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DOE OSTI2015

Improvement of the wear resistance of electroplated Au-Ni coatings by Zr ion bombardment of Ni-B sublayer

The effect of bombardment of the Ni-B sublayer by Zr ion beams on the surface morphology and tribomechanical properties of Au-Ni coatings was investigated. It was found that the treatment has no significant effect on the surface roughness and grain size of the Au-Ni coatings, while it provides essential reducing of their friction coefficient and improvement of wear resistance. It is shown that increased wear resistance of these coatings was caused by their strain hardening resulted from localization of plastic strain. The optimal Zr fluence were determined that provide the maximum reduction of linear wear of the coatings.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Design and analysis of a ten-turbine floating wind farm with shared mooring lines

This paper discusses the development and analysis of a novel design for a 10-turbine floating wind farm with shared mooring lines. Shared mooring lines tether adjacent floating platforms together, reducing the number of anchors required but increasing system complexity. We present a systematic, multistage design process for shared mooring systems, involving linearized analysis of array layout options, quasi-static mooring line optimization, and design refinement based on coupled dynamic loads analysis. The design developed from this process is thought to represent one of the most advantageous shared-mooring configurations for this scale of floating wind array. It features perpendicular anchor line pairs and allows shared, multiline anchors, making it an example of a shared-mooring-and-anchor array. Comparing the performance and cost characteristics of the shared-mooring design with more conventional three-line individual mooring systems shows equivalent dynamic response characteristics and stationkeeping system cost savings of 25% when using shared mooring lines and shared anchors. The design is also advantageous in the case of a mooring line failure, with offsets and redundancy characteristics similar to four-line individual mooring systems.

17 WIND ENERGY↗

DOE OSTI2024

Uniform accuracy of implicit-explicit Runge-Kutta (IMEX-RK) schemes for hyperbolic systems with relaxation

Implicit-explicit Runge-Kutta (IMEX-RK) schemes are popular methods to treat multiscale equations that contain a stiff part and a non-stiff part, where the stiff part is characterized by a small parameter. Here, in this work, we prove rigorously the uniform stability and uniform accuracy of a class of IMEX-RK schemes for a linear hyperbolic system with stiff relaxation. The result we obtain is optimal in the sense that it holds regardless of the value of and the order of accuracy is the same as the design order of the original scheme, i.e., there is no order reduction.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Orbital angular momentum constraints in the variational optimization of the two-electron reduced-density matrix

The direct variational determination of the two-electron reduced-density matrix (2-RDM) corresponding to an atomic or molecular system is usually carried out in a basis of real-valued atom-centered Gaussian basis functions, under the assumption that the 2-RDM is a real-valued quantity. Furthermore, for systems that possess orbital angular momentum symmetry, the description of states with a well-defined, nonzero z projection of the orbital angular momentum requires a computational framework generalized to include either complex basis functions or a complex-valued 2-RDM. We consider a semidefinite program suitable for the direct optimization of a complex-valued 2-RDM and explore the role of orbital angular momentum constraints in systems that possess the relevant symmetries. For atomic systems, constraints on the expectation values of the square and z projection of the orbital angular momentum operator allow one to optimize 2-RDMs for multiple orbital angular momentum states. Similarly, in linear molecules, orbital angular momentum projection constraints enable the description of multiple electronic states and, moreover, the application of such constraints is essential for a qualitatively correct description of the electronic structure. For example, in the case of molecular oxygen, we demonstrate that orbital angular momentum constraints are necessary to recover the correct energy ordering of the lowest-energy singlet and triplet states near the equilibrium geometry. However, care must still be taken in the description of the dissociation limit, because the 2-RDM-based approach is not size consistent, and the size-consistency error varies dramatically, depending on the z projections of the spin and orbital angular momenta.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2024

A Performance and Energy Study of GPU-Resident Preconditioners for Conjugate Gradient Solvers: In the Context of Existing and Novel Approaches

Optimizing a particular subprogram out of the set of Basic (sparse) Linear Algebra Subprograms (BLAS) for a given architecture is a common topic of research. In applications, however, these BLAS functions rarely appear in isolation; usually, many of them are used together, in various combinations and with varying inputs. As the need to solve a large, sparse linear system is ubiquitous throughout HPC applications, linear solvers constitute a realistic, sufficiently complex and well-defined representative use case for composite BLAS routines. To this end, based on a representative set of matrices drawn from a diverse set of fields, we present a framework to study, from the performance and energy perspective, the efficacy of GPU- resident parallel Conjugate Gradient (CG) linear solver with different preconditioner options, including Gauss-Seidel, Jacobi, and incomplete Cholesky. We also propose a novel GPU-based preconditioner, in which the triangular solves are approximated by an iterative process. The development of this preconditioner was motivated by solving large graph Laplacian linear systems, for which the existing preconditioners either perform slow on GPU-based platforms or are not applicable. We compare the performance of these preconditioners on different hardware accelerator architectures, i.e., AMD MI250X, MI100, Nvidia A100, V100, and Jetson. Our experiments reveal performance trade-offs and provide information on how to select the best strategy for the given linear system, dictated by its properties, and the platform of interest. We demonstrate the application of our novel preconditioner for solving CG and graph Laplacian systems. Overall, the framework can be utilized as a benchmark to guide informed decisions in choosing a specific preconditioner, i.e., whether it is better to rely on the performance of a triangular solver or on the performance of sparse matrix-vector product. Finally, by considering power consumption to solve the linear systems, we report the energy footprint for the solvers.

Preconditioned Conjugate Gradient, GPUs, iterative↗

DOE OSTI2017

Multiresonant Feedback Control of a Three-Degree-of-Freedom Wave Energy Converter

For a three-degree-of-freedom wave energy converter (heave, pitch, and surge), the equations of motion could be coupled depending on the buoy shape. This paper presents a multiresonant feedback control, in a general framework, for this type of a wave energy converter that is modeled by linear time invariant dynamic systems. The proposed control strategy finds the optimal control in the sense that it computes the control based on the complex conjugate criteria. This control strategy is relatively easy to implement since it is a feedback control in the time domain that requires only measurements of the buoy motion. Numerical tests are presented for two different buoy shapes: a sphere and a cylinder. Regular, Bretschnieder, and Ochi-Hubble waves are tested. Simulation results show that the proposed controller harvests energy in the pitch-surge-heave modes that is about three times the energy that can be harvested using a heave-only device. In conclusion, this multiresonant control can also be used to shift the energy harvesting between the coupled modes, which can be exploited to eliminate one of the actuators while maintaining about the same level of energy harvesting.

42 ENGINEERING↗

DOE OSTI2014

Economic and Physical Modeling of Land Use in GCAM 3.0 and an Application to Agricultural Productivity, Land, and Terrestrial Carbon

We explore the impact of changes in agricultural productivity on global land use and terrestrial carbon using the new agriculture and land use modeling approach developed for Global Change Assessment Model (GCAM) version 3.0. This approach models economic land use decisions with regional, physical, and technological specificity while maintaining economic and physical integration with the rest of the GCAM model. Physical land characteristics and quantities are tracked explicitly, and crop production practices are modeled discretely to facilitate coupling with physical models. Economic land allocation is modeled with non-linear functions in a market equilibrium rather than through a constrained optimization. In this paper, we explore three scenarios of future agriculture productivity in all regions of the globe over this century, ranging from a high growth to a zero growth level. The higher productivity growth scenario leads to lower crop prices, increased production of crops in developing nations, preservation of global forested lands and lower terrestrial carbon emissions. The scenario with no productivity improvement results in higher crop prices, an expansion of crop production in the developed world, loss of forested lands globally, and higher terrestrial carbon emissions.

Wise, Marshall A.↗

DOE OSTI2025

Data for "RT-EZ: A Golden Gate Assembly Toolkit for Streamlined Genetic Engineering of Rhodotorula toruloides"

For economic and sustainable biomanufacturing, the oleaginous yeast Rhodotorula toruloides has emerged as a promising platform for producing biofuels, pharmaceuticals, and other valuable chemicals. However, genetic manipulation of R. toruloides has been limited by its high GC content and the lack of a replicating plasmid, necessitating gene integration into the genome of the yeast. To address these challenges, we developed the RT-EZ ( R. toruloides Efficient Zipper) toolkit, a versatile tool based on Golden Gate assembly, designed to streamline R. toruloides engineering with improved efficiency and flexibility. The RT-EZ toolkit simplifies vector construction by incorporating new features such as bidirectional promoters and 2A peptides, color-based screening using RFP, and sequences optimized for both Agrobacterium tumefaciens-mediated transformation (ATMT) and easy linearization, enabling straightforward selection and transformation. Notably, the RT-EZ kit can be used to construct an expression cassette with four different genes in one assembly reaction, significantly improving vector construction speed and efficiency. The utility of the RT-EZ toolkit was demonstrated through the successful synthesis of arachidonic acid in R. toruloides by coexpressing fatty acid elongases and desaturases. This result underscores the potential of the RT-EZ toolkit to advance synthetic biology in R. toruloides , providing a streamlined method for addressing genetic engineering challenges in the yeast.

gene editing↗

DOE OSTI2015

Development of Metallic Magnetic Calorimeters for Nuclear Safeguards Applications

Many nuclear safeguards applications could benefit from high-resolution gamma-ray spectroscopy achievable with metallic magnetic calorimeters. This dissertation covers the development of a system for these applications based on gamma-ray detectors developed at the University of Heidelberg. It demonstrates new calorimeters of this type, which achieved an energy resolution of 45.5 eV full-width at half-maximum at 59.54 keV, roughly ten times better than current state of the art high purity germanium detectors. This is the best energy resolution achieved with a gamma-ray metallic magnetic calorimeter at this energy to date. In addition to demonstrating a new benchmark in energy resolution, an experimental system for measuring samples with metallic magnetic calorimeters was constructed at Lawrence Livermore National Laboratory. This system achieved an energy resolution of 91.3 eV full-width at half-maximum at 59.54 keV under optimal conditions. Using this system it was possible to characterize the linearity of the response, the count-rate limitations, and the energy resolution as a function of temperature of the new calorimeter. With this characterization it was determined that it would be feasible to measure 242Pu in a mixed isotope plutonium sample. A measurement of a mixed isotope plutonium sample was performed over the course of 12 days with a single two-pixel metallic magnetic calorimeter. The relative concentration of 242Pu in comparison to other plutonium isotopes was determined by direct measurement to less than half a percent accuracy. This is comparable with the accuracy of the best-case scenario using traditional indirect methods. The ability to directly measure the relative concentration of 242Pu in a sample could enable more accurate accounting and detection of indications of undeclared activities in nuclear safeguards, a better constraint on source material in forensic samples containing plutonium, and improvements in verification in a future plutonium disposition treaty.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

DOE OSTI2015

A Bound- and Equality-Constrained Quadratic Programming Method for Image Reconstruction

Image deblurring is modeled as an ill-posed, linear inverse problem and can be written in terms of an optimization problem. By adding bound and equality constraints and/or penalty terms to the objective function, the problem is regularized and a viable solution exists; however, there are few methods available for solving such constrained problems. Here we formulate two regularized solutions into constrained optimization problems and adapt an iterative augmented Lagrangian solver. Results are shown on synthetic data in one- and two-dimensions, as well as on a radiograph used to calibrate the transmission curve of a pulsed power X-ray source at a U.S. Department of Energy radiography facility.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2013

Adaptation of the CVT algorithm for catheter optimization in high dose rate brachytherapy

Purpose: An innovative, simple, and fast method to optimize the number and position of catheters is presented for prostate and breast high dose rate (HDR) brachytherapy, both for arbitrary templates or template-free implants (such as robotic templates).Methods: Eight clinical cases were chosen randomly from a bank of patients, previously treated in our clinic to test our method. The 2D Centroidal Voronoi Tessellations (CVT) algorithm was adapted to distribute catheters uniformly in space, within the maximum external contour of the planning target volume. The catheters optimization procedure includes the inverse planning simulated annealing algorithm (IPSA). Complete treatment plans can then be generated from the algorithm for different number of catheters. The best plan is chosen from different dosimetry criteria and will automatically provide the number of catheters and their positions. After the CVT algorithm parameters were optimized for speed and dosimetric results, it was validated against prostate clinical cases, using clinically relevant dose parameters. The robustness to implantation error was also evaluated. Finally, the efficiency of the method was tested in breast interstitial HDR brachytherapy cases.Results: The effect of the number and locations of the catheters on prostate cancer patients was studied. Treatment plans with a better or equivalent dose distributions could be obtained with fewer catheters. A better or equal prostate V100 was obtained down to 12 catheters. Plans with nine or less catheters would not be clinically acceptable in terms of prostate V100 and D90. Implantation errors up to 3 mm were acceptable since no statistical difference was found when compared to 0 mm error (p > 0.05). No significant difference in dosimetric indices was observed for the different combination of parameters within the CVT algorithm. A linear relation was found between the number of random points and the optimization time of the CVT algorithm. Because the computation time decrease with the number of points and that no effects were observed on the dosimetric indices when varying the number of sampling points and the number of iterations, they were respectively fixed to 2500 and to 100. The computation time to obtain ten complete treatments plans ranging from 9 to 18 catheters, with the corresponding dosimetric indices, was 90 s. However, 93% of the computation time is used by a research version of IPSA. For the breast, on average, the Radiation Therapy Oncology Group recommendations would be satisfied down to 12 catheters. Plans with nine or less catheters would not be clinically acceptable in terms of V100, dose homogeneity index, and D90.Conclusions: The authors have devised a simple, fast and efficient method to optimize the number and position of catheters in interstitial HDR brachytherapy. The method was shown to be robust for both prostate and breast HDR brachytherapy. More importantly, the computation time of the algorithm is acceptable for clinical use. Ultimately, this catheter optimization algorithm could be coupled with a 3D ultrasound system to allow real-time guidance and planning in HDR brachytherapy.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2015

Investigations into the Effect of Current Velocity on Amidoxime-Based Polymeric Uranium Adsorbent Performance

The Fuel Resources Program at the U.S. Department of Energy’s (DOE), Office of Nuclear Energy (DOE-NE) is developing adsorbent technology to extract uranium from seawater. This technology is being developed to provide a sustainable and economically viable supply of uranium fuel for nuclear reactors (DOE, 2010). Among the key environmental variables to understand for adsorbent deployment in the coastal ocean is what effect flow-rates or linear velocity has on uranium adsorption capacity. The goal is to find a flow conditions that optimize uranium adsorption capacity in the shortest exposure time. Understanding these criteria will be critical in choosing a location for deployment of a marine adsorbent farm. The objective of this study was to identify at what linear velocity the adsorption kinetics for uranium extraction starts to drop off due to limitations in mass transport of uranium to the surface of the adsorbent fibers. Two independent laboratory-based experimental approaches using flow-through columns and recirculating flumes for adsorbent exposure were used to assess the effect of flow-rate (linear velocity) on the kinetic uptake of uranium on amidoxime-based polymeric adsorbent material. Time series observations over a 56 day period were conducted with flow-through columns over a 35-fold range in linear velocity from 0.29 to 10.2 cm/s, while the flume study was conducted over a narrower 11-fold range, from 0.48 to 5.52 cm/s. These ranges were specifically chosen to focus on the lower end of oceanic currents and expand above and below the linear velocity of ~ 2.5 cm/s adopted for marine testing of adsorbent material at PNNL.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2016

Frame average optimization of cine-mode EPID images used for routine clinical in vivo patient dose verification of VMAT deliveries

Purpose: The in vivo 3D dose delivered to a patient during volumetric modulated arc therapy (VMAT) delivery can be calculated using electronic portal imaging device (EPID) images. These images must be acquired in cine-mode (i.e., “movie” mode) in order to capture the time-dependent delivery information. The angle subtended by each cine-mode EPID image during an arc can be changed via the frame averaging number selected within the image acquisition software. A large frame average number will decrease the EPID’s angular resolution and will result in a decrease in the accuracy of the dose information contained within each image. Alternatively, less EPID images acquired per delivery will decrease the overall 3D patient dose calculation time, which is appealing for large-scale clinical implementation. Therefore, the purpose of this study was to determine the optimal frame average value per EPID image, defined as the highest frame averaging that can be used without an appreciable loss in 3D dose reconstruction accuracy for VMAT treatments. Methods: Six different VMAT plans and six different SBRT-VMAT plans were delivered to an anthropomorphic phantom. Delivery was carried out on a Varian 2300ix model linear accelerator (Linac) equipped with an aS1000 EPID running at a frame acquisition rate of 7.5 Hz. An additional PC was set up at the Linac console area, equipped with specialized frame-grabber hardware and software packages allowing continuous acquisition of all EPID frames during delivery. Frames were averaged into “frame-averaged” EPID images using MATLAB. Each frame-averaged data set was used to calculate the in vivo dose to the patient and then compared to the single EPID frame in vivo dose calculation (the single frame calculation represents the highest possible angular resolution per EPID image). A mean percentage dose difference of low dose (<20% prescription dose) and high dose regions (>80% prescription dose) was calculated for each frame averaged scenario for each plan. The authors defined their unacceptable loss of accuracy as no more than a ±1% mean dose difference in the high dose region. Optimal frame average numbers were then determined as a function of the Linac’s average gantry speed and the dose per fraction. Results: The authors found that 9 and 11 frame averages were suitable for all VMAT and SBRT-VMAT treatments, respectively. This resulted in no more than a 1% loss to any of the dose region’s mean percentage difference when compared to the single frame reconstruction. The optimized number was dependent on the treatment’s dose per fraction and was determined to be as high as 14 for 12 Gy/fraction (fx), 15 for 8 Gy/fx, 11 for 6 Gy/fx, and 9 for 2 Gy/fx. Conclusions: The authors have determined an optimal EPID frame averaging number for multiple VMAT-type treatments. These are given as a function of the dose per fraction and average gantry speed. These optimized values are now used in the authors’ clinical, 3D, in vivo patient dosimetry program. This provides a reduction in calculation time while maintaining the authors’ required level of accuracy in the dose reconstruction.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2023

Explicit model predictive control through robust optimization

A strategy that calculates an explicit state feedback policy to regulate constrained uncertain discrete‐time uncertain linear systems is presented. We consider uncertain processes, affected by box‐bounded multiplicative uncertainty as well as bounded additive uncertainty with linear state and inputs constraints. The proposed method includes (i) the calculation of a terminal set constraint and (ii) the robust reformulation of state constraints in the prediction horizon. These features allow the derivation of the desired policy by solving a single multiparametric quadratic programming problem that guarantees feasible operation in the presence of uncertainty. Additionally, we employ variable and constraint elimination approaches to enhance the computational performance of the strategy. We demonstrate the steps and benefits of these developments with a numerical example and a chemical engineering case study.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2013

Two-dimensional inverse planning and delivery with a preclinical image guided microirradiator

Purpose: Recent advances in preclinical radiotherapy systems have provided the foundation for scaling many of the elements of clinical radiation therapy practice to the dimensions and energy demanded in small animal studies. Such systems support the technical capabilities to accurately deliver highly complex dose distributions, but methods to optimize and deliver such distributions remain in their infancy. This study developed an optimization method based on empirically measured two-dimensional dose kernel measurements to deliver arbitrary planar dose distributions on a recently developed small animal radiotherapy platform.Methods: A two-dimensional dose kernel was measured with repeated radiochromic film measurements for the circular 1 mm diameter fixed collimator of the small animal radiotherapy system at 1 cm depth in a solid water phantom. This kernel was utilized in a sequential quadratic programming optimization framework to determine optimal beam positions and weights to deliver an arbitrary desired dose distribution. The positions and weights were then translated to a set of stage motions to automatically deliver the optimized dose distribution. End-to-end efficacy of the framework was quantified through five repeated deliveries of two dosimetric challenges: (1) a 5 mm radius bullseye distribution, and (2) a “sock” distribution contained within a 9 × 13 mm bounding box incorporating rectangular, semicircular, and exponentially decaying geometric constructs and a rectangular linear dose gradient region. These two challenges were designed to gauge targeting, geometric, and dosimetric fidelity.Results: Optimization of the bullseye and sock distributions required 2.1 and 5.9 min and utilized 50 and 77 individual beams for delivery, respectively. Automated delivery of the resulting optimized distributions, validated using radiochromic film measurements, revealed an average targeting accuracy of 0.32 mm, and a dosimetric delivery error along four line profiles taken through the sock distribution of 3.9%. Mean absolute delivery error across the 0–1 Gy linear dose gradient over 7.5 mm was 0.01 Gy.Conclusions: The work presented here demonstrates the potential for complex dose distributions to be planned and automatically delivered with millimeter scale heterogeneity at submillimeter accuracy. This capability establishes the technical foundation for preclinical validation of biologically guided radiotherapy investigations and development of unique radiobiological experiments.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2014

SU-C-17A-07: The Development of An MR Accelerator-Enabled Planning-To-Delivery Technique for Stereotactic Palliative Radiotherapy Treatment of Spinal Metastases

Purpose: To develop an MR accelerator-enabled online planning-todelivery technique for stereotactic palliative radiotherapy treatment of spinal metastases. The technical challenges include; automated stereotactic treatment planning, online MR-based dose calculation and MR guidance during treatment. Methods: Using the CT data of 20 patients previously treated at our institution, a class solution for automated treatment planning for spinal bone metastases was created. For accurate dose simulation right before treatment, we fused geometrically correct online MR data with pretreatment CT data of the target volume (TV). For target tracking during treatment, a dynamic T2-weighted TSE MR sequence was developed. An in house developed GPU based IMRT optimization and dose calculation algorithm was used for fast treatment planning and simulation. An automatically generated treatment plan developed with this treatment planning system was irradiated on a clinical 6 MV linear accelerator and evaluated using a Delta4 dosimeter. Results: The automated treatment planning method yielded clinically viable plans for all patients. The MR-CT fusion based dose calculation accuracy was within 2% as compared to calculations performed with original CT data. The dynamic T2-weighted TSE MR Sequence was able to provide an update of the anatomical location of the TV every 10 seconds. Dose calculation and optimization of the automatically generated treatment plans using only one GPU took on average 8 minutes. The Delta4 measurement of the irradiated plan agreed with the dose calculation with a 3%/3mm gamma pass rate of 86.4%. Conclusions: The development of an MR accelerator-enabled planning-todelivery technique for stereotactic palliative radiotherapy treatment of spinal metastases was presented. Future work will involve developing an intrafraction motion adaptation strategy, MR-only dose calculation, radiotherapy quality-assurance in a magnetic field, and streamlining the entire treatment process on an MR accelerator.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2015

Feasibility of a unified approach to intensity-modulated radiation therapy and volume-modulated arc therapy optimization and delivery

Purpose: To study the feasibility of unified intensity-modulated arc therapy (UIMAT) which combines intensity-modulated radiotherapy (IMRT) and volumetric-modulated arc therapy (VMAT) optimization and delivery to produce superior radiation treatment plans, both in terms of dose distribution and efficiency of beam delivery when compared with either VMAT or IMRT alone. Methods: An inverse planning algorithm for UIMAT was prototyped within the PINNACLE treatment planning system (Philips Healthcare). The IMRT and VMAT deliveries are unified within the same arc, with IMRT being delivered at specific gantry angles within the arc. Optimized gantry angles for the IMRT and VMAT phases are assigned automatically by the inverse optimization algorithm. Optimization of the IMRT and VMAT phases is done simultaneously using a direct aperture optimization algorithm. Five treatment plans each for prostate, head and neck, and lung were generated using a unified optimization technique and compared with clinical IMRT or VMAT plans. Delivery verification was performed with an ArcCheck phantom (Sun Nuclear) on a Varian TrueBeam linear accelerator (Varian Medical Systems). Results: In this prototype implementation, the UIMAT plans offered the same target dose coverage while reducing mean doses to organs at risk by 8.4% for head-and-neck cases, 5.7% for lung cases, and 3.5% for prostate cases, compared with the VMAT or IMRT plans. In addition, UIMAT can be delivered with similar efficiency as VMAT. Conclusions: In this proof-of-concept work, a novel radiation therapy optimization and delivery technique that interlaces VMAT or IMRT delivery within the same arc has been demonstrated. Initial results show that unified VMAT/IMRT has the potential to be superior to either standard IMRT or VMAT.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2025

Efficient shallow Ritz method for 1D diffusion problems

This paper studies the shallow Ritz method for solving the one-dimensional diffusion problem. It is shown that the shallow Ritz method improves the order of approximation dramatically for non-smooth problems. To realize this optimal or nearly optimal order of the shallow Ritz approximation, we develop a damped block Newton (dBN) method that alternates between updates of the linear and non-linear parameters. Per each iteration, the linear and the non-linear parameters are updated by exact inversion and one step of a modified, damped Newton method applied to a reduced non-linear system, respectively. The computational cost of each dBN iteration is $\mathcal{O}$(n). Starting with the non-linear parameters as a uniform partition of the interval, numerical experiments show that the dBN is capable of efficiently moving mesh points to nearly optimal locations. In conclusion, to improve the efficiency of the dBN further, we propose an adaptive damped block Newton (AdBN) method by combining the dBN with the adaptive neuron enhancement (ANE) method [28].

Diffusion problems↗