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Volumetric analysis and mesh generation of real and artificial microstructural geometries

Producing a viable finite element mesh of realistic microstructural structural geometry is a critical step in analyzing the thermo-mechanical behavior of complex multi-material composites. Advancements in imaging technology such as micro computed tomography have allowed modelers to access high resolution mesoscale geometries for direct numerical simulation. However, converting from voxel based 3D images to usable finite element meshes has been challenging. A robust method including algorithms and software scripts for generating finite element meshes from 3D imaged microstructures is presented in this paper. It includes a routine for inserting cohesive elements around material interfaces to enable modeling of interface properties including delamination and damage. The algorithms and procedures presented in this method leverage currently available software packages for processing surface based geometry into volume based meshes. In addition to converting real geometry from physical imaging systems, algorithms for producing numerically generated and statistically equivalent microstructural geometry are also included. These artificial microstructures can be a valuable resource for modelers when physical specimens do not exist or are limited in quantity: Method establishes a workflow from voxel data to viable finite element mesh including interface information, and Includes a method for synthetic geometry generation based on metrics from real microstructures.

36 MATERIALS SCIENCE↗

Crosslink V.0.11.x User Manual

CrossLink is a novel two-dimensional and three-dimensional geometry and mesh generation software package developed by the Simulation Tools team at Los Alamos National Laboratory. This software represents the third generation of topology-based mesh generation technology developed by the Department of Defense and the Department of Energy with a special focus on complex multi-material hydrodynamic applications, mesh scalability, and high-order element mesh generation. The topology-based meshing approach offered by CrossLink enables users to quickly and easily mesh complex geometries in a repeatable and robust manner. CrossLink’s topology-based meshing approach is well-suited for parametric design studies, parametric design optimization, damage scenario assessment, and iterative design modification (i.e. feature addition and/or removal). CrossLink’s python API allows workflow scripting of the geometry creation and mesh generation process for traceability, repeatability, data provenance, and version control. CrossLink consists of three main components: a graphical user interface (GUI), a geometry creation and mesh generation engine, and a python API that provides a workflow scripting interface to the geometry and meshing functions.

97 MATHEMATICS AND COMPUTING↗

MESHMAKER (MM) V1.5

MeshMaker v1.5 is a code that describes the system geometry and discretizes the domain in problems of flow and transport through porous and fractured media that are simulated using the TOUGH+ [Moridis and Pruess, 2014] or TOUGH2 [Pruess et al., 1999; 2012] families of codes. It is a significantly modified and drastically enhanced version of an earlier simpler facility that was embedded in the TOUGH2 codes [Pruess et al., 1999; 2012], from which it could not be separated. The code (MeshMaker.f90) is a stand-alone product written in FORTRAN 95/2003, is written according to the tenets of Object-Oriented Programming, has a modular structure and can perform a number of mesh generation and processing operations. It can generate two-dimensional radially symmetric (r,z) meshes, and one-, two-, and three-dimensional rectilinear (Cartesian) grids in (x,y,z). The code generates the file MESH, which includes all the elements and connections that describe the discretized simulation domain and conforming to the requirements of the TOUGH+ and TOUGH2 codes. Multiple-porosity processing for simulation of flow in naturally fractured reservoirs can be invoked by means of a keyword MINC, which stands for Multiple INteracting Continua. The MINC process operates on the data of the primary (porous medium) mesh as provided on disk file MESH, and generates a secondary mesh containing fracture and matrix elements with identical data formats on file MINC.

MORIDIS, GEORGE↗

Design and Testing of the Address in Real-Time Data Driver Card for the Micromegas Detector of the ATLAS New Small Wheel Upgrade

The Address in Real Time Data Driver Card (ADDC) is designed to transmit the trigger data in the Micro-Mesh Gaseous Structure (Micromegas) detector of the ATLAS New Small Wheel (NSW) upgrade. The Address in Real Time (ART) signals are generated by the front-end ASIC, named VMM chip, to indicate the address of the first above-threshold event. A custom ASIC (ART ASIC) is designed to receive the ART signals from the VMM chip and implement the hit-selection. The processed data from the ART ASIC will be transmitted out of the NSW through the GBTx serializer, the unidirectional Versatile Twin Transmitter (VTTx) and fiber optical links. The ART signal is critical for the ATLAS experiment trigger selection thus the performance and stability of the ADDC is very important. To ensure extensive testing of the ADDC, an FPGA Mezzanine Card (FMC) based testing platform and a special designed firmware/software are developed. We find that this test platform works with the commercial Xilinx VC707 FPGA development kit, independent of the other electronics of the NSW it can test all the functions of the ADDC and its long-term stability. This paper will introduce the design, testing procedure and results of the ADDC and the FMC testing platform.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Engagement of Metal Debris into a Gear Mesh

A series of bench top experiments was conducted to determine the effects of metallic debris being dragged through meshing gear teeth. A test rig that is typically used to conduct contact fatigue experiments was used for these tests. Several sizes of drill material, shim stock, and pieces of gear teeth were introduced and then driven through the meshing region. The level of torque required to drive the "chip" through the gear mesh was measured. From the data gathered, chip size sufficient to jam the mechanism can be determined. INTRODUCTION In some space mechanisms the loading can be so high that there is some possibility that a gear chip might be liberated while in operation of the mechanism [1-5]. Also, due to the closely packed nature of some space mechanisms and the fact that a space grease is used for lubrication, chips that are released can then be introduced to other gear meshes within this mechanism. In this instance, it is desirable to know the consequences of a gear chip entering in between meshing gear teeth. To help provide some understanding, a series of bench-top experiments was conducted to engage chips of simulated and gear material fragments into a meshing gear pair. One purpose of the experiments was to determine the relationship of chip size to the torque required to rotate the gear set through the mesh cycle. The second purpose was to determine the condition of the gear chip material after engagement by the meshing gears, primarily to determine if the chip would break into pieces and to observe the motion of the chip as the engagement was completed. This document also presents preliminary testing done with metal debris other than chips from gears, namely steel shim stock and drill bits of various sizes and diameters.

Handschuh, Robert F.↗

Automatic algebraic coordinate generation

A computer software system has been developed to automatically generate two-dimensional coordinates from algebraic transformations. For topologically complex regions, a smooth assembly of the transformations can be used to automatically produce a composite mesh where a general gridded format is retained. The algebraic mesh generation system consists of a collection of operator subroutines which are applied to an established data structure and which automatically perform the necessary parts of mesh construction from a sequence of multisurface transformations. The system operators are discussed, taking into account the data base, the order of application, direct surface generators, geometric surface operators, surface generators from existing surfaces, transverse operators, mesh operators, assembly operators, and data visualization operators. Attention is given to applications related to airfoils.

Eiseman, P. R.↗

Modeling the spatiotemporal variability in subsurface thermal regimes across a low-relief polygonal tundra landscape

Vast carbon stocks stored in permafrost soils of Arctic tundra are under risk of release to the atmosphere under warming climate scenarios. Ice-wedge polygons in the low-gradient polygonal tundra create a complex mosaic of microtopographic features. This microtopography plays a critical role in regulating the fine-scale variability in thermal and hydrological regimes in the polygonal tundra landscape underlain by continuous permafrost. Modeling of thermal regimes of this sensitive ecosystem is essential for understanding the landscape behavior under the current as well as changing climate. Here, we present an end-to-end effort for high-resolution numerical modeling of thermal hydrology at real-world field sites, utilizing the best available data to characterize and parameterize the models. We also develop approaches to model the thermal hydrology of polygonal tundra and apply them at four study sites near Barrow, Alaska, spanning across low to transitional to high-centered polygons, representing a broad polygonal tundra landscape. A multiphase subsurface thermal hydrology model (PFLOTRAN) was developed and applied to study the thermal regimes at four sites. Using a high-resolution lidar digital elevation model (DEM), microtopographic features of the landscape were characterized and represented in the high-resolution model mesh. The best available soil data from field observations and literature were utilized to represent the complex heterogeneous subsurface in the numerical model. Simulation results demonstrate the ability of the developed modeling approach to capture – without recourse to model calibration – several aspects of the complex thermal regimes across the sites, and provide insights into the critical role of polygonal tundra microtopography in regulating the thermal dynamics of the carbon-rich permafrost soils. Moreover, areas of significant disagreement between model results and observations highlight the importance of field-based observations of soil thermal and hydraulic properties for modeling-based studies of permafrost thermal dynamics, and provide motivation and guidance for future observations that will help address model and data gaps affecting our current understanding of the system.

54 ENVIRONMENTAL SCIENCES↗

PUMIPic: A mesh-based approach to unstructured mesh Particle-In-Cell on GPUs

Unstructured mesh particle-in-cell, PIC, simulations executing on the current and next generation of massively parallel systems require new methods for both the mesh and particles to achieve performance and scalability on GPUs. The traditional approach to implementing PIC simulations defines data structures and algorithms in terms of particles with a full copy of the unstructured mesh on every process. To effectively scale the unstructured mesh and particles, mesh-based PIC uses the unstructured mesh as the predominant data structure with the particles stored in terms of the mesh entities. Here, this paper details the PUMIPic library, a framework for developing efficient and performance-portable mesh-based PIC simulations on GPU systems. A pseudo physics simulation based on a five-dimensional gyro-kinetic code for modeling plasma physics is used to examine the performance of PUMIPic. Scaling studies of the unstructured mesh partition and number of particles are performed up to 4096 nodes of the Summit system at Oak Ridge National Laboratory. The studies show that mesh-based PIC can utilize a partitioned mesh and maintain scaling up to system limitations.

97 MATHEMATICS AND COMPUTING↗

FY2021 Improvements to the New CTH Code Verification & Validation Test Suite

Over the past few years, the CTH multiphysics hydrocode has overhauled its software quality and testing processes, implementing current best practices in software quality and building a robust V&V test suite comprised of traditional hydrocode verification problems, including ASC Tri-Lab Test Suite and Enhanced Tri-Lab Test Suite problems, as well as validation problems for some of CTH’s most frequently used equations of state, materials models, and other key capabilities. Substantial progress towards building this new test suite was made in FY19 and FY20. In FY21, the test suite has been expanded to include verification and validation tests of the Steinberg-Guinan-Lund (ST) viscoplastic model and the Johnson Cook (JFRAC) fracture model. Additionally, two new verification tests were added, covering hydrodynamics and high explosive (HE) modeling capabilities: the Kidder Gaussian density problem and the Escape of HE Products (EHEP) problem from the Tri-Lab Test Suite. This report discusses each of these test problems in detail. Verification test results are compared to analytic solutions. Validation test results are compared to experimental data. Wherever possible, convergence or mesh refinement studies are included. Additionally, while implementing the Kidder verification problem, a bug was identified that affects the use of tables to initialize pressure or density in 1D or 2D calculations. A brief discussion of the bug and its fix is included. CTH demonstrates good performance overall on the new test suite problems. Simulation results showed good agreement with analytic solutions for the Kidder problem, with convergence rates ranging between 1.8 and sub-linear, and relatively good agreement for the EHEP problem, though convergence rates for pressure and density were nearly 0. The ST and JFRAC strain rate loading verification tests show good agreement with analytic solutions. Likewise, CTH simulation results show good agreement with experimental validation data, including Taylor rod impact testing, for the materials tested. Future V&V work will focus on adding 2D and 3D versions of existing verification tests as well as adding validation tests of other frequently used capabilities such as other fracture models.

42 ENGINEERING↗

Mesh generation/refinement using fractal concepts and iterated function systems

A novel method of mesh generation is proposed which is based on the use of fractal concepts to derive contractive, affine transformations. The transformations are constructed in such a manner that the attractors of the resulting maps are a union of the points, lines and surfaces in the domain. In particular, the mesh nodes may be generated recursively as a sequence of points which are obtained by applying the transformations to a coarse background mesh constructed from the given boundary data. A Delaunay triangulation or similar edge connection approach can then be performed on the resulting set of nodes in order to generate the mesh. Local refinement of an existing mesh can also be performed using the procedure. The method is easily extended to three dimensions, in which case the Delaunay triangulation is replaced by an analogous 3D tesselation.

Bova, S. W.↗

Validation Data Acquisition in HTTF during PCC Events

A validation experimental campaign was conducted in an Integral Effect Test (IET) facility of High Temperature Gas Reactors (HTGR), the High-Temperature Test Facility (HTTF) at Oregon State University (OSU). The HTTF simulates Depressurized and Pressurized Conduction Cooldowns (DCC and PCC). This campaign required the development of a new laser spectroscopic diagnostic to measure velocity in the challenging conditions of the HTTF: low speed (~1 m/s) gas flows at HTGR prototypical temperature and 1/10th pressure. This was a collaborative effort between co-PIs at The George Washington University (GW), Oregon State University (OSU), and NASA Langley Research Center. The main accomplishments of this project include the record for dynamic range for velocimetry, highest accuracy obtained with this technique, successful deployment in an IET leading to new validation matrix for CFD. These are detailed below and in manuscript appended to this executive summary. For this project, we introduced a new class of laser spectroscopic diagnostics to Thermal-Hydraulics to measure velocity of gases; furthermore, the diagnostic was demonstrated in-situ in an IET during DCC events. In such scenarios, particles used in mainstream techniques, like Particle Image Velocimetry (PIV) are not appropriate as they settle down too rapidly and also contaminate the experimental facility. Molecular tracers stay mixed within the working gas and can seed the flow in a technique called Molecular Tagging Velocimetry (MTV). In MTV a molecular tracer is photo-dissociated by a first (write) laser into radicals or molecules. The pattern created by the write laser is then interrogated with planar laser-induced fluorescence (PLIF), the read pulse(s), which are recorded with a camera. The pattern is probed and matched at two times (interval or probe time, dt), resulting in a time-of-flight velocimetry technique. This project demonstrated a new application range for MTV in gases. MTV has been extensively used for high-speed gas dynamics: molecules do not suffer from inertia associated with particles in regions of high accelerations (such as shock waves). For high-speed flows, the probe time is on the order of 0.1-10 µs. In time-of-flight techniques, the velocity is reconstructed from the recorded displacement, dx, between time interval dt: U = dx/dt. To first order, the resolution of the pattern matching is typically a (fixed) fraction of a pixel; therefore the resolution of the velocity measurement increases with dx and, for a given flow velocity, dt. For the low-speed flows of interest here, this requires long probe time, and therefore finding tracers that are stable for a long time. After an extensive literature survey we identified 6 tracers that would be suitable. We also worked with Spectra Physics to design a custom laser system that is flexible enough to probe these various tracers. The final instrument is made of 4 lasers that are integrated into a compact and movable cart to facilitate the deployment of the instrument off-site. One unique aspect of the laser system is the tunable dye laser (needed to do PLIF of the radicals). By being pumped by two Nd:YAG lasers, this laser is able to provide two pulses with any probe time (dt) for wavelengths between 200 and 900 nm with a linewidth of 3 pm. Accommodating the dual-pulse capability required customizing the pump lasers and the dye laser, making this system unique. Additionally, a custom UV-intensified CCD camera capable of frame-straddling and exposure time as short as 10 ns was acquired. More than two-third of the instrument cost (~$200k) was covered by a cost sharing from the PI’s startup funds. Of the 6 potential tracers identified, two were tested extensively (H2O and N2O) at high-temperature and elevated pressure at GW prior to conducting the tests at OSU. For both tracers, an Ar-F laser (193 nm, 10 ns, 10 mJ/pulse) photo-dissociates trace amounts (0.1 – 5% molar fraction) of the gases into OH and NO. OH is probed at 281.905 nm and NO at 226.186 nm (4-30mJ, 10 ns pulse). NO is very stable in inert environment and we could reconstruct velocities precisely with probe delay times as long at 40 ms, compared to 2 ms for OH, resulting in increased precision. Therefore, for the tests in the HTTF, N2O was selected as the final tracer and its optimal concentration was determined to be 0.5% molar. In the GW laboratory, we obtained a velocity measurement precision of 4 mm/s at conditions mimicking the HTTF tests. We also demonstrated the benefit of molecular tracers over particles and the flexibility of our instrument by continuously measuring velocity from 1000 to 0.1 m/s in a blow down test. This represents a dynamic range on velocity of 80 dB, which is unprecedented for velocimetry! Once the diagnostic was optimized, two two-week campaigns were conducted in the HTTF. This experimental campaign required numerous practical solutions to successfully and rapidly deploy this very sensitive table-top diagnostic in-situ. This was accomplished thanks to very extensive planning from all parties involved in the project. Due to constraints on availability of the HTTF, only adiabatic DCC tests were conducted. Specifically, the velocity was measured at the exit of the hot leg into the Reactor Cavity Simulation Tank (RCST). We were able to record the gas velocity associated with the air ingress for long times (up to one hour). Depending on the initial conditions (density of the gases in the Reactor Pressure Vessel and the RCST) the lock exchange lasted 30-60 s past the valve openings. Large vortices were identified within the shear layer at the interface of the cross flow. These vortices are an indication of shear-driven instability between the counter streams of different density. After the lock-exchange, a small residual flow was still present and its strength decayed exponentially. It finds its source in a buoyancy difference between the gases in both vessels due to the mixing and diffusion of the gases in the cross-over duct and the RPV lower plenum. We did not expect to capture this part of the transient, which would have been less significant (if not negligible) in the presence of a heated core; the precision of our measurement in the HTTF was 6 mm/s, which exceeded our expectations for such a complex test! Using commercial software (Fluent) we simulated the experiment with Computational Fluid Dynamic (CFD) using Reynolds Averaged Navier-Stokes (RANS) turbulence models. We were not able to accurately reproduce the shear layer instability, mixing, and diffusion captured in our experimental data, even with large 3D meshes (>10 M points). We attributed this to the inadequacy of the RANS models for the flow of interest: our experimental Reynolds number was too low and was outside the applicability range of the RANS models. Instead, we should have employed CFD with less modeling, such as Large Eddy (LES) or even Direct Numerical (DNS) simulations. Unfortunately, we did not have the computational resources to do so. Finally, it should be noted that this experimental technique holds great promises for measuring velocity in thermalhydraulics. MTV has an application domain (highlighted in the narrative) that is complimentary to more established (and simpler) techniques, such as PIV. It has attracted the attention of several thermalhydraulics researchers and sponsors to measure velocity in harsh environments. The spectroscopic nature of this technique also enables to expand it to measure temperature and concentration simultaneously to velocity. In lieu of a narrative, 4 detailed journal publications are appended to this executive summary to describe the various development and accomplishments during this project. They include 2 published manuscripts (Experiments in Fluids and Measurement Science and Technology), and two invited contributions following the NURETH-17 conference (Nuclear Science and Technology). Our current Nuclear Engineering and Design draft is not included at this time.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Atmospheric analysis and prediction model development, volume 1

A set of hemispheric atmospheric analysis and prediction models was designed and tested. All programs were executed on either a 63 x 63 or 187 x 187 polar stereographic grid of the Northern Hemisphere. Parameters for objective analysis included sea surface temperature, sea level pressure, and twelve levels (from 1,000 to 100 millibars) of temperatures, heights, and winds. Stratospheric extensions (up to 10 millibars) were also provided. Four versions of a complex atmospheric prediction model, based on primitive equations, were programmed and tested. These models were executed on either the 63 x 63 or 187 x 187 grid, using either five or ten computational layers. The coarse-mesh (63 x 63) models were tested using real data for the period 21-23 April 1976. The fine-mesh (187 x 187) models were debugged, but insufficient computer resources precluded production tests. Preliminary test results for the 63 x 63 models are provided. Problem areas and proposed solutions are discussed.

Kesel, P. G.↗

A High-Quality Workflow for Multi-Resolution Scientific Data Reduction and Visualization

Multi-resolution methods such as Adaptive Mesh Refinement (AMR) can enhance storage efficiency for HPC applications generating vast volumes of data. However, their applicability is limited and cannot be universally deployed across all applications. Furthermore, integrating lossy compression with multi-resolution techniques to further boost storage efficiency encounters significant barriers. To this end, we introduce an innovative workflow that facilitates high-quality multi-resolution data compression for both uniform and AMR simulations. Initially, to extend the usability of multi-resolution techniques, our workflow employs a compression-oriented Region of Interest (ROI) extraction method, transforming uniform data into a multi-resolution format. Subsequently, to bridge the gap between multi-resolution techniques and lossy compressors, we optimize three distinct compressors, ensuring their optimal performance on multi-resolution data. These optimizations can improve the compression ratio of SOTA approaches by up to 3.3× under the same data quality loss. Lastly, we incorporate an advanced uncertainty visualization method into our workflow to understand the potential impacts of lossy compression. Experimental evaluation demonstrates that our workflow achieves significant compression quality improvements.

Wang, Daoce↗

High order interpolation of magnetic fields with vector potential reconstruction for particle simulations

We propose a method for interpolating divergence-free continuous magnetic fields via vector potential reconstruction using Hermite interpolation, which ensures high-order continuity for applications requiring adaptive, high-order ordinary differential equation (ODE) integrators, such as the Dormand-Prince method. The method provides C(m) continuity and achieves high-order accuracy, making it particularly suited for particle trajectory integration and Poincaré section analysis under optimal integration order and timestep adjustments. Through numerical experiments, we demonstrate that the Hermite interpolation method preserves volume and continuity, which are critical for conserving toroidal canonical momentum and magnetic moment in guiding center simulations, especially over long-term trajectory integration. Furthermore, we analyze the impact of insufficient derivative continuity on Runge-Kutta schemes and show how it degrades accuracy at low error tolerances, introducing discontinuity-induced truncation errors. Lastly, we demonstrate performant Poincaré section analysis in two relevant settings of field data collocated from finite element meshes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

What can we learn from in-soil imaging of a live plant: X-ray Computed Tomography and 3D numerical simulation of root-soil system

Plant roots play a critical role in plant-soil-microbe interactions that occur in the rhizosphere, as well as processes with important implications to farming, forest management and climate change. X-ray computed tomography (XCT) has been proven to be an effective tool for non-invasive root imaging and analysis. A combination of XCT, open-source software, and our own code was used to noninvasively image a prairie dropseed (Sporobolus heterolepis) specimen, segment the root data to obtain a 3D image of the root structure at 31µm resolution, and extract quantitative information (root volume and surface area) from the 3D data, respectively. Based on the mesh generated from the root structure, computational fluid dynamics (CFD) simulations were applied to numerically investigate the root-soil-groundwater system. The plant root conductivity, soil hydraulic conductivity and transpiration rate were shown to control the groundwater distribution. The flow variability and soil water distributions under different scenarios were investigated. Parameterizations were evaluated to show their impacts on the average conductivity. The pore-scale modeling approach provides realistic simulations of rhizosphere flow processes and provides useful information that can be linked to upscaled models.

54 ENVIRONMENTAL SCIENCES↗

First coupled GENE–XGC microturbulence simulations

Covering the core and the edge region of a tokamak, respectively, the two gyrokinetic turbulence codes Gyrokinetic Electromagnetic Numerical Experiment (GENE) and X-point Gyrokinetic Code (XGC) have been successfully coupled by exchanging three-dimensional charge density data needed to solve the gyrokinetic Poisson equation over the entire spatial domain. Certain challenges for the coupling procedure arise from the fact that the two codes employ completely different numerical methods. This includes, in particular, the necessity to introduce mapping procedures for the transfer of data between the unstructured triangular mesh of XGC and the logically rectangular grid (in a combination of real and Fourier space) used by GENE. Constraints on the coupling scheme are also imposed by the use of different time integrators. First, coupled simulations are presented. We have considered collisionless ion temperature gradient turbulence, in both circular and fully shaped plasmas. Coupled simulations successfully reproduce both GENE and XGC reference results, confirming the validity of the code coupling approach toward a whole device model. Here, many lessons learned in the present context, in particular, the need for a coupling procedure as flexible as possible, should be valuable to our and other efforts to couple different kinds of codes in pursuit of a more comprehensive description of complex real-world systems and will drive our further developments of a whole device model for fusion plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

SU-F-J-211: Scatter Correction for Clinical Cone-Beam CT System Using An Optimized Stationary Beam Blocker with a Single Scan

Purpose: X-ray scatter photons result in significant image quality degradation of cone-beam CT (CBCT). Measurement based algorithms using beam blocker directly acquire the scatter samples and achieve significant improvement on the quality of CBCT image. Within existing algorithms, single-scan and stationary beam blocker proposed previously is promising due to its simplicity and practicability. Although demonstrated effectively on tabletop system, the blocker fails to estimate the scatter distribution on clinical CBCT system mainly due to the gantry wobble. In addition, the uniform distributed blocker strips in our previous design results in primary data loss in the CBCT system and leads to the image artifacts due to data insufficiency. Methods: We investigate the motion behavior of the beam blocker in each projection and design an optimized non-uniform blocker strip distribution which accounts for the data insufficiency issue. An accurate scatter estimation is then achieved from the wobble modeling. Blocker wobble curve is estimated using threshold-based segmentation algorithms in each projection. In the blocker design optimization, the quality of final image is quantified using the number of the primary data loss voxels and the mesh adaptive direct search algorithm is applied to minimize the objective function. Scatter-corrected CT images are obtained using the optimized blocker. Results: The proposed method is evaluated using Catphan@504 phantom and a head patient. On the Catphan©504, our approach reduces the average CT number error from 115 Hounsfield unit (HU) to 11 HU in the selected regions of interest, and improves the image contrast by a factor of 1.45 in the high-contrast regions. On the head patient, the CT number error is reduced from 97 HU to 6 HU in the soft tissue region and image spatial non-uniformity is decreased from 27% to 5% after correction. Conclusion: The proposed optimized blocker design is practical and attractive for CBCT guided radiation therapy. This work is supported by grants from Guangdong Innovative Research Team Program of China (Grant No. 2011S013), National 863 Programs of China (Grant Nos. 2012AA02A604 and 2015AA043203), the National High-tech R&D Program for Young Scientists by the Ministry of Science and Technology of China (Grant No. 2015AA020917)

60 APPLIED LIFE SCIENCES↗

Optimal expression evaluation for data parallel architectures

A data parallel machine represents an array or other composite data structure by allocating one processor per data item. A pointwise operation can be performed between two such arrays in unit time, provided their corresponding elements are allocated in the same processors. If the arrays are not aligned in this fashion, the cost of moving one or both of them is part of the cost of operation. The choice of where to perform the operation then affects this cost. If an expression with several operands is to be evaluated, there may be many choices of where to perform the intermediate operations. An efficient algorithm is given to find the minimum cost way to evaluate an expression, for several different data parallel architectures. The algorithm applies to any architecture in which the metric describing the cost of moving an array has a property called robustness. This encompasses most of the common data parallel communication architectures, including meshes of arbitrary dimension and hypercubes.

Gilbert, J. R.↗