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Designing chemical analogs to PbTe with intrinsic high band degeneracy and low lattice thermal conductivity

High-efficiency thermoelectric materials require simultaneously high power factors and low thermal conductivities. Aligning band extrema to achieve high band degeneracy, as realized in PbTe, is one of the most efficient approaches to enhance power factor. However, this approach usually relies on band structure engineering, e.g., via chemical doping or strain. By employing first-principles methods with explicit computation of phonon and carrier lifetimes, here we show two full-Heusler compounds Li 2 TlBi and Li 2 InBi have exceptionally high power factors and low lattice thermal conductivities at room temperature. The expanded rock-salt sublattice of these compounds shifts the valence band maximum to the middle of the Σ line, increasing the band degeneracy by a factor of three. Meanwhile, resonant bonding in the PbTe-like sublattice and soft Tl–Bi (In–Bi) bonding interaction is responsible for intrinsic low lattice thermal conductivities. Our results present an alternative strategy of designing high performance thermoelectric materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Collective Summary of sCO2 Materials Development (Supercritical Transformational Electric Power Generation (STEP) Level 2 Milestone Report) (Parts I - II)

Polymers such as PTFE (polytetrafluorethylene or Teflon), EPDM (ethylene propylene diene monomer) rubber, FKM fluoroelastomer (Viton), Nylon 11, Nitrile butadiene (NBR) rubber, hydrogenated nitrile rubber (HNBR) and perfluoroelastomers (FF_202) are commonly employed in super critical CO 2 (sCO2) energy conversion systems. O-rings and gaskets made from these polymers face stringent performance conditions such as elevated temperatures, high pressures, pollutants, and corrosive humid environments. In FY 2019, we conducted experiments at high temperatures (100°C and 120°C) under isobaric conditions (20 MPa). Findings showed that elevated temperatures accelerated degradation of polymers in sCO2, and that certain polymer microstructures are more susceptible to degradation over others. In FY 2020, the focus was to understand the effect of sCO2 on polymers at low (10 MPa) and high pressures (40 MPa) under isothermal conditions (100°C). It was clear that the same selectivity was observed in these experiments wherein certain polymeric functionalities showed more propensity to failure over others. Fast diffusion, supported by higher pressures and long exposure times (1000 hours) at the test temperature, caused increased damage in sCO2 environments to even the most robust polymers. We also looked at polymers under compression in sCO2 at 100°C and 20 MPa pressure to imitate actual sealing performance required of these materials in sCO2 systems. Compression worsened the physical damage that resulted from chemical attack of the polymers under these test conditions. In FY 2021, the effect of cycling temperature (from 50°C to 150°C to 50°C) for polymers under a steady sCO2 pressure of 20 MPa was studied. The aim was to understand the influence of cycling temperatures of sCO2 for typical polymers under isobaric (20 MPa) conditions. Thermoplastic polymers (Nylon, and PTFE) and elastomers (EPDM, Viton, Buna N, Neoprene, FF202, and HNBR) were subjected to 20 MPa sCO2 pressure for 50 cycles and 100 cycles in separate experiments. Samples were extracted for ex-situ characterization at 50 cycles and upon the completion of 100 cycles. Each cycle constituted of 175 minutes of cycling from 50°C to 150°C. The polymer samples were examined for physical and chemical changes by Dynamic Mechanical and Thermal Analysis (DMTA), Fourier Transform Infrared (FTIR) spectroscopy, and compression set. Density and mass changes immediately after removal from test were measured for degree of swell comparisons. Optical microscopy techniques and micro computer tomography (micro CT) images were collected on select specimens. Evaluations conducted showed that exposures to super-critical CO2 environments resulted in combinations of physical and/or chemical changes. For each polymer, the dominance of cycling temperatures under sCO2 pressures, were evaluated. Attempts were made to qualitatively link the permanent sCO2 effects to polymer micro- structure, free volume, backbone substitutions, presence of polar groups, and degree of crystallinity differences. This study has established that soft polymeric materials are conducive to failure in sCO2 through mechanisms of failure that are dependent on polymer microstructure and chemistry. Polar pendant groups, large atom substitutions on the backbone are some of the factors that are influential structural factors.

36 MATERIALS SCIENCE↗

Effect of Hydrophilicity-Imparting Substituents on Exciton Delocalization in Squaraine Dye Aggregates Covalently Templated to DNA Holliday Junctions

Molecular aggregates exhibit emergent properties, including the collective sharing of electronic excitation energy known as exciton delocalization, that can be leveraged in applications such as quantum computing, optical information processing, and light harvesting. In a previous study, we found unexpectedly large excitonic interactions (quantified by the excitonic hopping parameter J m,n ) in DNA-templated aggregates of squaraine (SQ) dyes with hydrophilic-imparting sulfo and butylsulfo substituents. Here, we characterize DNA Holliday junction (DNA-HJ) templated aggregates of an expanded set of SQs and evaluate their optical properties in the context of structural heterogeneity. Specifically, we characterized the orientation of and J m,n between dyes in dimer aggregates of non-chlorinated and chlorinated SQs. Here, three new chlorinated SQs that feature a varying number of butylsulfo substituents were synthesized and attached to a DNA-HJ via a covalent linker to form adjacent and transverse dimers. Various characteristics of the dye, including its hydrophilicity (in terms of log P o/w ) and surface area, and of the substituents, including their local bulkiness and electron withdrawing capacity, were quantified computationally.

59 BASIC BIOLOGICAL SCIENCES↗

RAVEN User Manual

RAVEN is a generic software framework to perform parametric and probabilistic analy- sis based on the response of complex system codes. The initial development was aimed to provide dynamic risk analysis capabilities to the Thermo-Hydraulic code RELAP-7, currently under development at the Idaho National Laboratory (INL). Although the initial goal has been fully accomplished, RAVEN is now a multi-purpose probabilistic and uncer- tainty quantification platform, capable to agnostically communicate with any system code. This agnosticism includes providing Application Programming Interfaces (APIs). These APIs are used to allow RAVEN to interact with any code as long as all the parameters that need to be perturbed are accessible by inputs files or via python interfaces. RAVEN is capable of investigating the system response, and investigating the input space using Monte Carlo, Grid, or Latin Hyper Cube sampling schemes, but its strength is focused to- ward system feature discovery, such as limit surfaces, separating regions of the input space leading to system failure, using dynamic supervised learning techniques. The development of RAVEN has started in 2012, when, within the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, the need to provide a modern risk evaluation framework became stronger. RAVEN principal assignment is to provide the necessary software and algorithms in order to employ the concept developed by the Risk Informed Safety Margin Characterization (RISMC) program. RISMC is one of the pathways defined within the Light Water Reactor Sustainability (LWRS) program. In the RISMC approach, the goal is not just the individuation of the frequency of an event potentially leading to a system failure, but the closeness (or not) to key safety-related events. Hence, the approach is in- terested in identifying and increasing the safety margins related to those events. A safety margin is a numerical value quantifying the probability that a safety metric (e.g. for an important process such as peak pressure in a pipe) is exceeded under certain conditions. The initial development of RAVEN has been focused on providing dynamic risk assess- ment capability to RELAP-7, currently under develop-ment at the INL and, likely, future replacement of the RELAP5-3D code. Most the capabilities that have been implemented having RELAP-7 as principal focus are easily deployable for other system codes. For this reason, several side activates are currently ongoing for coupling RAVEN with soft- ware such as RELAP5-3D, etc. The aim of this document is the explaination of the input requirements, focalizing on the input structure.

97 MATHEMATICS AND COMPUTING↗

Cone-Beam Computed Tomography-Guided Percutaneous Radiologic Gastrostomy

The purpose of this study was to investigate the feasibility of a flat-detector C-arm-guided radiographic technique (cone-beam computed tomography [CBCT]) for percutaneous radiologic gastrostomy (PRG) insertion. Eighteen patients (13 men and 5 women; mean age 62 years) in whom percutaneous endoscopic gastrostomy (PEG) had failed underwent CBCT-guided PRG insertion. PEG failure or unsuitability was caused by upper gastrointestinal tract obstruction in all cases. Indications for gastrostomy were esophageal and head and neck malignancies, respectively. Before the PRG procedure, initial C-arm CBCT scans were acquired. Three- and 2-dimensional soft-tissue reconstructions of the epigastrium region were generated on a dedicated workstation. Subsequently, gastropexy was performed with T-fasteners after CBCT-guided puncture of the stomach bubble, followed by insertion of an 14F balloon-retained catheter through a peel-away introducer. Puncture of the stomach bubble and PRG insertion was technically successful in all patients without alteration of the epigastric region. There was no malpositioning of the tube or other major periprocedural complications. In 2 patients, minor complications occurred during the first 30 days of follow-up (PRG malfunction: n = 1; slight infection: n = 1). Late complications, which were mainly tube disturbances, were observed in 2 patients. The mean follow-up time was 212 days. CBCT-guided PRG is a safe, well-tolerated, and successful method of gastrostomy insertion in patients in whom endoscopic gastrostomy is not feasible. CBCT provides detailed imaging of the soft tissue and surrounding structures of the epigastric region in one diagnostic tour and thus significantly improves the planning of PRG procedures.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Axisymmetric toroidal modes of general relativistic magnetized neutron star models

We calculate axisymmetric toroidal modes of magnetized neutron stars with a solid crust in the general relativistic Cowling approximation. We assume that the interior of the star is threaded by a poloidal magnetic field, which is continuous at the surface with an outside dipole field. We examine the cases of the field strength B{sub S} ∼ 10{sup 16} G at the surface. Since separation of variables is not possible for the oscillations of magnetized stars, we employ finite series expansions for the perturbations using spherical harmonic functions. We find discrete normal toroidal modes of odd parity, but no toroidal modes of even parity are found. The frequencies of the toroidal modes form distinct mode sequences and the frequency in a given mode sequence gradually decreases as the number of radial nodes of the eigenfunction increases. From the frequency spectra computed for neutron stars of different masses, we find that the frequency is almost exactly proportional to B{sub S} and is well represented by a linear function of R/M for a given B{sub S}, where M and R are the mass and radius of the star. The toroidal mode frequencies for B{sub S} ∼ 10{sup 15} G are in the frequency range of the quasi-periodic oscillations (QPOs) detected in the soft-gamma-ray repeaters, but we find that the toroidal normal modes cannot explain all the detected QPO frequencies.

79 ASTRONOMY AND ASTROPHYSICS↗

A FOURIER-TRANSFORMED BREMSSTRAHLUNG FLASH MODEL FOR THE PRODUCTION OF X-RAY TIME LAGS IN ACCRETING BLACK HOLE SOURCES

Accreting black hole sources show a wide variety of rapid time variability, including the manifestation of time lags during X-ray transients, in which a delay (phase shift) is observed between the Fourier components of the hard and soft spectra. Despite a large body of observational evidence for time lags, no fundamental physical explanation for the origin of this phenomenon has been presented. We develop a new theoretical model for the production of X-ray time lags based on an exact analytical solution for the Fourier transform describing the diffusion and Comptonization of seed photons propagating through a spherical corona. The resulting Green's function can be convolved with any source distribution to compute the associated Fourier transform and time lags, hence allowing us to explore a wide variety of injection scenarios. We show that thermal Comptonization is able to self-consistently explain both the X-ray time lags and the steady-state (quiescent) X-ray spectrum observed in the low-hard state of Cyg X-1. The reprocessing of bremsstrahlung seed photons produces X-ray time lags that diminish with increasing Fourier frequency, in agreement with the observations for a wide range of sources.

79 ASTRONOMY AND ASTROPHYSICS↗

Resummation of jet veto logarithms at N 3 LL a + NNLO for W + W ? production at the LHC

We compute the resummed on-shell W+W- production cross section under a jet veto at the LHC to partial N3LL order matched to the fixed-order NNLO result. Differential NNLO cross sections are obtained from an implementation of qT subtraction in Sherpa. The two-loop virtual corrections to the qq¯→W+W- amplitude, used in both fixed-order and resummation predictions, are extracted from the public code qqvvamp. We perform resummation using soft collinear effective theory, with approximate beam functions where only the logarithmic terms are included at two-loop. In addition to scale uncertainties from the hard matching scale and the factorization scale, rapidity scale variations are obtained within the analytic regulator approach. Our resummation results show a decrease in the jet veto cross section compared to NNLO fixed-order predictions, with reduced scale uncertainties compared to NNLL+NLO resummed predictions. We include the loop-induced gg contribution with jet veto resummation to NLL+LO. The prediction shows good agreement with recent LHC measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Computer-Based Procedures Among Older Adults: Findings from the Rancor Microworld Simulator

As with many industries worldwide, nuclear energy is experiencing an aging workforce; older than other energy sources and the national average. For example, while almost one in three nuclear industry professionals are 55+ years, for oil and gas that number is one in five. The challenges brought about by an aging workforce are one of the industry’s top concerns. However, the industry lacks for empirical research that examines the effects of developmental aging in older workers, as well as the interactions between aging and new digital technologies. We present the results of an experiment that tested three different computer-based procedures in a sample of 30 older adults (55+ years). While the industry has traditionally relied on paper-based procedures, these are being modernized by digital technology. Participants were randomly assigned to one of three procedure-types that varied by the level of digitalization, based on the IEEE Standard-1786. Type 1 essentially represents a digital representation of a paper-based procedure, Type 2 adds embedded indicators, and Type 3 adds soft controls. Participants performed two different operational scenarios (startup and loss of feedwater) on a simplified nuclear power plant simulator. Results revealed a weak signal that Type 2 may produce lower workload and lower completion times in some instances. However, there were no significant effects of procedure-type across any other outcomes, including simulator log data, situation awareness, and preference ratings. We discuss our findings in terms of optimal levels of digitalization/automation for an aging nuclear workforce and suggest pathways for future directions.

46 - INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AN↗

An “Off-the-Shelf” System for Intraprocedural Electrical Current Evaluation and Monitoring of Irreversible Electroporation Therapy

IntroductionIrreversible electroporation (IRE) ablation uses a series of brief electric pulses to create nanoscale defects in cell membranes, killing the cells. It has shown promise in numerous soft-tissue tumor applications. Larger voltages between electrodes will increase ablation volume, but exceeding electrical limits may risk damage to the patient, cause ineffective therapy delivery, or require generator restart. Monitoring electrical current for these conditions in real-time enables managing these risks. This capacity is not presently available in clinical IRE generators.MethodsWe describe a system using a Tektronix TCP305 AC/DC Current Probe connected to a TCPA300 AC/DC Current Probe Amplifier, which is read on a computer using a Protek DSO-2090 USB computer-interfacing oscilloscope. Accuracy of the system was tested with a resistor circuit and by comparing measured currents with final outputs from the NanoKnife clinical electroporation pulse generator.ResultsAccuracy of measured currents was 1.64 ± 2.4 % relative to calculations for the resistor circuit and averaged 0.371 ± 0.977 % deviation from the NanoKnife. During clinical pulse delivery, the system offers real-time evaluation of IRE procedure progress and enables a number of methods for identifying approaching issues from electrical behavior of therapy delivery, facilitating protocol changes before encountering therapy delivery issues.ConclusionsThis system can monitor electrical currents in real-time without altering the electric pulses or modifying the pulse generator. This facilitates delivering electric pulse protocols that remain within the optimal range of electrical currents—sufficient strength for clinically relevant ablation volumes, without the risk of exceeding safe electric currents or causing inadequate ablation.

60 APPLIED LIFE SCIENCES↗

Water–Hydrocarbon Interactions in Anionic Pyrene Monohydrate

Interactions between water and polycyclic aromatic hydrocarbons are essential in many aspects of chemistry, from interstellar and atmospheric processes to interfacial hydrophobicity and wetting phenomena. Despite their growing importance, the intermolecular potentials of the water-hydrocarbon interactions are underdeveloped compared to water-water potentials, and there are similarly few experimental probes that are sensitive to the details of the water-hydrocarbon potential. We present a combined experimental and computational study of anionic pyrene monohydrate, one of the simplest water/hydrocarbon clusters. The action spectrum in the OH region of the mass-selected cluster ion provides a rigorous benchmark for intermolecular potentials and computational methodologies. We identify missing intermolecular interactions and shortcomings in conventional dynamics calculations by comparing experimental data to density functional theory and classical molecular dynamics calculations. Kinetic trapping is prevalent, even for one water molecule and one pyrene molecule, leading to slow equilibration in conventional molecular dynamics calculations, even on nanosecond timescales and at low temperatures (50 K). At constant energy, temperature fluctuations for the pair of molecules are substantial. Immersing the system in a bath of soft spheres and employing parallel tempering alleviates kinetic trapping and dampens temperature fluctuations, bringing the system closer to the thermodynamic limit. With such augmented sampling, a simple, flexible water model reproduces the linewidth and the asymmetric broadening of the symmetric OH stretching mode, which we assign to spectral diffusion. In the OH stretching region, dynamics calculations predict a more intense antisymmetric peak than experiments observe but do not predict the bimodal split symmetric peak that the experiments show. Furthermore, our work suggests that electronic polarization, missing in the empirical force field, is responsible for the first discrepancy and that quantum nuclear effects, captured neither in density functional theory nor in classical dynamics, may be responsible for the second.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Optimization of a coherent soft x-ray beamline for coherent scattering experiments at NSLS-II

The coherent soft x-ray and full polarization control (CSX) beamline at the National Synchrotron Light Source - II (NSLS-II) will deliver 1013 coherent photons per second in the energy range of 0.2-2 keV with a resolving power of 2000. The source, a dual elliptically polarizing undulator (EPU), and beamline optics should be optimized to deliver the highest possible coherent flux in a 10-30 {micro}m spot for use in coherent scattering experiments. Using the computer code Synchrotron Radiation Workshop (SRW), we simulate the photon source and focusing optics in order to investigate the conditions which provide the highest usable coherent intensity on the sample. In particular, we find that an intermediate phasing magnet is needed to correct for the relative phase between the two EPUs and that the optimum phase setting produces a spectrum in which the desired wavelength is slightly red-shifted thus requiring a larger aperture than originally anticipated. This setting is distinct from that which produces an on-axis spectrum similar to a single long undulator. Furthermore, partial coherence calculations, utilizing a multiple electron approach, indicate that a high degree of spatial coherence is still obtained at the sample location when such an aperture is used. The aperture size which maximizes the signal-to-noise ratio of a double-slit experiment is explored. This combination of high coherence and intensity is ideally suited for x-ray ptychography experiments which reconstruct the scattering density from micro-diffraction patterns. This technique is briefly reviewed and the effects on the image quality of proximity to the beamline focus are explored.

36 MATERIALS SCIENCE↗

Surface and superficial dose dosimetric verification for postmastectomy radiotherapy

In patients given postmastectomy radiotherapy (PMRT), the chest wall is a very thin layer of soft tissue with a low-density lung tissue behind. Chest wall treated in this situation with a high-energy photon beam presents a high dosimetric uncertainty region for both calculation and measurement. The purpose of this study was to measure and to evaluate the surface and superficial doses for patients requiring PMRT with different treatment techniques. An elliptic cylinder cork and superflab boluses were used to simulate the lung and the chest wall, respectively. Sets of computed tomography (CT) images with different chest wall thicknesses were acquired for the study phantom. Hypothetical clinical target volumes (CTVs) were outlined and modified to fit a margin of 1-3 mm, depending on the chest wall thickness, away from the surface for the sets of CT images. The planning target volume (PTV) was initially created by expanding an isotropic 3-mm margin from the CTV, and then a margin of 3 mm was shrunk from the phantom surface to avoid artifact-driven results in the beam-let intensity. Treatment techniques using a pair of tangential wedged fields (TWFs) and 4-field intensity-modulated radiation therapy (IMRT) were designed with a prescribed fraction dose (D{sub p}) of 180 cGy. Superficial dose profiles around the phantom circumference at depths of 0, 1, 2, 3, and 5 mm were obtained for each treatment technique using radiochromic external beam therapy (EBT) films. EBT film exhibits good characteristics for dose measurements in the buildup region. Underdoses at the median and lateral regions of the TWF plans were shown. The dose profiles at shallow depths for the TWF plans show a dose buildup about 3 mm at the median and lateral tangential incident regions with a surface dose of about 52% of D{sub p}. The dose was gradually increased toward the most obliquely tangential angle with a maximum dose of about 118% of D{sub p.} Dose profiles were more uniform in the PTV region for the 4-F IMRT plans. Most of the PTV region had doses >94% of D{sub p} at depths >1 mm. The mean surface dose was about 65% of D{sub p} for the 4-F IMRT plans. The maximum dose for the 4-F IMRT plans was <118.4% of D{sub p}. The application of added bolus has to consider the treatment technique, tumor coverage, and possible skin reactions. For PMRT, if the chest surface and wall are treated adequately, at least 3 mm bolus should be added to the chest wall when tangential beams and 6-MV photon energy are arranged. However, when the surface and superficial regions are not high-risk areas, an IMRT plan with tangential beams and 6-MV photon energy can provide uniform dose distributions within the PTV, spare the skin reaction, and deliver sufficient doses to the chest wall at depths >1 mm.

61 RADIATION PROTECTION AND DOSIMETRY↗

Comment on “Superconductivity at low density near a ferroelectric quantum critical point: Doped SrTiO 3 ”

Wölfle and Balatsky have proposed a microscopic pairing mechanism for doped SrTiO 3 (STO) based on the gradient coupling of electronic density to the soft transverse optical (TO) phonon mode. Since this coupling to TO phonons is usually weak, this conclusion is surprising, especially for a low-density superconductor such as STO, where the density of states is small. A crucial step in the argument made by Wölfle and Balatsky is that the displacement vector of the TO mode is not strictly perpendicular to the momentum vector, making a deformation coupling possible. We show that they have made a mistake in computing the eigenvector and have grossly overestimated this lack of orthogonality. When corrected, the coupling is negligible. We also use transport data to put upper bounds on the coupling constant which are much smaller than the estimate by Wölfle and Balatsky. Lastly, we also object to their use of the Eliashberg equation when the phonon frequency is larger than the Fermi energy.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Robust Predictive Control for Modular Solid-State Transformer With Reduced DC Link and Parameter Mismatch

This paper presents the analysis and implementation of a predictive control method for dc-link regulation and voltage balance in a cascaded modular reduced dc-link solid-state transformer (SST). Passive components like bulky dc links limit the power density of power converters, especially medium-voltage (MV) SST. Reduced dc-link or low-inertia converters can dramatically reduce the size, cost, and weight by tolerating larger dc-link ripples and improve the reliability with electrolytic capacitor-less dc link. However, a small dc link leads to tight coupling between the input and the output stages, which is a challenge for control design. In stacked low-inertia converters (SLIC), the low-inertia converter modules are stacked for MV applications, resulting in coupling between the modules and making the control more challenging. A new model predictive control method which can achieve deadbeat regulation on the dc link without weighting factors has been proposed to address this novel problem. This paper focuses on analyzing the condition of the low-inertia dc link up to 80% ripple, the robustness of the control under parameter mismatches, high-order terms, and important implementation issues such as model-based sampling and computation delay compensation. Significantly, the high-order terms are introduced because of the large dc-link ripple. These high-order terms are unique to the SLIC and negligible in conventional high-inertia converters. A discrete-time large-signal model is built to capture the dc-link’s nonlinear dynamics, and the eigenvalues of a small-signal Jacobian matrix are analyzed with Floquet theory to evaluate stability, using the modular soft-switching solid-state transformer (M-S4T) as an example of the SLIC. Simulation and experimental results of an MVDC M-S4T verify the analysis and the predictive control method. Finally, the general application of the predictive control to low-inertia converters is compared against a conventional PI controller using a reduced dc-link active-front-end (AFE) rectifier as an example.

14 SOLAR ENERGY↗

QCD corrections to the Drell-Yan process for the Large Hadron Collider (LHC): Vertex functions and gluon bremsstrahlung

With an eye to future experiments at the Large Hadron Collider (LHC), O(aa{sub s}) QCD corrections to the Drell-Yan process are calculated for vertex functions and gluon bremsstrahlung. Use is made of fully differential cross sections, so that the result obtained in the present study can readily be applied in analyzing experimental data (in correcting data from future experiments at LHC). It is shown both analytically and numerically that the results are independent of unphysical parameters, including the parameter separating the regions of soft and hard gluons and the quark mass. A numerical analysis of radiative effects was performed by means of the FORTRAN code READY with allowance for the experimental cuts used at the Compact Muon Solenoid (CMS) detector

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Subcontract B635525 (Final Report)

During my visits to LLNL July 8–12 and July 22–26, 2019, I worked on linear system solvers. The two level hierarchical solver that initiated our study was developed to solve linear systems arising from $\textit{hp}$ adaptive finite element calculations, and is implemented in the $\textit{PLTMG}$ software package, version 13. This preconditioner typically requires 3–20% of the space used by the stiffness matrix for higher order elements. It has multigrid like convergence rates for a wide variety of PDEs (self-adjoint positive definite elliptic equations, convection dominated convection-diffusion equations, and highly indefinite Helmholtz equations, among others). The convergence rate is not independent of the polynomial degree $\textit{p}$ as $\textit{p} → ∞$, but remains strong for $\textit{p}$ ≤ 9, which is the highest polynomial degree allowed in $\textit{PLTMG}$, due to limitations of the numerical quadrature rules implemented in the soft- ware package. A more complete description of the method and some numerical experiments illustrating its effectiveness appear in. Like traditional geometric multilevel methods, this scheme relies on knowledge of the underlying finite element space in order to construct the smoother and the coarse grid correction.

97 MATHEMATICS AND COMPUTING↗