression Ignition (GCI) on a Light-Duty Multi-Cylinder Engine Using a Wide Range of Fuel Reactivities and Heavy Fuel Stratification

Many research studies have focused on utilizing gasoline in modern compression ignition engines to reduce emissions and improve efficiency. Collectively, this combustion mode has become known as gasoline compression ignition (GCI). One of the biggest challenges with GCI operation is maintaining control over the combustion process through the fuel injection strategy, such that the engine can be controlled on a cycle-by-cycle basis. Research studies have investigated a wide variety of GCI injection strategies (i.e., fuel stratification levels) to maintain control over the heat release rate while achieving low temperature combustion (LTC). This work shows that at loads relevant to light-duty engines, partial fuel stratification (PFS) with gasoline provides very little controllability over the timing of combustion. On the contrary, heavy fuel stratification (HFS) provides very linear and pronounced control over the timing of combustion. However, the HFS strategy has challenges achieving LTC operation due to the air handling burdens associated with the high EGR rates that are required to reduce NOx emissions to near zero levels. In this work, a wide variety of gasoline fuel reactivities (octane numbers ranging from < 40 to 87) were investigated to understand the engine performance and emissions of HFS-GCI operation on a multi-cylinder light-duty engine. The results indicate that over an EGR sweep at 4 bar BMEP, the gasoline fuels can achieve LTC operation with ultra-low NOx and soot emissions, while conventional diesel combustion (CDC) is unable to simultaneously achieve low NOx and soot. At 10 bar BMEP, all the gasoline fuels were compared to diesel, but using mixing controlled combustion and not LTC.

Dempsey, Adam↗
DOE OSTI2025

Identification of contamination in the pulse-compression chamber of the OMEGA EP Laser System originating from clean room garments

The contamination of optical components with microscopic particles strongly impacts their ability to handle high-power or high-intensity laser pulses via an array of mechanisms. This work explores the nature and origin of a subset of contamination particles found inside the pulse-compression chamber of the OMEGA EP Laser System. Using Raman microscopy accompanied by other analytical methods, it was shown that sodium nitrate constitutes a significant fraction of the particles that possess diameters on the order of a few micrometers. Further investigation aiming to reveal the origin of these particles suggests that these sodium nitrate particles are deposited via shedding from the reusable clean room garments worn in the Laser Bay and compression chamber. Raman microscopy also revealed various plastic particles such as polystyrene, polyethylene, and poly(diallyl isophthalate).

Raman spectroscopy↗
DOE OSTI2016

Subsampling-based compression and flow visualization

As computational capabilities increasingly outpace disk speeds on leading supercomputers, scientists will, in turn, be increasingly unable to save their simulation data at its native resolution. One solution to this problem is to compress these data sets as they are generated and visualize the compressed results afterwards. We explore this approach, specifically subsampling velocity data and the resulting errors for particle advection-based flow visualization. We compare three techniques: random selection of subsamples, selection at regular locations corresponding to multi-resolution reduction, and introduce a novel technique for informed selection of subsamples. Furthermore, we explore an adaptive system which exchanges the subsampling budget over parallel tasks, to ensure that subsampling occurs at the highest rate in the areas that need it most. We perform supercomputing runs to measure the effectiveness of the selection and adaptation techniques. Overall, we find that adaptation is very effective, and, among selection techniques, our informed selection provides the most accurate results, followed by the multi-resolution selection, and with the worst accuracy coming from random subsamples.

Agranovsky, Alexy↗
DOE OSTI2014

Prior data assisted compressed sensing: A novel MR imaging strategy for real time tracking of lung tumors

Purpose: Hybrid radiotherapy-MRI devices promise real time tracking of moving tumors to focus the radiation portals to the tumor during irradiation. This approach will benefit from the increased temporal resolution of MRI's data acquisition and reconstruction. In this work, the authors propose a novel spatial-temporal compressed sensing (CS) imaging strategy for the real time MRI–-prior data assisted compressed sensing (PDACS), which aims to improve the image quality of the conventional CS without significantly increasing reconstruction times. Methods: Conventional 2D CS requires a random sampling of partial k-space data, as well as an iterative reconstruction that simultaneously enforces the image's sparsity in a transform domain as well as maintains the fidelity to the acquired k-space. PDACS method requires the additional acquisition of the prior data, and for reconstruction, it additionally enforces fidelity to the prior k-space domain similar to viewsharing. In this work, the authors evaluated the proposed PDACS method by comparing its results to those obtained from the 2D CS and viewsharing methods when performed individually. All three methods are used to reconstruct images from lung cancer patients whose tumors move and who are likely to benefit from lung tumor tracking. The patients are scanned, using a 3T MRI, under free breathing using the fully sampled k-space with 2D dynamic bSSFP sequence in a sagittal plane containing lung tumor. These images form a reference set for the evaluation of the partial k-space methods. To create partial k-space, the fully sampled k-space is retrospectively undersampled to obtain a range of acquisition acceleration factors, and reconstructed with 2D-CS, PDACS, and viewshare methods. For evaluation, metrics assessing global image artifacts as well as tumor contour shape fidelity are determined from the reconstructed images. These analyses are performed both for the original 3T images and those at a simulated 0.5T equivalent noise level. Results: In the 3.0T images, the PDACS strategy is shown to give superior results compared to viewshare and conventional 2D CS using all metrics. The 2D-CS tends to perform better than viewshare at the low acceleration factors, while the opposite is true at the high acceleration factors. At simulated 0.5T images, PDACS method performs only marginally better than the viewsharing method, both of which are superior compared to 2D CS. The PDACS image reconstruction time (0.3 s/image) is similar to that of the conventional 2D CS. Conclusions: The PDACS method can potentially improve the real time tracking of moving tumors by significantly increasing MRI's data acquisition speeds. In 3T images, the PDACS method does provide a benefit over the other two methods in terms of both the overall image quality and the ability to accurately and automatically contour the tumor shape. MRI's data acquisition may be accelerated using the simpler viewsharing strategy at the lower, 0.5T magnetic field, as the marginal benefit of the PDACS method may not justify its additional reconstruction times.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

TH-E-17A-06: Anatomical-Adaptive Compressed Sensing (AACS) Reconstruction for Thoracic 4-Dimensional Cone-Beam CT

Purpose: The Feldkamp-Davis-Kress (FDK) algorithm currently used for clinical thoracic 4-dimensional (4D) cone-beam CT (CBCT) reconstruction suffers from noise and streaking artifacts due to projection under-sampling. Compressed sensing theory enables reconstruction of under-sampled datasets via total-variation (TV) minimization, but TV-minimization algorithms such as adaptive-steepest-descent-projection-onto-convex-sets (ASD-POCS) often converge slowly and are prone to over-smoothing anatomical details. These disadvantages can be overcome by incorporating general anatomical knowledge via anatomy segmentation. Based on this concept, we have developed an anatomical-adaptive compressed sensing (AACS) algorithm for thoracic 4D-CBCT reconstruction. Methods: AACS is based on the ASD-POCS framework, where each iteration consists of a TV-minimization step and a data fidelity constraint step. Prior to every AACS iteration, four major thoracic anatomical structures - soft tissue, lungs, bony anatomy, and pulmonary details - were segmented from the updated solution image. Based on the segmentation, an anatomical-adaptive weighting was applied to the TV-minimization step, so that TV-minimization was enhanced at noisy/streaky regions and suppressed at anatomical structures of interest. The image quality and convergence speed of AACS was compared to conventional ASD-POCS using an XCAT digital phantom and a patient scan. Results: For the XCAT phantom, the AACS image represented the ground truth better than the ASD-POCS image, giving a higher structural similarity index (0.93 vs. 0.84) and lower absolute difference (1.1*10{sup 4} vs. 1.4*10{sup 4}). For the patient case, while both algorithms resulted in much less noise and streaking than FDK, the AACS image showed considerably better contrast and sharpness of the vessels, tumor, and fiducial marker than the ASD-POCS image. In addition, AACS converged over 50% faster than ASD-POCS in both cases. Conclusions: The proposed AACS algorithm was shown to reconstruct thoracic 4D-CBCT images more accurately and with faster convergence compared to ASD-POCS. The superior image quality and rapid convergence makes AACS promising for future clinical use.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

WE-G-207-04: Non-Local Total-Variation (NLTV) Combined with Reweighted L1-Norm for Compressed Sensing Based CT Reconstruction

Purpose: Compressed sensing (CS) has been used for CT (4DCT/CBCT) reconstruction with few projections to reduce dose of radiation. Total-variation (TV) in L1-minimization (min.) with local information is the prevalent technique in CS, while it can be prone to noise. To address the problem, this work proposes to apply a new image processing technique, called non-local TV (NLTV), to CS based CT reconstruction, and incorporate reweighted L1-norm into it for more precise reconstruction. Methods: TV minimizes intensity variations by considering two local neighboring voxels, which can be prone to noise, possibly damaging the reconstructed CT image. NLTV, contrarily, utilizes more global information by computing a weight function of current voxel relative to surrounding search area. In fact, it might be challenging to obtain an optimal solution due to difficulty in defining the weight function with appropriate parameters. Introducing reweighted L1-min., designed for approximation to ideal L0-min., can reduce the dependence on defining the weight function, therefore improving accuracy of the solution. This work implemented the NLTV combined with reweighted L1-min. by Split Bregman Iterative method. For evaluation, a noisy digital phantom and a pelvic CT images are employed to compare the quality of images reconstructed by TV, NLTV and reweighted NLTV. Results: In both cases, conventional and reweighted NLTV outperform TV min. in signal-to-noise ratio (SNR) and root-mean squared errors of the reconstructed images. Relative to conventional NLTV, NLTV with reweighted L1-norm was able to slightly improve SNR, while greatly increasing the contrast between tissues due to additional iterative reweighting process. Conclusion: NLTV min. can provide more precise compressed sensing based CT image reconstruction by incorporating the reweighted L1-norm, while maintaining greater robustness to the noise effect than TV min.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

Impact of compressed breast thickness and dose on lesion detectability in digital mammography: FROC study with simulated lesions in real mammograms

Purpose: The aim of this work was twofold: (1) to examine whether, with standard automatic exposure control (AEC) settings that maintain pixel values in the detector constant, lesion detectability in clinical images decreases as a function of breast thickness and (2) to verify whether a new AEC setup can increase lesion detectability at larger breast thicknesses. Methods: Screening patient images, acquired on two identical digital mammography systems, were collected over a period of 2 yr. Mammograms were acquired under standard AEC conditions (part 1) and subsequently with a new AEC setup (part 2), programmed to use the standard AEC settings for compressed breast thicknesses ≤49 mm, while a relative dose increase was applied above this thickness. The images were divided into four thickness groups: T1 ≤ 29 mm, T2 = 30–49 mm, T3 = 50–69 mm, and T4 ≥ 70 mm, with each thickness group containing 130 randomly selected craniocaudal lesion-free images. Two measures of density were obtained for every image: a BI-RADS score and a map of volumetric breast density created with a software application (VolparaDensity, Matakina, NZ). This information was used to select subsets of four images, containing one image from each thickness group, matched to a (global) BI-RADS score and containing a region with the same (local) VOLPARA volumetric density value. One selected lesion (a microcalcification cluster or a mass) was simulated into each of the four images. This process was repeated so that, for a given thickness group, half the images contained a single lesion and half were lesion-free. The lesion templates created and inserted in groups T3 and T4 for the first part of the study were then inserted into the images of thickness groups T3 and T4 acquired with higher dose settings. Finally, all images were visualized using the ViewDEX software and scored by four radiologists performing a free search study. A statistical jackknife-alternative free-response receiver operating characteristic analysis was applied. Results: For part 1, the alternative free-response receiver operating characteristic curves for the four readers were 0.80, 0.65, 0.55 and 0.56 in going from T1 to T4, indicating a decrease in detectability with increasing breast thickness. P-values and the 95% confidence interval showed no significant difference for the T3-T4 comparison (p = 0.78) while all the other differences were significant (p < 0.05). Separate analysis of microcalcification clusters presented the same results while for mass detection, the only significant difference came when comparing T1 to the other thickness groups. Comparing the scores of part 1 and part 2, results for the T3 group acquired with the new AEC setup and T3 group at standard AEC doses were significantly different (p = 0.0004), indicating improved detection. For this group a subanalysis for microcalcification detection gave the same results while no significant difference was found for mass detection. Conclusions: These data using clinical images confirm results found in simple QA tests for many mammography systems that detectability falls as breast thickness increases. Results obtained with the AEC setup for constant detectability above 49 mm showed an increase in lesion detection with compressed breast thickness, bringing detectability of lesions to the same level.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2017

Pressure compression of CdSe nanoparticles into luminescent nanowires

Oriented attachment (OA) of synthetic nanocrystals is emerging as an effective means of fabricating low-dimensional nanoscale materials. However, OA relies on energetically favorable nanocrystal facets to grow nanostructured materials. Consequently, nanostructures synthesized through OA are generally limited to a specific crystal facet in their final morphology. We report our discovery that high-pressure compression can induce consolidation of spherical CdSe nanocrystal arrays, leading to unexpected one-dimensional semiconductor nanowires that do not exhibit the typical crystal facet. In particular, in situ high-pressure synchrotron x-ray scattering, optical spectroscopy, and high-resolution transmission electron microscopy characterizations indicate that by manipulating the coupling between nanocrystals through external pressure, a reversible change in nanocrystal assemblies and properties can be achieved at modest pressure. When pressure is increased above a threshold, these nanocrystals begin to contact one another and consolidate, irreversibly forming one-dimensional luminescent nanowires. High-fidelity molecular dynamics (MD) methods were used to calculate surface energies and simulate compression and coalescence mechanisms of CdSe nanocrystals. The MD results provide new insight into nanowire assembly dynamics and phase stability of nanocrystalline structures.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2022

Diamond formation kinetics in shock-compressed C$-$H$-$O samples recorded by small-angle x-ray scattering and x-ray diffraction

Extreme conditions inside ice giants such as Uranus and Neptune can result in peculiar chemistry and structural transitions, e.g., the precipitation of diamonds or superionic water, as so far experimentally observed only for pure C$-$H and H 2 O systems, respectively. Here, we investigate a stoichiometric mixture of C and H 2 O by shock-compressing polyethylene terephthalate (PET) plastics and performing in situ x-ray probing. We observe diamond formation at pressures between 72 ± 7 and 125 ± 13 GPa at temperatures ranging from ~3500 to ~6000 K. Combining x-ray diffraction and small-angle x-ray scattering, we access the kinetics of this exotic reaction. The observed demixing of C and H 2 O suggests that diamond precipitation inside the ice giants is enhanced by oxygen, which can lead to isolated water and thus the formation of superionic structures relevant to the planets’ magnetic fields. Moreover, our measurements indicate a way of producing nanodiamonds by simple laser-driven shock compression of cheap PET plastics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2013

Optical transitions of holes in uniaxially compressed germanium

Spontaneous emission and photoconductivity of germanium with gallium impurity are studied for determining the energy spectrum of hole states in this material in which radiation can be induced as a result of transitions of holes between these states. Holes were excited by electric field pulses with a strength up to 12 kV/cm at T = 4.2 K under uniaxial compression of samples up to 12 kbar. It has been found that hole emission spectra for transitions between resonant and local states of the impurity have a structure identical to the photoconductivity and absorption spectra. Transitions from resonance states, which are associated with the heavy hole subband, have not been detected. It has been found that in an electric field lower than 100 V/cm, a compressed crystal emits as a result of transitions of heavy holes. In a strong electric field (1-3 kV/cm), emission is observed in the energy range up to 140 meV, and transitions with emission of TA and LO phonons appear in such a field. The emission spectra under pressures of 0 and 12 kbar differ insignificantly. Hence, it follows that the contributions from heavy and light holes in a strong electric field are indistinguishable.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

First-principles calculation of the reflectance of shock-compressed xenon

Within electron density functional theory (DFT), the reflectance of radiation from shock-compressed xenon plasma is calculated. The dependence of the reflectance on the frequency of the incident radiation and on the plasma density is considered. The Fresnel formula is used. The expression for the longitudinal dielectric tensor in the long-wavelength limit is used to calculate the imaginary part of the dielectric function (DF). The real part of the DF is determined by the Kramers-Kronig transformation. The results are compared with experimental data. An approach is proposed to estimate the plasma frequency in shock-compressed xenon.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Sliced-Inverse-Regression--Aided Rotated Compressive Sensing Method for Uncertainty Quantification

Compressive-sensing-based uncertainty quantification methods have become a pow- erful tool for problems with limited data. In this paper, we use the sliced inverse regression (SIR) method to provide an initial guess for the alternating direction method, which is used to enhance sparsity of the Hermite polynomial expansion of stochastic state variables. The sparsity improvement increases both the efficiency and accuracy of the compressive-sensing-based uncertainty quantification method. We demonstrate that the initial guess from SIR is more suitable for the cases when the available data is very limited (Algorithm 4). We also propose another algorithm (Algorithm 5) that performs dimension reduction first with sliced inverse regression, then constructs a Hermite polynomial expansion of the reduced model. This method allows us to approximate the statistics accurately with even less available data. Both methods are non-intrusive and require no a priori information of the sparsity of the system. We demonstrate the effectiveness of these two methods (Algorithms 4 and 5) using problems with up to 500 random dimensions.

Yang, Xiu↗
DOE OSTI2023

A Fast Butterfly-Compressed Hadamard–Babich Integrator for High-Frequency Helmholtz Equations in Inhomogeneous Media with Arbitrary Sources

Here we present a butterfly-compressed representation of the Hadamard-Babich (HB) ansatz for the Green's function of the high-frequency Helmholtz equation in smooth inhomogeneous media. For a computational domain discretized with Nv discretization cells, the proposed algorithm first solves and tabulates the phase and HB coefficients via eikonal and transport equations with observation points and point sources located at the Chebyshev nodes using a set of much coarser computation grids, and then butterfly compresses the resulting HB interactions from all Nv cell centers to each other. The overall CPU time and memory requirement scale as O(Nv log2 Nv) for any bounded two-dimensional (2D) domains with arbitrary excitation sources. A direct extension of this scheme to bounded 3D domains yields an O(Nv4/3) CPU complexity, which can be further reduced to quasi-linear complexities with proposed remedies. The scheme can also efficiently handle scattering problems involving inclusions in inhomogeneous media. Although the current construction of our HB integrator does not accommodate caustics, the resulting HB integrator itself can be applied to certain sources, such as concave-shaped sources, to produce caustic effects. Compared to finite-difference frequency domain methods, the proposed HB integrator is free of numerical dispersion and requires fewer discretization points per wavelength. As a result, it can solve wave propagation problems well beyond the capability of existing solvers. Remarkably, the proposed scheme can accurately model wave propagation in 2D domains with 640 wavelengths per direction and in 3D domains with 54 wavelengths per direction on a state-of-the-art supercomputer at Lawrence Berkeley National Laboratory.

Hadamard--Babich ansatz↗