Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Iterative methods”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,045 records · Page 58
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Being WISE II: reducing the influence of star formation history on the mass-to-light ratio of quiescent galaxies

Stellar population synthesis models can now reproduce the photometry of old stellar systems (age > 2 Gyr) in the near-infrared (NIR) bands at 3.4 and 4.6 μm (WISE W1 and W2 or IRAC 1 and 2). In this paper, we derive stellar mass-to-light ratios for these and optical bands, and confirm that the NIR M/L shows dramatically reduced sensitivity to both age and metallicity compared to optical bands, and further, that this behavior leads to significantly more robust stellar masses for quiescent galaxies with [Fe/H] ≳ −0.5 regardless of star-formation history (SFH). We then use realistic early-type galaxy SFHs and metallicity distributions from the EAGLE simulations of galaxy formation to investigate two methods to determine the appropriate M/L for a galaxy. (1) We show that the uncertainties introduced by an unknown SFH can be largely removed using a spectroscopically inferred luminosity-weighted age and metallicity for the population to select the appropriate single stellar population (SSP) equivalent M/L. Using this method, the maximum systematic error due to SFH on the M/L of an early-type galaxy is <4% at 3.4 μm and typical uncertainties due to errors in the age and metallicity create a scatter of ≲13%. The equivalent values for optical bands are more than two to three times greater, even before considering uncertainties associated with internal dust extinction. (2) We demonstrate that if the EAGLE SFHs and metallicities accurately reproduce the true properties of early-type galaxies, the use of an iterative approach to select a mass dependent M/L can provide even more accurate stellar masses for early-type galaxies, with typical uncertainties of <9%.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Automatic projection image registration for nanoscale X-ray tomographic reconstruction

Novel developments in X-ray sources, optics and detectors have significantly advanced the capability of X-ray microscopy at the nanoscale. Depending on the imaging modality and the photon energy, state-of-the-art X-ray microscopes are routinely operated at a spatial resolution of tens of nanometres for hard X-rays or ~ 10 nm for soft X-rays. The improvement in spatial resolution, however, has led to challenges in the tomographic reconstruction due to the fact that the imperfections of the mechanical system become clearly detectable in the projection images.Without proper registration of the projection images, a severe point spread function will be introduced into the tomographic reconstructions, causing the reduction of the three-dimensional (3D) spatial resolution as well as the enhancement of image artifacts. In this work, the development of a method that iteratively performs registration of the experimentally measured projection images to those that are numerically calculated by reprojecting the 3D matrix in the corresponding viewing angles is shown. Multiple algorithms are implemented to conduct the registration, which corrects the translational and/ or the rotational errors. A sequence that offers a superior performance is presented and discussed. Going beyond the visual assessment of the reconstruction results, the morphological quantification of a battery electrode particle that has gone through substantial cycling is investigated. The results show that the presented method has led to a better quality tomographic reconstruction, which, subsequently, promotes the fidelity in the quantification of the sample morphology.

42 ENGINEERING↗
DOE OSTI2015

SU-E-T-500: Initial Implementation of GPU-Based Particle Swarm Optimization for 4D IMRT Planning in Lung SBRT

Purpose 4D-IMRT planning, combined with dynamic MLC tracking delivery, utilizes the temporal dimension as an additional degree of freedom to achieve improved OAR-sparing. The computational complexity for such optimization increases exponentially with increase in dimensionality. In order to accomplish this task in a clinically-feasible time frame, we present an initial implementation of GPU-based 4D-IMRT planning based on particle swarm optimization (PSO). Methods The target and normal structures were manually contoured on ten phases of a 4DCT scan of a NSCLC patient with a 54cm3 right-lower-lobe tumor (1.5cm motion). Corresponding ten 3D-IMRT plans were created in the Eclipse treatment planning system (Ver-13.6). A vendor-provided scripting interface was used to export 3D-dose matrices corresponding to each control point (10 phases × 9 beams × 166 control points = 14,940), which served as input to PSO. The optimization task was to iteratively adjust the weights of each control point and scale the corresponding dose matrices. In order to handle the large amount of data in GPU memory, dose matrices were sparsified and placed in contiguous memory blocks with the 14,940 weight-variables. PSO was implemented on CPU (dual-Xeon, 3.1GHz) and GPU (dual-K20 Tesla, 2496 cores, 3.52Tflops, each) platforms. NiftyReg, an open-source deformable image registration package, was used to calculate the summed dose. Results The 4D-PSO plan yielded PTV coverage comparable to the clinical ITV-based plan and significantly higher OAR-sparing, as follows: lung Dmean=33%; lung V20=27%; spinal cord Dmax=26%; esophagus Dmax=42%; heart Dmax=0%; heart Dmean=47%. The GPU-PSO processing time for 14940 variables and 7 PSO-particles was 41% that of CPU-PSO (199 vs. 488 minutes). Conclusion Truly 4D-IMRT planning can yield significant OAR dose-sparing while preserving PTV coverage. The corresponding optimization problem is large-scale, non-convex and computationally rigorous. Our initial results indicate that GPU-based PSO with further software optimization can make such planning clinically feasible. This work was supported through funding from the National Institutes of Health and Varian Medical Systems.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

Leveraging operator learning to accelerate convergence of the preconditioned conjugate gradient method

We propose a new deflation strategy to accelerate the convergence of the preconditioned conjugate gradient (PCG) method for solving parametric large-scale linear systems of equations. Unlike traditional deflation techniques that rely on eigenvector approximations or recycled Krylov subspaces, we generate the deflation subspaces using operator learning, specifically the Deep Operator Network (DeepONet). To this aim, we introduce two complementary approaches for assembling the deflation operators. The first approach approximates near-null space vectors of the discrete PDE operator using the basis functions learned by the DeepONet. The second approach directly leverages solutions predicted by the DeepONet. To further enhance convergence, we also propose several strategies for prescribing the sparsity pattern of the deflation operator. Here, a comprehensive set of numerical experiments encompassing steady-state, time-dependent, scalar, and vector-valued problems posed on both structured and unstructured geometries is presented and demonstrates the effectiveness of the proposed DeepONet-based deflated PCG method, as well as its generalization across a wide range of model parameters and problem resolutions.

Deflation↗
DOE OSTI2019

What a difference a delay makes! CT urogram: a pictorial essay

Purpose: The aim of this pictorial essay is to demonstrate several cases where the diagnosis would have been difficult or impossible without the excretory phase image of CT urography. Methods: A brief discussion of CT urography technique and dose reduction is followed by several cases illustrating the utility of CT urography. Results: CT urography has become the primary imaging modality for evaluation of hematuria, as well as in the staging and surveillance of urinary tract malignancies. CT urography includes a non-contrast phase and contrast-enhanced nephrographic and excretory (delayed) phases. While the three phases add to the diagnostic ability of CT urography, it also adds potential patient radiation dose. Several techniques including automatic exposure control, iterative reconstruction algorithms, higher noise tolerance, and split-bolus have been successfully used to mitigate dose. The excretory phase is timed such that the excreted contrast opacifies the urinary collecting system and allows for greater detection of filling defects or other abnormalities. Sixteen cases illustrating the utility of excretory phase imaging are reviewed. Conclusions: Excretory phase imaging of CT urography can be an essential tool for detecting and appropriately characterizing urinary tract malignancies, renal papillary and medullary abnormalities, CT radiolucent stones, congenital abnormalities, certain chronic inflammatory conditions, and perinephric collections.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2015

Passive seismic tomography application for cave monitoring in DOZ underground mine PT. Freeport Indonesia

It is already known that tomography has a great impact for analyzing and mapping unknown objects based on inversion, travel time as well as waveform inversion. Therefore, tomography has used in wide area, not only in medical but also in petroleum as well as mining. Recently, tomography method is being applied in several mining industries. A case study of tomography imaging has been carried out in DOZ ( Deep Ore Zone ) block caving mine, Tembagapura, Papua. Many researchers are undergoing to investigate the properties of DOZ cave not only outside but also inside which is unknown. Tomography takes a part for determining this objective.The sources are natural from the seismic events that caused by mining induced seismicity and rocks deformation activity, therefore it is called as passive seismic. These microseismic travel time data are processed by Simultaneous Iterative Reconstruction Technique (SIRT). The result of the inversion can be used for DOZ cave monitoring. These information must be used for identifying weak zone inside the cave. In addition, these results of tomography can be used to determine DOZ and cave information to support mine activity in PT. Freeport Indonesia.

58 GEOSCIENCES↗
DOE OSTI2013

A new, coupled transport-diffusion method for radiative transfer calculations

We derive and present a new frequency- and angle-integrated low-order system of equations designed to enhance the accuracy of a coupled, high-order (transport) solution of the thermal radiative transfer equations. In particular, our new low-order system is designed to use intensity-weighted opacities and anisotropic diffusion coefficients generated by a solution of the Implicit Monte Carlo (IMC) equations in order to predict the spatial dependence of the material temperature and radiation energies in the ensuing time cycle. The predicted temperature solution can then be exploited to generate appropriately time-centered opacities, specific heats, and Planck emission spectra for the upcoming IMC solution. Additionally, the relatively inexpensive solution of the low-order system can be iteratively solved to recommend an adaptive time step size before the IMC solution is computed. A test implementation has been implemented using existing software available from the Jayenne and Capsaicin projects at Los Alamos National Laboratory. We present initial results from a new driver code that has integrated these stochastic and deterministic software packages. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

TU-F-BRF-04: Registration of 3D Transesophageal Echocardiography and X-Ray Fluoroscopy Using An Inverse Geometry X-Ray System

Purpose: To develop a method for the fusion of 3D echocardiography and Scanning-Beam Digital X-ray (SBDX) fluoroscopy to assist with catheter device and soft tissue visualization during interventional procedures. Methods: SBDX is a technology for low-dose inverse geometry x-ray fluoroscopy that performs digital tomosynthesis at multiple planes in real time. In this study, transesophageal echocardiography (TEE) images were fused with SBDX images by estimating the 3D position and orientation (the “pose”) of the TEE probe within the x-ray coordinate system and then spatially transforming the TEE image data to match this pose. An initial pose estimate was obtained through tomosynthesis-based 3D localization of points along the probe perimeter. Position and angle estimates were then iteratively refined by comparing simulated projections of a 3D probe model against SBDX x-ray images. Algorithm performance was quantified by imaging a TEE probe in different known orientations and locations within the x-ray field (0-30 degree tilt angle, up to 50 mm translation). Fused 3D TEE/SBDX imaging was demonstrated by imaging a tissue-mimicking polyvinyl alcohol cylindrical cavity as a catheter was navigated along the cavity axis. Results: Detected changes in probe tilt angle agreed with the known changes to within 1.2 degrees. For a 50 mm translation along the source-detector axis, the detected translation was 50.3 mm. Errors for in-plane translations ranged from 0.1 to 0.9 mm. In a fused 3D TEE/SBDX display, the catheter device was well visualized and coincident with the device shadow in the TEE images. The TEE images portrayed phantom boundaries that were not evident under x-ray. Conclusion: Registration of soft tissue anatomy derived from TEE imaging and device imaging from SBDX x-ray fluoroscopy is feasible. The simultaneous 3D visualization of these two modalities may be useful in interventional procedures involving the navigation of devices to soft tissue anatomy.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2015

SU-E-J-56: Static Gantry Digital Tomosynthesis From the Beam’s-Eye-View

Purpose We have designed a novel TumoTrak™ x-ray system that delivers 19 distinct kV views with the linac gantry stationary. It images MV treatment beam above and below the patient with a kV tomosysthesis slice image from the therapy beam’s-eye-view. Results will be high quality images without MLC shadowing for notable improvements relative to conventional fluoroscopic MV imaging and fluoroscopic kV imaging. Methods A complete design has a kV electron beam multisource X-ray tube that fits around the MV treatment beam path, with little interference with normal radiotherapy and unblocked by the multi-leaf-collimator. To simulate digital tomosynthesis, we used cone-beam CT projection data from a lung SBRT patient. These data were acquired at 125 kVp and 11 fps (0.4 mAs per projection). We chose 19 projections evenly spaced over 27° around one of the treatment angles (240°). Digital tomosynthesis reconstruction of a slice through the tumor was performed using iterative reconstruction. The visibility of the lesion was assessed for the reconstructed digital tomosynthesis (DTS), using fluoroscopy MV images acquired during radiation therapy, and a kV single projection image acquired at the same angle as the treatment field (240°). Results The fluoroscopic DTS images provide the best tumor contrast, surpassing the conventional radiographic and the in-treatment MV portal images. The electron beam multisource X-ray tube design has been completed and the tube is being fabricated. The estimated time to cycle through all 19 projections is 700 ms, enabling high frame-rate imaging. While the initial proposed use case is for image guided and gated treatment delivery, the enhanced imaging will also deliver superior radiographic images for patient setup. Conclusion The proposed device will deliver high quality planar images from the beam’s-eye-view without MLC obstruction. The prototype has been designed and is being assembled with first imaging scheduled for May 2015. L. Partain, J. Kwon, D. Boyd: NIH/SBIR R43CA192489-01. J. Rottmann, G. Zentai, R. Berbeco: NIH/NCI 1R01CA188446-01. R. Berbeco: E. Research Grant, Varian Medical Systems.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

SU-E-T-498: Energy Minimization and Dose-Volume Inverse Optimization in Prostate Cancer

Purpose: To compare dose-volume (DVH) and energy minimization-based (EM) optimization for prostate cancer cases. Methods: A dozen of prostate plans were retrospectively studied. For each case two IMRT plans were generated, one with DVH and the other with EM objective cost function. Those different objective functions were used only for the organs at risk (OARs), while target objectives were achieved through DVH cost functions. The plans used the same beam angles, maximum number of segments per plan, minimum segment area and MUs per segment. Both plans were normalized such that 95% of the PTV was covered by the same prescription dose. After prescription was achieved, doses to the OARs were iteratively lowered until the standard deviation of the dose across the PTV was ~3.5%. Plan quality was evaluated by several dose indices (DIs). A DI represents the dose delivered to certain volume of a structure. Tallied DIs were for rectum and bladder 10%, 40%, 60% volumes, and 1% volumes of the femoral heads as surrogate for maximum doses. Statistical significance in the differences among DIs was quantified with two-tailed paired t-tests. Results: On average EM plans performed better than DVH plans. Statistically significant dose reduction in rectum DI10, DI40, and DI60, were 2.6%, 25.7%, and 35.9%, respectively. For bladder DI10, DI40, and DI60 the differences were 1.1%, 20.8%, and 29.7%. Left and right femoral head DI1s were better by 33.8% and 27.8% in EM plans. The quoted dose reduction is with respect to EM absolute doses for the DIs. Conclusion: The performance of EM optimization with respect to DVH optimization is patient and DI dependent. While in some cases specific DIs were better with DVH optimization, on average the energy minimization allows better (ranging from 1% to ~40%) OAR sparing than DVH optimization. NIH-NCI.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

Permanent-magnet energy spectrometer for electron beams from radiotherapy accelerators

Purpose: The purpose of this work was to adapt a lightweight, permanent magnet electron energy spectrometer for the measurement of energy spectra of therapeutic electron beams. Methods: An irradiation geometry and measurement technique were developed for an approximately 0.54-T, permanent dipole magnet spectrometer to produce suitable latent images on computed radiography (CR) phosphor strips. Dual-pinhole electron collimators created a 0.318-cm diameter, approximately parallel beam incident on the spectrometer and an appropriate dose rate at the image plane (CR strip location). X-ray background in the latent image, reduced by a 7.62-cm thick lead block between the pinhole collimators, was removed using a fitting technique. Theoretical energy-dependent detector response functions (DRFs) were used in an iterative technique to transform CR strip net mean dose profiles into energy spectra on central axis at the entrance to the spectrometer. These spectra were transformed to spectra at 95-cm source to collimator distance (SCD) by correcting for the energy dependence of electron scatter. The spectrometer was calibrated by comparing peak mean positions in the net mean dose profiles, initially to peak mean energies determined from the practical range of central-axis percent depth-dose (%DD) curves, and then to peak mean energies that accounted for how the collimation modified the energy spectra (recalibration). The utility of the spectrometer was demonstrated by measuring the energy spectra for the seven electron beams (7–20 MeV) of an Elekta Infinity radiotherapy accelerator. Results: Plots of DRF illustrated their dependence on energy and position in the imaging plane. Approximately 15 iterations solved for the energy spectra at the spectrometer entrance from the measured net mean dose profiles. Transforming those spectra into ones at 95-cm SCD increased the low energy tail of the spectra, while correspondingly decreasing the peaks and shifting them to slightly lower energies. Energy calibration plots of peak mean energy versus peak mean position of the net mean dose profiles for each of the seven electron beams followed the shape predicted by the Lorentz force law for a uniform z-component of the magnetic field, validating its being modeled as uniform (0.542 ± 0.027 T). Measured Elekta energy spectra and their peak mean energies correlated with the 0.5-cm (7–13 MeV) and the 1.0-cm (13–20 MeV) R{sub 90} spacings of the %DD curves. The full-width-half-maximum of the energy spectra decreased with decreasing peak mean energy with the exception of the 9-MeV beam, which was anomalously wide. Similarly, R{sub 80–20} decreased linearly with peak mean energy with the exception of the 9 MeV beam. Both were attributed to suboptimal tuning of the high power phase shifter for the recycled radiofrequency power reentering the traveling wave accelerator. Conclusions: The apparatus and analysis techniques of the authors demonstrated that an inexpensive, lightweight, permanent magnet electron energy spectrometer can be used for measuring the electron energy distributions of therapeutic electron beams (6–20 MeV). The primary goal of future work is to develop a real-time spectrometer by incorporating a real-time imager, which has potential applications such as beam matching, ongoing beam tune maintenance, and measuring spectra for input into Monte Carlo beam calculations.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

Tau-REx I: A next generation retrieval code for exoplanetary atmospheres

Spectroscopy of exoplanetary atmospheres has become a well established method for the characterization of extrasolar planets. We here present a novel inverse retrieval code for exoplanetary atmospheres. T-REx(Tau Retrieval for Exoplanets) is a line-by-line radiative transfer fully Bayesian retrieval framework. T-REx includes the following features:(1) the optimized use of molecular line lists from the ExoMol project; (2) an unbiased atmospheric composition prior selection, through custom built pattern recognition software; (3) the use of two independent algorithms to fully sample the Bayesian likelihood space: nested sampling as well as a more classical Markov Chain Monte Carlo approach; (4) iterative Bayesian parameter and model selection using the full Bayesian Evidence as well as the Savage–Dickey Ratio for nested models; and (5) the ability to fully map very large parameter spaces through optimal code parallelization and scalability to cluster computing. In this publication we outline the T-REx framework and demonstrate, using a theoretical hot-Jupiter transmission spectrum, the parameter retrieval and model selection. We investigate the impact of signal-to-noise ratio and spectral resolution on the retrievability of individual model parameters, both in terms of error bars on the temperature and molecular mixing ratios as well as its effect on the model’s global Bayesian evidence.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Chebyshev polynomial filtered subspace iteration in the discontinuous Galerkin method for large-scale electronic structure calculations

The Discontinuous Galerkin (DG) electronic structure method employs an adaptive local basis (ALB) set to solve the Kohn-Sham equations of density functional theory in a discontinuous Galerkin framework. The adaptive local basis is generated on-the-fly to capture the local material physics and can systematically attain chemical accuracy with only a few tens of degrees of freedom per atom. A central issue for large-scale calculations, however, is the computation of the electron density (and subsequently, ground state properties) from the discretized Hamiltonian in an efficient and scalable manner. We show in this work how Chebyshev polynomial filtered subspace iteration (CheFSI) can be used to address this issue and push the envelope in large-scale materials simulations in a discontinuous Galerkin framework. We describe how the subspace filtering steps can be performed in an efficient and scalable manner using a two-dimensional parallelization scheme, thanks to the orthogonality of the DG basis set and block-sparse structure of the DG Hamiltonian matrix. The on-the-fly nature of the ALB functions requires additional care in carrying out the subspace iterations. We demonstrate the parallel scalability of the DG-CheFSI approach in calculations of large-scale twodimensional graphene sheets and bulk three-dimensional lithium-ion electrolyte systems. In conclusion, employing 55 296 computational cores, the time per self-consistent field iteration for a sample of the bulk 3D electrolyte containing 8586 atoms is 90 s, and the time for a graphene sheet containing 11 520 atoms is 75 s.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

SU-E-I-89: Assessment of CT Radiation Dose and Image Quality for An Automated Tube Potential Selection Algorithm Using Pediatric Anthropomorphic and ACR Phantoms

Purpose: To assess the impact of General Electrics automated tube potential algorithm, kV assist (kVa) on radiation dose and image quality, with an emphasis on optimizing protocols based on noise texture. Methods: Radiation dose was assessed by inserting optically stimulated luminescence dosimeters (OSLs) throughout the body of a pediatric anthropomorphic phantom (CIRS). The baseline protocol was: 120 kVp, 80 mA, 0.7s rotation time. Image quality was assessed by calculating the contrast to noise ratio (CNR) and noise power spectrum (NPS) from the ACR CT accreditation phantom. CNRs were calculated according to the steps described in ACR CT phantom testing document. NPS was determined by taking the 3D FFT of the uniformity section of the ACR phantom. NPS and CNR were evaluated with and without kVa and for all available adaptive iterative statistical reconstruction (ASiR) settings, ranging from 0 to 100%. Each NPS was also evaluated for its peak frequency difference (PFD) with respect to the baseline protocol. Results: For the baseline protocol, CNR was found to decrease from 0.460 ± 0.182 to 0.420 ± 0.057 when kVa was activated. When compared against the baseline protocol, the PFD at ASiR of 40% yielded a decrease in noise magnitude as realized by the increase in CNR = 0.620 ± 0.040. The liver dose decreased by 30% with kVa activation. Conclusion: Application of kVa reduces the liver dose up to 30%. However, reduction in image quality for abdominal scans occurs when using the automated tube voltage selection feature at the baseline protocol. As demonstrated by the CNR and NPS analysis, the texture and magnitude of the noise in reconstructed images at ASiR 40% was found to be the same as our baseline images. We have demonstrated that 30% dose reduction is possible when using 40% ASiR with kVa in pediatric patients.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

SU-E-I-99: Estimation of Effective Charge Distribution by Dual-Energy CT Reconstruction

Purpose: Computed Tomography (CT) is a method to produce slice image of specific volume from the scanned x-ray projection images. The contrast of CT image is correlated with the attenuation coefficients of the x-ray in the object. The attenuation coefficient is strongly dependent on the x-ray energy and the effective charge of the material. The purpose of this presentation is to show the effective charge distribution predicted by CT images reconstructed with kilovoltage(kV) and megavoltage(MV) x-ray energy. Methods: The attenuation coefficients of x-ray can be characterized by cross section of photoionization and Compton scattering for the specific xray energy. In particular, the photoionization cross section is strongly correlated with the effective charge of the object. Hence we can calculate effective charge by solving the coupled equation between the attenuation coefficient and the theoretical cross section. For this study, we use the megavoltage (MV) and kilovoltage (kV) x-rays of Elekta Synergy as the dual source x-ray, and CT image of the Phantom Laboratory CatPhan is reconstructed by the filtered back projection (FBP) and iterative algorithm for cone-beam CT (CBCT). Results: We report attenuation coefficients of each component of the CatPhan specified by each x-ray source. Also the effective charge distribution is evaluated by the MV and kV dual x-ray sources. The predicted effective charges are comparable with the nominal ones. Conclusion: We developed the MV and kV dual-source CBCT reconstruction to yield the effective charge distribution. For more accuracy, it is critical to remove an effect of the scattering photon in the CBCT reconstruction algorithm. The finding will be fine reference of the effective charge of tissue and lead to the more realistic absorbed-dose calculation. This work was partly supported by the JSPS Core-to-Core Program(No. 23003), and this work was partly supported by JSPS KAKENHI 24234567.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2018

Block preconditioning for fault/fracture mechanics saddle-point problems

The efficient simulation of fault and fracture mechanics is a key issue in several applications and is attracting a growing interest by the scientific community. Using a formulation based on Lagrange multipliers, the Jacobian matrix resulting from the Finite Element discretization of the governing equations has a non-symmetric generalized saddle-point structure. In this work, we propose a family of block preconditioners to accelerate the convergence of Krylov methods for such problems. We critically review possible advantages and difficulties of using various Schur complement approximations, based on both physical and algebraic considerations. In conclusion, the proposed approaches are tested in a number of real-world applications, showing their robustness and efficiency also in large-size and ill-conditioned problems.

42 ENGINEERING↗
DOE OSTI2016

WE-AB-207A-04: Random Undersampled Cone Beam CT: Theoretical Analysis and a Novel Reconstruction Method

Purpose: Reducing x-ray exposure and speeding up data acquisition motived studies on projection data undersampling. It is an important question that for a given undersampling ratio, what the optimal undersampling approach is. In this study, we propose a new undersampling scheme: random-ray undersampling. We will mathematically analyze its projection matrix properties and demonstrate its advantages. We will also propose a new reconstruction method that simultaneously performs CT image reconstruction and projection domain data restoration. Methods: By representing projection operator under the basis of singular vectors of full projection operator, matrix representations for an undersampling case can be generated and numerical singular value decomposition can be performed. We compared properties of matrices among three undersampling approaches: regular-view undersampling, regular-ray undersampling, and the proposed random-ray undersampling. To accomplish CT reconstruction for random undersampling, we developed a novel method that iteratively performs CT reconstruction and missing projection data restoration via regularization approaches. Results: For a given undersampling ratio, random-ray undersampling preserved mathematical properties of full projection operator better than the other two approaches. This translates to advantages of reconstructing CT images at lower errors. Different types of image artifacts were observed depending on undersampling strategies, which were ascribed to the unique singular vectors of the sampling operators in the image domain. We tested the proposed reconstruction algorithm on a Forbid phantom with only 30% of the projection data randomly acquired. Reconstructed image error was reduced from 9.4% in a TV method to 7.6% in the proposed method. Conclusion: The proposed random-ray undersampling is mathematically advantageous over other typical undersampling approaches. It may permit better image reconstruction at the same undersampling ratio. The novel algorithm suitable for this random-ray undersampling was able to reconstruct high-quality images.

60 APPLIED LIFE SCIENCES↗
NASA NTRS1996

Quasi-Optimal Schwarz Methods for the Conforming Spectral Element Discretization

Fast methods are proposed for solving the system K(sub N)x = b resulting from the discretization of self-adjoint elliptic equations in three dimensional domains by the spectral element method. The domain is decomposed into hexahedral elements, and in each of these elements the discretization space is formed by polynomials of degree N in each variable. Gauss-Lobatto-Legendre (GLL) quadrature rules replace the integrals in the Galerkin formulation. This system is solved by the preconditioned conjugate gradients method. The conforming finite element space on the GLL mesh consisting of piecewise Q(sub 1) elements produces a stiffness matrix K(sub h) that is spectrally equivalent to the spectral element stiffness matrix K(sub N). The action of the inverse of K(sub h) is expensive for large problems, and is therefore replaced by a Schwarz preconditioner B(sub h) of this finite element stiffness matrix. The preconditioned operator then becomes B(sub h)(exp -l)K(sub N). The technical difficulties stem from the nonregularity of the mesh. Tools to estimate the convergence of a large class of new iterative substructuring and overlapping Schwarz preconditioners are developed. This technique also provides a new analysis for an iterative substructuring method proposed by Pavarino and Widlund for the spectral element discretization.

Casarin, Mario↗