Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “normalization method”

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 1,477 records · Page 82

A numerical classical flutter analysis of advanced propellers

A three-dimensional Euler solver is coupled with a three-dimensional structural dynamics model to investigate flutter of propfans. An implicit-explicit hybrid scheme is used to reduce computational time for the solution of Euler equations. The aeroelastic equations are formulated in normal modes and are solved for flutter in frequency domain. The required generalized forces are obtained using a pulse response method. Computations show that the instability is dominated by the second mode frequency as was observed in experiment.

Srivastava, R.↗

Heating of the nighttime D region by very low frequency transmitters

VLF signals propagating in the Earth-ionosphere waveguide are used to probe the heated nighttime D region over three U.S. Navy very low frequency (VLF,3-30 kHz) transmitters. Ionospheric cooling and heating are observed when a transmitter turns off and on in the course of normal operations. Heating by the 24.0-kHz NAA transmitter in Cutler, Maine, (1000 kW radiated power) was observed by this method in 41 of 52 off/on episodes during December 1992, increasing the amplitude and retarding the phase of the 21.4-kHz NSS probe wave propagating from Annapolis, Maryland, to Gander, Newfoundland, by as much as 0.84 dB and 5.3 deg, respectively. In 6 of these 41 episodes, the amplitude of the 28.5-kHz NAU probe wave propagating from Puerto Rico to Gander was also perturbed by as much as 0.29 dB. The latter observations were unexpected due to the greater than 770 km distance between NAA and the NAU-Gander great circle path. Heating by the NSS (21.4 kHz, 265 kW) and NLK (24.8 kHz, 850 kW) transmitters was observed serendipitously in data from earlier measurements of the amplitudes of VLF signals propagating in the Earth-ionosphere waveguide. A three-dimensional model of wave absorption and electron heating in a magnetized, weakly ionized plasma is used to calculate the extent nad shape of the collision frequency (i.e., electron temperature) enhancement above a VLF transmitter. The enhancements are annular, with a geomagnetic north-south asymmetry and a radius at the outer half-maximum of the collision frequency enhancement of about 150 km. Heating by the NAA transmitter is predicted to increase the nighttime D region electron temperature by as much as a factor of 3. The calculated changes in the D region conductivity are used in a three-dimensional model of propagation in the Earth-ionosphere wavelength to predict the effect of the heated patch on a subionospheric VLF probe wave. The range of predicted scattered field amplitudes is in general consistent with the observed signal perturbations. Discrepanices in the predictions are attributed to lack of knowledge of the D region electron density profile along the probe wave great circle paths.

Rodriguez, Juan V.↗

Discovery of Cepheids in NGC 5253: Absolute peak brightness of SN Ia 1895B and SN Ia 1972E and the value of H(sub 0)

Observations of the Hubble Space Telescope (HST) between 1993 May 31 and 1993 July 19 in 20 epochs in the F555W passband and five epochs in the F785LP passband have led to the discovery of 14 Cepheids in the Amorphous galaxy NGC 5253. The apparent V distance modulus is (m-M)(sub AV) = 28.08 +/- 0.10 determined from the 12 Cepheids with normal amplitudes. The distance modulus using the F785LP data is consistent with the V value to within the errors. Five methods used to determine the internal reddening are consistent with zero differential reddening, accurate to a level of E(B-V) less than 0.05 mag, over the region occupied by Cepheids and the two supernovae (SNe) produced by NGC 5253. The apparent magnitudes at maximum for the two SNe in NGC 5253 are adopted as B(sub max) = 8.33 +/- 0.2 mag for SN 1895B, and B(sub max) = 8.56 +/- 0.1 and V(sub max) = 8.60 +/- 0.1 for SN 1972E which is a prototype SN of Type Ia. The apparent magnitude system used by Walker (1923) for SN 1859B has been corrected to the modern B scale and zero point to determine its adopted B(sub max) value.

Saha, A.↗

Study of the effects of MeV Ag, Cu, Au, and Sn implantation on the optical properties of LiNbO3

The authors present the results of characterization of linear absorption and nonlinear refractive index of Au, Ag, Cu and Sn ion implantation into LiNbO3. Ag was implanted at 1.5 MeV to fluences of 2 to 17 x 17(exp 16)/sq cm at room temperature. Au and Cu were implanted to fluences of 5 to 20 x 10(exp 16)/sq cm at an energy of 2.0 MeV. Sn was implanted to a fluence of 1.6 x 10(exp 17)/sq cm at 160 kV. Optical absorption spectrometry indicated an absorption peak for the Au implanted samples after heat treatment at 1,000 C at approx. 620 nm. The Ag implanted samples absorption peaks shifted from approx. 450 nm before heat treatment to 550 nm after 500 C for 1h. Heat treatment at 800 C returned the Ag implanted crystals to a clear state. Cu nanocluster absorption peaks disappears at 500 C. No Sn clusters were observed by optical absorption or XRD. The size of the Ag and Au clusters as a function of heat treatment were determined from the absorption peaks. The Ag clusters did not change appreciably in size with heat treatment. The Au clusters increased from 3 to 9 nm diameter upon heat treatment at 1000 C. TEM analysis performed on a Au implanted crystal indicated the formation of Au nanocrystals with facets normal to the c-axis. Measurements of the nonlinear refractive indices were carried out using the Z-scan method with a tunable dye laser pumped by a frequency doubled mode-locked Nd:YAG laser. The dye laser had a 4.5 ps pulse duration time and 76 MHz pulse repetition rate (575 nm).

Williams, E. K.↗

Scaling the Non-linear Impact Response of Flat and Curved Composite Panels

The application of scaling laws to thin flat and curved composite panels exhibiting nonlinear response when subjected to low-velocity transverse impact is investigated. Previous research has shown that the elastic impact response of structural configurations exhibiting geometrically linear response can be effectively scaled. In the present paper, a preliminary experimental study is presented to assess the applicability of the scaling laws to structural configurations exhibiting geometrically nonlinear deformations. The effect of damage on the scalability of the structural response characteristics, and the effect of scale on damage development are also investigated. Damage is evaluated using conventional methods including C-scan, specimen de-plying and visual inspection of the impacted panels. Coefficient of restitution and normalized contact duration are also used to assess the extent of damage. The results confirm the validity of the scaling parameters for elastic impacts. However, for the panels considered in the study, the extent and manifestation of damage do not scale according to the scaling laws. Furthermore, the results indicate that even though the damage does not scale, the overall panel response characteristics, as indicated by contact force profiles, do scale for some levels of damage.

Ambur, Damodar R.↗

Synthesis of Elongated Microcapsules

One of the factors that influence the effectiveness of self-healing in functional materials is the amount of liquid healing agents that can be delivered to the damaged area. The use of hollow tubes or fibers and the more sophisticated micro-vascular networks has been proposed as a way to increase the amount of healing agents that can be released when damage is inflicted. Although these systems might be effective in some specific applications, they are not practical for coatings applications. One possible practical way to increase the healing efficiency is to use microcapsules with high-aspect-ratios, or elongated microcapsules. It is understood that elongated microcapsules will be more efficient because they can release more healing agent than a spherical microcapsule when a crack is initiated in the coating. Although the potential advantage of using elongated microcapsules for self healing applications is clear, it is very difficult to make elongated microcapsules from an emulsion system because spherical microcapsules are normally formed due to the interfacial tension between the dispersed phase and the continuous phase. This paper describes the two methods that have been developed by the authors to synthesize elongated microcapsules. The first method involves the use of an emulsion with intermediate stability and the second involves the application of mechanical shear conditions to the emulsion.

Li, Wenyan↗

NASA Tech Briefs, Februrary 2013

Topics covered include: Measurements of Ultra-Stable Oscillator (USO) Allan Deviations in Space; Gaseous Nitrogen Orifice Mass Flow Calculator; Validation of Proposed Metrics for Two-Body Abrasion Scratch Test Analysis Standards; Rover Low Gain Antenna Qualification for Deep Space Thermal Environments; Automated, Ultra-Sterile Solid Sample Handling and Analysis on a Chip; Measuring and Estimating Normalized Contrast in Infrared Flash Thermography; Spectrally and Radiometrically Stable, Wideband, Onboard Calibration Source; High-Reliability Waveguide Vacuum/Pressure Window; Methods of Fabricating Scintillators With Radioisotopes for Beta Battery Applications; Magnetic Shield for Adiabatic Demagnetization Refrigerators (ADR); CMOS-Compatible SOI MESFETS for Radiation-Hardened DC-to-DC Converters; Silicon Heat Pipe Array; Adaptive Phase Delay Generator; High-Temperature, Lightweight, Self-Healing Ceramic Composites for Aircraft Engine Applications; Treatment to Control Adhesion of Silicone-Based Elastomers; High-Temperature Adhesives for Thermally Stable Aero-Assist Technologies; Rockballer Sample Acquisition Tool; Rock Gripper for Sampling, Mobility, Anchoring, and Manipulation; Advanced Magnetic Materials Methods and Numerical Models for Fluidization in Microgravity and Hypogravity; Data Transfer for Multiple Sensor Networks Over a Broad Temperature Range; Using Combustion Synthesis to Reinforce Berms and Other Regolith Structures; Visible-Infrared Hyperspectral Image Projector; Three-Axis Attitude Estimation With a High-Bandwidth Angular Rate Sensor Change_Detection.m; AGATE: Adversarial Game Analysis for Tactical Evaluation; Ionospheric Simulation System for Satellite Observations and Global Assimilative; Modeling Experiments (ISOGAME); An Extensible, User- Modifiable Framework for Planning Activities; Mission Operations Center (MOC) - Precipitation Processing System (PPS) Interface Software System (MPISS); Automated 3D Damaged Cavity Model Builder for Lower Surface Acreage Tile on Orbiter; Mixed Linear/Square-Root Encoded Single-Slope Ramp Provides Low-Noise ADC with High Linearity for Focal Plane Arrays; RUSHMAPS: Real-Time Uploadable Spherical Harmonic Moment Analysis for Particle Spectrometers; Powered Descent Guidance with General Thrust-Pointing Constraints; X-Ray Detection and Processing Models for Spacecraft Navigation and Timing; and Extreme Ionizing-Radiation-Resistant Bacterium

Source record↗

Anomaly forecasting and early warning generation

The example embodiments are directed to a system and method for forecasting anomalies in feature detection. In one example, the method includes storing feature behavior information of at least one monitoring node of an asset, including a normalcy boundary identifying normal feature behavior and abnormal feature behavior for the at least one monitoring node in feature space, receiving input signals from the at least one monitoring node of the asset and transforming the input signals into feature values in the feature space, wherein the feature values are located within the normalcy boundary, forecasting that a future feature value corresponding to a future input signal from the at least one monitoring node is going to be positioned outside the normalcy boundary based on the feature values within the normalcy boundary, and outputting information concerning the forecasted future feature value being outside the normalcy boundary for display.

Abbaszadeh, Masoud↗

Application of Monte Carlo code SHIFT for MSBR dose rate calculations

This paper presents a study that applied the Monte Carlo code SHIFT to calculate the radiological environment within a detailed Molten Salt Breeder Reactor (MSBR) model. It represents one of the first applications of the SHIFT code in stand-alone simulations for non-light water reactors to help demonstrate the code's potential uses in the design, licensing, and operation of advanced reactors. The radiological conditions of the MSBR were modeled when the reactor is at two different operation modes: normal full power and a drained state. The Forward Weighted-Consistent Adjoint Driven Importance Sampling (FW-CADIS) hybrid method in SHIFT was applied successfully to calculate the ex-core neutron and gamma dose rates for the MSBR at full power. Neutron and gamma dose rates within the drain cell were also calculated for the MSBR at the drained state by integrating the source terms obtained from an ORIGEN-S depletion calculation into the SHIFT simulation. The results indicate that in the drained state, the delayed gammas from the depleted fuel salt are the main contributors to the dose rates. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Application of the method of characteristics to supersonic rotational flow

A system for calculating the physical properties of supersonic rotational flow with axial symmetry and supersonic rotational flow in a two-dimensional field was determined by use of the characteristics method. The system was applied to the study of external and internal flow for supersonic inlets with axial symmetry. For a circular conical inlet the shock that occurred at the lip of the inlet became stronger as it approached the axis of the inlet and became a normal shock at the axis. The region in which strong shock occurred increased with increase of the angle of internal cone at the lip of the inlet. For an inlet with a central body the method of characteristics was applied to the design of an internal channel shape that, theoretically, results in very efficient recompression in the inlet. It was shown that if an effuser is connected with the diffuser a body of revolution with very small shock-wave drag can be determined. (author)

Ferri, Antonio↗

Trithiol ligand provides tumor-targeting 191 Pt-complexes with high molar activity and promising in vivo properties

The Auger electron-emitting radionuclide 191 Pt is a promising candidate for radiopharmaceutical therapy. Herein, we explored novel labeling methods for 191 Pt using thiol-containing ligands to improve the in vivo stability and targeting ability of 191 Pt-labeled complexes. We synthesized dithiol-containing N 2 S 2 and NS 2 ligands, and a trithiol ligand, and then compared their radiochemical reactivity with 191 Pt. [ 191 Pt]Pt-trithiol was synthesized and its biodistribution was evaluated in mice and compared with free 191 Pt. Finally, a 191 Pt-trithiol complex targeting prostate-specific membrane antigen (PSMA): [ 191 Pt]Pt-trithiol-PSMA was developed and evaluated in mice bearing tumor xenografts and compared with a 191 Pt-complex labeled via monothiol-containing Cys ([ 191 Pt]Pt-Cys-PSMA). A comparison of N 2 S 2 , NS 2 , and trithiol showed that the trithiol ligand is the best for producing 191 Pt-labeled compounds in high yield and as a single peak in preparative HPLC. Notably, the trithiol ligand made 191 Pt-labeled compounds and precursors separatable, achieving 191 Pt-labeled products with a high molar activity: 200–400 mCi/μmol (7.4–14.8 GBq/μmol) at EOS. Additionally, [ 191 Pt]Pt-trithiol and [ 191 Pt]Pt-trithiol-PSMA were stable in vivo with rapid clearance compared with free 191 Pt and [ 191 Pt]Pt-Cys-PSMA. [ 191 Pt]Pt-trithiol-PSMA resulted in a low uptake in most normal organs and a high uptake in the kidneys and prostate cancer with PSMA expression. Furthermore, this study demonstrated that a labeling method with trithiol for Pt radionuclides achieves 191 Pt-labeled products with high molar activity. 191 Pt-trithiol-PSMA showed promising in vivo stability and tumor-targeting specificity, which should facilitate the pharmaceutical development of Pt radionuclides for radiopharmaceutical therapy, especially Auger electron cancer therapy.

Auger emitters↗

Lagrangian displacement field estimators in cosmology

The late-time nonlinear Lagrangian displacement field is highly correlated with the initial field, so reconstructing it could enable us to extract primordial cosmological information. Our previous work carefully studied the displacement field reconstructed from the late-time density field using the iterative method proposed and found that it does not fully converge to the true, underlying displacement field (e.g., ~8 % offset at k ~ 0.2 h Mpc –1 at z = 0.6 ). We also constructed the Lagrangian perturbation theory model for the reconstructed field, but the model could not explain the discrepancy between the true and the reconstructed fields in the previous work. Here, the main sources of the discrepancy were speculated to be a numerical artifact in the displacement estimator due to the discreteness of the sample. In this paper, we develop two new estimators of the displacement fields to reduce such a numerical discreteness effect, the normalized momentum estimator and the rescaled resumed estimator. We show that the discrepancy reported is not due to the numerical artifacts. We conclude that the method cannot fully reconstruct the shape of the nonlinear displacement field at the redshift we studied, while it is still an efficient baryon acoustic oscillation reconstruction method. In parallel, by properly accounting for the UV-sensitive term in a reconstruction procedure with an effective field theory approach, we improve the theoretical model for the reconstructed displacement field, by almost 5 times, from ~15% to the level of a few percent at k ~ 0.2 h Mpc –1 at the redshift z = 0.6.

79 ASTRONOMY AND ASTROPHYSICS↗

CarcSeq Measurement of Rat Mammary Cancer Driver Mutations and Relation to Spontaneous Mammary Neoplasia

Abstract The ability to deduce carcinogenic potential from subchronic, repeat dose rodent studies would constitute a major advance in chemical safety assessment and drug development. This study investigated an error-corrected NGS method (CarcSeq) for quantifying cancer driver mutations (CDMs) and deriving a metric of clonal expansion predictive of future neoplastic potential. CarcSeq was designed to interrogate subsets of amplicons encompassing hotspot CDMs applicable to a variety of cancers. Previously, normal human breast DNA was analyzed by CarcSeq and metrics based on mammary-specific CDMs were correlated with tissue donor age, a surrogate of breast cancer risk. Here we report development of parallel methodologies for rat. The utility of the rat CarcSeq method for predicting neoplastic potential was investigated by analyzing mammary tissue of 16-week-old untreated rats with known differences in spontaneous mammary neoplasia (Fischer 344, Wistar Han, and Sprague Dawley). Hundreds of mutants with mutant fractions ≥ 10−4 were quantified in each strain, most were recurrent mutations, and 42.5% of the nonsynonymous mutations have human homologs. Mutants in the mammary-specific target of the most tumor-sensitive strain (Sprague Dawley) showed the greatest nonsynonymous/synonymous mutation ratio, indicative of positive selection consistent with clonal expansion. For the mammary-specific target (Hras, Pik3ca, and Tp53 amplicons), median absolute deviation correlated with percentages of rats that develop spontaneous mammary neoplasia at 104 weeks (Pearson r = 1.0000, 1-tailed p = .0010). Therefore, this study produced evidence CarcSeq analysis of spontaneously occurring CDMs can be used to derive an early metric of clonal expansion relatable to long-term neoplastic outcome.

McKim, Karen L.↗

Changes in Oculomotor Behavior and PVT Reaction Time During One Night of Sleep Deprivation

INTRODUCTION: The Psychomotor Vigilance Test (PVT) is a widely used objective measure of sustained attention, alertness, and fatigue. Previous studies consistently show that prolonged wakefulness and disrupted sleep patterns lead to increased lapses of attention and slower reaction times. These findings have critical implications for various professions, including healthcare, aviation, transportation safety, and spaceflight. In this study, we employed linear mixed models (LMM) to investigate hourly-measured 5-minute PVT reaction times during one night of total sleep deprivation. Our goal was to characterize the contribution of homeostatic sleep pressure (time awake) and circadian phase (salivary melatonin levels) on the dynamics of PVT reaction time. MATERIALS & METHODS: Data from twelve human participants were used in the analysis. Participants were healthy non-smokers, aged 18 and 40, with normal sleep habits defined as Pittsburg Sleep Quality Index scores < 5, and Morningness – Eveningness Questionnaire scores > 42 and < 58, respectively. Participants followed a constant-routine protocol and arrived at the NASA sleep laboratory approximately 1 to 2 hours after their habitual waking time. Tympanic temperature was measured every 30 min to provide a real-time estimate of circadian phase. Participants were required to stay awake throughout the laboratory experiment, which continued until their tympanic temperature had returned to baseline levels. This approach ensured that we could capture each participant's circadian trough and recovery, typically occurring between 24 and 26 hours after waking. The PVT and saliva melatonin were measured every hour, starting approximately from 3 hours after awakening. More information about the measurement protocol can be found in the publication by Stone et al. We used PVT reaction times between 100 and 10000 ms to calculate Reciprocal Reaction Times (RRTs). LMM models were employed to assess the contribution of time awake and saliva melatonin levels on changes in RRTs. Two models were created: the first model treated time awake as a fixed effect and the second model considered both the salivary melatonin level and time awake as fixed effects. Participants were included as a random effect in both models. We compared the models using an Analysis of Variance (ANOVA). The models were computed using the 'lmer' function from the 'lme4' package in R, and LMM p-values were determined using Satterthwaite's method. RESULTS: We found that time awake had a statistically significant effect on PVT RRTs during one night of sleep deprivation [χ2 = 2132.4, df = 1, p < 0.001]. In addition, the model including both saliva melatonin levels and time awake was statistically significantly better than one that uses just time awake [χ2 = 17.4, df = 1, p < 0.001]. DISCUSSION & CONCLUSION: As expected, these preliminary results suggest that the time awake and circadian phase each contribute to performance reductions as measured by the PVT. Future analyses will explore the contributions of other factors to the model.

sleep deprivation↗

PRODeepSyn: predicting anticancer synergistic drug combinations by embedding cell lines with protein–protein interaction network

Abstract Although drug combinations in cancer treatment appear to be a promising therapeutic strategy with respect to monotherapy, it is arduous to discover new synergistic drug combinations due to the combinatorial explosion. Deep learning technology holds immense promise for better prediction of in vitro synergistic drug combinations for certain cell lines. In methods applying such technology, omics data are widely adopted to construct cell line features. However, biological network data are rarely considered yet, which is worthy of in-depth study. In this study, we propose a novel deep learning method, termed PRODeepSyn, for predicting anticancer synergistic drug combinations. By leveraging the Graph Convolutional Network, PRODeepSyn integrates the protein–protein interaction (PPI) network with omics data to construct low-dimensional dense embeddings for cell lines. PRODeepSyn then builds a deep neural network with the Batch Normalization mechanism to predict synergy scores using the cell line embeddings and drug features. PRODeepSyn achieves the lowest root mean square error of 15.08 and the highest Pearson correlation coefficient of 0.75, outperforming two deep learning methods and four machine learning methods. On the classification task, PRODeepSyn achieves an area under the receiver operator characteristics curve of 0.90, an area under the precision–recall curve of 0.63 and a Cohen’s Kappa of 0.53. In the ablation study, we find that using the multi-omics data and the integrated PPI network’s information both can improve the prediction results. Additionally, the case study demonstrates the consistency between PRODeepSyn and previous studies.

Wang, Xiaowen↗

Current Status of Radiopharmaceutical Therapy

In radiopharmaceutical therapy (RPT), a radionuclide is systemically or locally delivered with the goal of targeting and delivering radiation to cancer cells while minimizing radiation exposure to untargeted cells. Examples of current RPTs include thyroid ablation with the administration of {sup 131}I, treatment of liver cancer with {sup 90}Y microspheres, the treatment of bony metastases with {sup 223}Ra, and the treatment of neuroendocrine tumors with {sup 177}Lu-DOTATATE. New RPTs are being developed where radionuclides are incorporated into systemic targeted therapies. To assure that RPT is appropriately implemented, advances in targeting need to be matched with advances in quantitative imaging and dosimetry methods. Currently, radiopharmaceutical therapy is administered by intravenous or locoregional injection, and the treatment planning has typically been implemented like chemotherapy, where the activity administered is either fixed or based on a patient’s body weight or body surface area. RPT pharmacokinetics are measurable by quantitative imaging and are known to vary across patients, both in tumors and normal tissues. Therefore, fixed or weight-based activity prescriptions are not currently optimized to deliver a cytotoxic dose to targets while remaining within the tolerance dose of organs at risk. Methods that provide dose estimates to individual patients rather than to reference geometries are needed to assess and adjust the injected RPT dose. Accurate doses to targets and organs at risk will benefit the individual patients and decrease uncertainties in clinical trials. Imaging can be used to measure activity distribution in vivo, and this information can be used to determine patient-specific treatment plans where the dose to the targets and organs at risk can be calculated. The development and adoption of imaging-based dosimetry methods is particularly beneficial in early clinical trials. In this work we discuss dosimetric accuracy needs in modern radiation oncology, uncertainties in the dosimetry in RPT, and best approaches for imaging and dosimetry of internal radionuclide therapy.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

A new color correlation method applied to XRF Al/Si ratios and other lunar remote sensing data

Orbital X-ray fluorescence Al/Si intensity ratios, corrected for variations in solar activity, are correlated with normal albedo, elevation measurements from laser altimetry data, and gamma ray data in the 2.75-8.60 MeV range. Each of these data sets is placed into a digital array consisting of 1/4 deg latitude by 1/4 deg longitude pixels. Information relative to the correlation of Al/Si ratios with each of the other data sets is presented in the following forms: (1) histograms are given for each data set to show the frequency distribution within the areas of common coverage; (2) density plots are produced from the plot of a two-dimensional array consisting of the Al/Si ratio vs the other parameter value for each pixel; and (3) color correlation maps are produced by placing the two-dimensional array into a 3 x 3 matrix consisting of nine equal subarrays containing an equal number of data points.

Clark, P. E.↗

An iterative method for the Helmholtz equation

An iterative algorithm for the solution of the Helmholtz equation is developed. The algorithm is based on a preconditioned conjugate gradient iteration for the normal equations. The preconditioning is based on an SSOR sweep for the discrete Laplacian. Numerical results are presented for a wide variety of problems of physical interest and demonstrate the effectiveness of the algorithm.

Bayliss, A.↗