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At least 451 records · Page 25
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

SU-F-T-431: Dosimetric Validation of Acuros XB Algorithm for Photon Dose Calculation in Water

Purpose: To validate the Acuros XB algorithm implemented in Eclipse Treatment planning system version 11 (Varian Medical System, Inc., Palo Alto, CA, USA) for photon dose calculation. Methods: Acuros XB is a Linear Boltzmann transport equation (LBTE) solver that solves LBTE equation explicitly and gives result equivalent to Monte Carlo. 6MV photon beam from Varian Clinac-iX (2300CD) was used for dosimetric validation of Acuros XB. Percentage depth dose (PDD) and profiles (at dmax, 5, 10, 20 and 30 cm) measurements were performed in water for field size ranging from 2×2,4×4, 6×6, 10×10, 20×20, 30×30 and 40×40 cm{sup 2}. Acuros XB results were compared against measurements and anisotropic analytical algorithm (AAA) algorithm. Results: Acuros XB result shows good agreement with measurements, and were comparable to AAA algorithm. Result for PDD and profiles shows less than one percent difference from measurements, and from calculated PDD and profiles by AAA algorithm for all field size. TPS calculated Gamma error histogram values, average gamma errors in PDD curves before dmax and after dmax were 0.28, 0.15 for Acuros XB and 0.24, 0.17 for AAA respectively, average gamma error in profile curves in central region, penumbra region and outside field region were 0.17, 0.21, 0.42 for Acuros XB and 0.10, 0.22, 0.35 for AAA respectively. Conclusion: The dosimetric validation of Acuros XB algorithms in water medium was satisfactory. Acuros XB algorithm has potential to perform photon dose calculation with high accuracy, which is more desirable for modern radiotherapy environment.

60 APPLIED LIFE SCIENCES↗
NASA NTRS2011

Space-Time Data Fusion

Space-time Data Fusion (STDF) is a methodology for combing heterogeneous remote sensing data to optimally estimate the true values of a geophysical field of interest, and obtain uncertainties for those estimates. The input data sets may have different observing characteristics including different footprints, spatial resolutions and fields of view, orbit cycles, biases, and noise characteristics. Despite these differences all observed data can be linked to the underlying field, and therefore the each other, by a statistical model. Differences in footprints and other geometric characteristics are accounted for by parameterizing pixel-level remote sensing observations as spatial integrals of true field values lying within pixel boundaries, plus measurement error. Both spatial and temporal correlations in the true field and in the observations are estimated and incorporated through the use of a space-time random effects (STRE) model. Once the models parameters are estimated, we use it to derive expressions for optimal (minimum mean squared error and unbiased) estimates of the true field at any arbitrary location of interest, computed from the observations. Standard errors of these estimates are also produced, allowing confidence intervals to be constructed. The procedure is carried out on a fine spatial grid to approximate a continuous field. We demonstrate STDF by applying it to the problem of estimating CO2 concentration in the lower-atmosphere using data from the Atmospheric Infrared Sounder (AIRS) and the Japanese Greenhouse Gasses Observing Satellite (GOSAT) over one year for the continental US.

Greenhouse Gases Observing Satellite (GOSAT)↗
DOE OSTI2014

SU-E-T-278: Realization of Dose Verification Tool for IMRT Plan Based On DPM

Purpose: To build a Monte Carlo dose verification tool for IMRT Plan by implementing a irradiation source model into DPM code. Extend the ability of DPM to calculate any incident angles and irregular-inhomogeneous fields. Methods: With the virtual source and the energy spectrum which unfolded from the accelerator measurement data,combined with optimized intensity maps to calculate the dose distribution of the irradiation irregular-inhomogeneous field. The irradiation source model of accelerator was substituted by a grid-based surface source. The contour and the intensity distribution of the surface source were optimized by ARTS (Accurate/Advanced Radiotherapy System) optimization module based on the tumor configuration. The weight of the emitter was decided by the grid intensity. The direction of the emitter was decided by the combination of the virtual source and the emitter emitting position. The photon energy spectrum unfolded from the accelerator measurement data was adjusted by compensating the contaminated electron source. For verification, measured data and realistic clinical IMRT plan were compared with DPM dose calculation. Results: The regular field was verified by comparing with the measured data. It was illustrated that the differences were acceptable (<2% inside the field, 2–3mm in the penumbra). The dose calculation of irregular field by DPM simulation was also compared with that of FSPB (Finite Size Pencil Beam) and the passing rate of gamma analysis was 95.1% for peripheral lung cancer. The regular field and the irregular rotational field were all within the range of permitting error. The computing time of regular fields were less than 2h, and the test of peripheral lung cancer was 160min. Through parallel processing, the adapted DPM could complete the calculation of IMRT plan within half an hour. Conclusion: The adapted parallelized DPM code with irradiation source model is faster than classic Monte Carlo codes. Its computational accuracy and speed satisfy the clinical requirement, and it is expectable to be a Monte Carlo dose verification tool for IMRT Plan. Strategic Priority Research Program of the China Academy of Science(XDA03040000); National Natural Science Foundation of China (81101132)

60 APPLIED LIFE SCIENCES↗
NASA NTRS1974

An elementary magnetic attitude control system

A three-axis closed-loop attitude-control system for earth-observatory momentum-bias spacecraft is proposed. A horizon scanner and magnetometer are employed to measure attitude errors; no yaw sensor is required. Appropriate control signals are generated and used to command variable-strength electromagnets, which interact with the geomagnetic field to reduce observed errors. This system provides for initial acquisition, precession control, nutation damping, and pitch-axis momentum control. All functions are performed autonomously - no ground-station interaction is required. Analytical expressions predicting system response are compared with numerical solutions of the governing equations, and with the results of the application of Floquet Theory.-

Stickler, A. C.↗
NASA NTRS2003

Divergence Free High Order Filter Methods for Multiscale Non-ideal MHD Flows

Low-dissipative high order filter finite difference methods for long time wave propagation of shock/turbulence/combustion compressible viscous MHD flows has been constructed. Several variants of the filter approach that cater to different flow types are proposed. These filters provide a natural and efficient way for the minimization of the divergence of the magnetic field (Delta . B) numerical error in the sense that no standard divergence cleaning is required. For certain 2-D MHD test problems, divergence free preservation of the magnetic fields of these filter schemes has been achieved.

Yee, H. C.↗
NASA NTRS1980

Solar Power Satellite /SPS/ antenna measurement considerations

An investigation carried out by the Georgia Institute of Technology that quantified the error contributors associated with both far-field and near-field antenna measurement concepts is discussed. Measurement errors are quantified into four sources: antenna range, structural/environmental, transmitter, and receiver. The study is carried out so as to control error sources to yield an overall gain uncertainty of plus or minus 0.04 dB. With regard to antenna positioners, it is found that a small angle positioner provides highly accurate scan capability over a plus or minus 1.5 deg sector for the purpose of beam integration. With regard to near-field measurement techniques, it is found that with adequate probe calibration and precision mechanical scanning, full 30 by 30 m mechanical module antenna measurements may be performed. The performance and relative cost considerations between planar near-field and conventional far-field methods indicate that the overall costs are roughly the same.

Kozakoff, D. J.↗
DOE OSTI2014

SU-E-J-09: A Monte Carlo Analysis of the Relationship Between Cherenkov Light Emission and Dose for Electrons, Protons, and X-Ray Photons

Purpose: A number of recent studies have proposed that light emitted by the Cherenkov effect may be used for a number of radiation therapy dosimetry applications. Here we investigate the fundamental nature and accuracy of the technique for the first time by using a theoretical and Monte Carlo based analysis. Methods: Using the GEANT4 architecture for medically-oriented simulations (GAMOS) and BEAMnrc for phase space file generation, the light yield, material variability, field size and energy dependence, and overall agreement between the Cherenkov light emission and dose deposition for electron, proton, and flattened, unflattened, and parallel opposed x-ray photon beams was explored. Results: Due to the exponential attenuation of x-ray photons, Cherenkov light emission and dose deposition were identical for monoenergetic pencil beams. However, polyenergetic beams exhibited errors with depth due to beam hardening, with the error being inversely related to beam energy. For finite field sizes, the error with depth was inversely proportional to field size, and lateral errors in the umbra were greater for larger field sizes. For opposed beams, the technique was most accurate due to an averaging out of beam hardening in a single beam. The technique was found to be not suitable for measuring electron beams, except for relative dosimetry of a plane at a single depth. Due to a lack of light emission, the technique was found to be unsuitable for proton beams. Conclusions: The results from this exploratory study suggest that optical dosimetry by the Cherenkov effect may be most applicable to near monoenergetic x-ray photon beams (e.g. Co-60), dynamic IMRT and VMAT plans, as well as narrow beams used for SRT and SRS. For electron beams, the technique would be best suited for superficial dosimetry, and for protons the technique is not applicable due to a lack of light emission. NIH R01CA109558 and R21EB017559.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2014

Detecting and Testing for Structural Error in Computer Models with Application to the Community Atmospheric Model

Bayesian calibration/inversion methods for uncertain input parameters to simulation codes have generated an increasing amount of interest in the climate community in the recent years. This approach uses multiple disparate observational datasets related to the output of the simulator of interest to yield a probabilistic constraint on the uncertain inputs (i.e. probability distribution). A major challenge in applying Bayesian calibration methods to simulation codes is related to the possible presence of a large structural error in the output fields of interest; that is, the presence of discrepancy between the observed and the simulated output that is neither explained by the uncertainty in the inputs nor the observations. We present here methods to test for and visualize structural error in an ensemble of input-perturbed simulations. The methods are based on bootstrap (resmpling) test statistics and well-known metrics to quantify the difference between two probability distributions. The proposed methods are demonstrated using selected precipitation output fields of the Community Atmospheric Model (CAM), which are compared to observations provided by the Global Precipitation Climatology Project (GPCP). The methods are found to be useful in identifying regions and seasons with a large structural error. The proposed structural error detection methodology can be used to screen multiple observational datasets of interest for structural error, making it possible to retain only the datasets with a small structural error for use in Bayesian calibration. In addition, information about the amount of structural error can be valuable to model developers.

58 GEOSCIENCES↗
DOE OSTI2020

Measuring Transverse Displacements Using Unmanned Aerial Systems Laser Doppler Vibrometer (UAS-LDV): Development and Field Validation

Measurement of bridge displacements is important for ensuring the safe operation of railway bridges. Traditionally, contact sensors such as Linear Variable Displacement Transducers (LVDT) and accelerometers have been used to measure the displacement of the railway bridges. However, these sensors need significant effort in installation and maintenance. Therefore, railroad management agencies are interested in new means to measure bridge displacements. This research focuses on mounting Laser Doppler Vibrometer (LDV) on an Unmanned Aerial System (UAS) to enable contact-free transverse dynamic displacement of railroad bridges. Researchers conducted three field tests by flying the Unmanned Aerial Systems Laser Doppler Vibrometer (UAS-LDV) 1.5 m away from the ground and measured the displacement of a moving target at various distances. The accuracy of the UAS-LDV measurements was compared to the Linear Variable Differential Transducer (LVDT) measurements. The results of the three field tests showed that the proposed system could measure non-contact, reference-free dynamic displacement with an average peak and root mean square (RMS) error for the three experiments of 10% and 8% compared to LVDT, respectively. Such errors are acceptable for field measurements in railroads, as the interest prior to bridge monitoring implementation of a new approach is to demonstrate similar success for different flights, as reported in the three results. This study also identified barriers for industrial adoption of this technology and proposed operational development practices for both technical and cost-effective implementation.

42 ENGINEERING↗
DOE OSTI2014

Supine Craniospinal Irradiation Using a Proton Pencil Beam Scanning Technique Without Match Line Changes for Field Junctions

Purpose: To propose and validate a craniospinal irradiation approach using a proton pencil beam scanning technique that overcomes the complexity of the planning associated with feathering match lines. Methods and Materials: Ten craniospinal irradiation patients had treatment planned with gradient dose optimization using the proton pencil beam scanning technique. The robustness of the plans was evaluated by shifting the isocenter of each treatment field by ±3 mm in the longitudinal direction and was compared with the original nonshifted plan with metrics of conformity number, homogeneity index, and maximal cord doses. An anthropomorphic phantom study using film measurements was carried out on a plan with 5-cm junction length. To mimic setup errors in the phantom study, fields were recalculated with isocenter shifts of 1, 3, 5, and 10 mm longitudinally, and compared with the original plans and measurements. Results: Uniform dose coverage to the entire target volumes was achieved using the gradient optimization approach with averaged junction lengths of 6.7 ± 0.5 cm. The average conformity number and homogeneity index equaled 0.78 ± 0.03 and 1.09 ± 0.01, respectively. Setup errors of 3 mm per field (6 mm in worst-case scenario) caused on average 4.6% lower conformity number 2.5% higher homogeneity index and maximal cord dose of 4216.1 ± 98.2 cGy. When the junction length was 5 cm or longer, setup errors of 6 mm resulted in up to 12% dosimetric deviation. Consistent results were reached between film measurements and planned dose profiles in the junction area. Conclusions: Longitudinal setup errors directly reduce the dosimetric accuracy of the proton craniospinal irradiation treatment with matched proton pencil beam scanning fields. The reported technique creates a slow dose gradient in the junction area, which makes the treatment more robust to longitudinal setup errors compared to conventional feathering methods.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
NASA NTRS1993

Lunar gravitational field estimation and the effects of mismodeling upon lunar satellite orbit prediction

Lunar spherical harmonic gravity coefficients are estimated from simulated observations of a near-circular low altitude polar orbiter disturbed by lunar mascons. Lunar gravity sensing missions using earth-based nearside observations with and without satellite-based far-side observations are simulated and least squares maximum likelihood estimates are developed for spherical harmonic expansion fit models. Simulations and parameter estimations are performed by a modified version of the Smithsonian Astrophysical Observatory's Planetary Ephemeris Program. Two different lunar spacecraft mission phases are simulated to evaluate the estimated fit models. Results for predicting state covariances one orbit ahead are presented along with the state errors resulting from the mismodeled gravity field. The position errors from planning a lunar landing maneuver with a mismodeled gravity field are also presented. These simulations clearly demonstrate the need to include observations of satellite motion over the far side in estimating the lunar gravity field. The simulations also illustrate that the eighth degree and order expansions used in the simulated fits were unable to adequately model lunar mascons.

Davis, John H.↗
DOE OSTI2020

Unmanned Aerial Vehicle Path Generation for Image Collection to Assist Heliostat Field Optical Characterization

This paper focuses on applications of unmanned aerial vehicles (UAVs) for measuring optical error of heliostats in concentrating solar power (CSP) plants. In CSP, there is a need to measure solar-field optical errors, which is critical for future production improvement as well as for operations and maintenance of a heliostat field. This latter need is particularly challenging because of the large number of heliostats (over 10,000 for a utility-scale power plant) that individually track the sun in the field. To address this issue, a camera-equipped UAV, with an optimized drone flight path developed and uploaded to it, collects images of a precise reflection of the tower on each heliostat to evaluate optical error sources without interrupting plant operation. Generation of the drone path for capturing the reflected images is affected by a number technical and realistic constraints, which include the camera angle used to capture the image, the blocking of the camera view due to surrounding heliostats, the location of the camera in reference to the target heliostat, and the target heliostat position with reference to the tower. The effect of these constraints on calculating the camera position will be discussed in detail in this article. An effective drone-path algorithm is generated to fulfil the need of image collection under various constraints.

concentrated solar power↗
DOE OSTI2023

Machine learning from RANS and LES to inform coarse grid simulations

Nuclear system thermal hydraulic analysis has historically relied on computationally inexpensive 1D codes. However, such tools are unable to capture multiscale multidimensional effects in large nuclear reactor enclosures. On the other hand, simulations with higher fidelity can be too expensive for such purposes. One of the ways to reduce computational cost is to perform simulations on a coarse grid, which, unfortunately, introduces large discretization errors. In this paper, two high-to-low data-driven approaches are investigated: (1) a coarse grid turbulence model to predict eddy viscosity and (2) correction of errors in coarse grid velocity fields. The approaches aim to reduce grid- and turbulence model-induced errors in coarse grid Reynolds-averaged Navier–Stokes (RANS) simulations. Two sources of high-fidelity data, RANS and large eddy simulations (LES), are explored. To extract the eddy viscosity from the LES data, an inverse optimization problem is solved. However, the LES eddy viscosity is shown to be comparable to the RANS eddy viscosity in terms of error reduction. Therefore, the directly available RANS eddy viscosity was used to develop a coarse grid data-driven turbulence model. Additionally, error correction in velocity is used to reduce the remaining uncertainties and bring the results closer to reality. In conclusion, the performance of the frameworks is demonstrated for a scaled upper plenum of a gas-cooled reactor facility.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2014

Beam characteristics of energy-matched flattening filter free beams

Purpose: Flattening filter free (FFF) linear accelerators can increase treatment efficiency and plan quality. There are multiple methods of defining a FFF beam. The Elekta control system supports tuning of the delivered FFF beam energy to enable matching of the percentage depth-dose (PDD) of the flattened beam at 10 cm depth. This is compared to FFF beams where the linac control parameters are identical to those for the flattened beam. All beams were delivered on an Elekta Synergy accelerator with an Agility multi-leaf collimator installed and compared to the standard, flattened beam. The aim of this study is to compare “matched” FFF beams to both “unmatched” FFF beams and flattened beams to determine the benefits of matching beams. Methods: For the three modes of operation 6 MV flattened, 6 MV matched FFF, 6 MV unmatched FFF, 10 MV flattened, 10 MV matched FFF, and 10 MV unmatched FFF beam profiles were obtained using a plotting tank and were measured in steps of 0.1 mm in the penumbral region. Beam penumbra was defined as the distance between the 80% and 20% of the normalized dose when the inflection points of the unflattened and flattened profiles were normalized with the central axis dose of the flattened field set as 100%. PDD data was obtained at field sizes ranging from 3 cm × 3 cm to 40 cm × 40 cm. Radiation protection measurements were additionally performed to determine the head leakage and environmental monitoring through the maze and primary barriers. Results: No significant change is made to the beam penumbra for FFF beams with and without PDD matching, the maximum change in penumbra for a 10 cm × 10 cm field was within the experimental error of the study. The changes in the profile shape with increasing field size are most significant for the matched FFF beam, and both FFF beams showed less profile shape variation with increasing depth when compared to flattened beams, due to consistency in beam energy spectra across the radiation field. The PDDs of the FFF beams showed less variation with field size, the d{sub max} value was deeper for the matched FFF beam than the FFF beam and deeper than the flattened beam for field sizes greater than 5 cm × 5 cm. The head leakage when using the machine in FFF mode is less than half that for a flattened beam, but comparable for both FFF modes. The radiation protection dose-rate measurements show an increase of instantaneous dose-rates when operating the machines in FFF mode but that increase is less than the ratio of MU/min produced by the machine. Conclusions: The matching of a FFF beam to a flattened beam at a depth of 10 cm in water by increasing the FFF beam energy does not reduce any of the reported benefits of FFF beams. Conversely, there are a number of potential benefits resulting from matching the FFF beam; the depth of maximum dose is deeper, the out of field dose is potentially reduced, and the beam quality and penetration more closely resembles the flattened beams currently used in clinical practice, making dose distributions in water more alike. Highlighted in this work is the fact that some conventional specifications and methods for measurement of beam parameters such as penumbra are not relevant and further work is required to address this situation with respect to “matched” FFF beams and to determine methods of measurement that are not reliant on an associated flattened beam.

43 PARTICLE ACCELERATORS↗
DOE OSTI2014

SU-E-T-377: Inaccurate Positioning Might Introduce Significant MapCheck Calibration Error in Flatten Filter Free Beams

Purpose: This study investigates the calibration error of detector sensitivity for MapCheck due to inaccurate positioning of the device, which is not taken into account by the current commercial iterative calibration algorithm. We hypothesize the calibration is more vulnerable to the positioning error for the flatten filter free (FFF) beams than the conventional flatten filter flattened beams. Methods: MapCheck2 was calibrated with 10MV conventional and FFF beams, with careful alignment and with 1cm positioning error during calibration, respectively. Open fields of 37cmx37cm were delivered to gauge the impact of resultant calibration errors. The local calibration error was modeled as a detector independent multiplication factor, with which propagation error was estimated with positioning error from 1mm to 1cm. The calibrated sensitivities, without positioning error, were compared between the conventional and FFF beams to evaluate the dependence on the beam type. Results: The 1cm positioning error leads to 0.39% and 5.24% local calibration error in the conventional and FFF beams respectively. After propagating to the edges of MapCheck, the calibration errors become 6.5% and 57.7%, respectively. The propagation error increases almost linearly with respect to the positioning error. The difference of sensitivities between the conventional and FFF beams was small (0.11 ± 0.49%). Conclusion: The results demonstrate that the positioning error is not handled by the current commercial calibration algorithm of MapCheck. Particularly, the calibration errors for the FFF beams are ~9 times greater than those for the conventional beams with identical positioning error, and a small 1mm positioning error might lead to up to 8% calibration error. Since the sensitivities are only slightly dependent of the beam type and the conventional beam is less affected by the positioning error, it is advisable to cross-check the sensitivities between the conventional and FFF beams to detect potential calibration errors due to inaccurate positioning. This work was partially supported by a DOD Grant No.; DOD W81XWH1010862.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS1990

Accuracy analysis of the semi-analytical method for shape sensitivity calculation

The semianalytical method of design sensitivity analysis that is widely used for calculating derivatives of static response with respect to design variables for structures modeled by finite elements is studied. It is shown that the method can have serious accuracy problems for shape design variables in structures modeled by beam, plate, truss, frame, and solid elements. Errors are shown to be associated with an incompatibility of the sensitivity field with the structure. An error index is developed to test the accuracy of the semianalytical method. It characterizes the difference in errors between a general finite-difference method and the semianalytical method. A method for improving the accuracy of the semianalytical method (when possible) is provided. Examples are presented to demonstrate the use of the error index.

Barthelemy, Bruno↗
NASA NTRS1991

Stray signal requirements for compact range reflectors based on RCS measurement errors

The authors present a performance criterion for compact range reflectors such that their edge diffracted stray signal levels meet a reasonable radar cross section (RCS) measurement error requirement. It is shown by example that one of the significant error sources is the diffracted fields emanating from the edges or junctions of the reflector. This measurement error is demonstrated by placing a diagonal square flat plate in the target zone and rotating it to appropriate angles. These angles are determined by bisecting the plane wave and stray signal directions. This results in a peak bistatic measurement of the edge diffracted stray signal. It is proposed that the diagonal flat plate be used to evaluate new reflector designs as well as existing systems. A reasonable stray signal performance level has been developed so that new reflector systems can be characterized in terms of an RCS measurement error requirement.

Lee, Teh-Hong↗
NASA NTRS2005

Application of Parallel Adjoint-Based Error Estimation and Anisotropic Grid Adaptation for Three-Dimensional Aerospace Configurations

This paper demonstrates the extension of error estimation and adaptation methods to parallel computations enabling larger, more realistic aerospace applications and the quantification of discretization errors for complex 3-D solutions. Results were shown for an inviscid sonic-boom prediction about a double-cone configuration and a wing/body segmented leading edge (SLE) configuration where the output function of the adjoint was pressure integrated over a part of the cylinder in the near field. After multiple cycles of error estimation and surface/field adaptation, a significant improvement in the inviscid solution for the sonic boom signature of the double cone was observed. Although the double-cone adaptation was initiated from a very coarse mesh, the near-field pressure signature from the final adapted mesh compared very well with the wind-tunnel data which illustrates that the adjoint-based error estimation and adaptation process requires no a priori refinement of the mesh. Similarly, the near-field pressure signature for the SLE wing/body sonic boom configuration showed a significant improvement from the initial coarse mesh to the final adapted mesh in comparison with the wind tunnel results. Error estimation and field adaptation results were also presented for the viscous transonic drag prediction of the DLR-F6 wing/body configuration, and results were compared to a series of globally refined meshes. Two of these globally refined meshes were used as a starting point for the error estimation and field-adaptation process where the output function for the adjoint was the total drag. The field-adapted results showed an improvement in the prediction of the drag in comparison with the finest globally refined mesh and a reduction in the estimate of the remaining drag error. The adjoint-based adaptation parameter showed a need for increased resolution in the surface of the wing/body as well as a need for wake resolution downstream of the fuselage and wing trailing edge in order to achieve the requested drag tolerance. Although further adaptation was required to meet the requested tolerance, no further cycles were computed in order to avoid large discrepancies between the surface mesh spacing and the refined field spacing.

Lee-Rausch, E. M.↗