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DOE OSTI2015

Utilizing many-core accelerators for halo and center finding within a cosmology simulation

Efficiently finding and computing statistics about “halos” (regions of high density) are essential analysis steps for N-body cosmology simulations. However, in state-of-the-art simulation codes, these analysis operators do not currently take advantage of the shared-memory data-parallelism available on multi-core and many-core architectures. The Hybrid / Hardware Accelerated Cosmology Code (HACC) is designed as an MPI+X code, but the analysis operators are parallelized only among MPI ranks, because of the difficulty in porting different X implementations (e.g., OpenMP, CUDA) across all architectures on which it is run. In this paper, we present portable data-parallel algorithms for several variations of halo finding and halo center finding algorithms. These are implemented with the PISTON component of the VTK-m framework, which uses Nvidia's Thrust library to construct data-parallel algorithms that allow a single implementation to be compiled to multiple backends to target a variety of multi-core and many-core architectures. Finally, we compare the performance of our halo and center finding algorithms against the original HACC implementations on the Moonlight, Stampede, and Titan supercomputers. The portability of Thrust allowed the same code to run efficiently on each of these architectures. On Titan, the performance improvements using our code have enabled halo analysis to be performed on a very large data set (81923 particles across 16,384 nodes of Titan) for which analysis using only the existing CPU algorithms was not feasible.

Sewell, Christopher↗
DOE OSTI2021

GPU-based Image Compression for Efficient Compositing in Distributed Rendering Applications

Visualizations of large-scale data sets are often created on graphics clusters that distribute the rendering task amongst many processes. When using real-time GPU-based graphics algorithms, the most time-consuming aspect of distributed rendering is typically the com-positing phase - combining all partial images from each rendering process into the final visualization. Compo siting requires image data to be copied off the GPU and sent over a network to other processes. While compression has been utilized in existing distributed rendering compositors to reduce the data being sent over the network, this compression tends to occur after the raw images are transferred from the GPU to main memory. In this paper, we present work that leverages OpenGL / CUDA interoperability to compress raw images on the GPU prior to transferring the data to main memory. This approach can significantly reduce the device-to-host data transfer time, thus enabling more efficient compositing of images generated by distributed rendering applications.

Lipinksi, Riley↗
DOE OSTI2015

Understanding Portability of a High-Level Programming Model on Contemporary Heterogeneous Architectures

Accelerator-based heterogeneous computing is gaining momentum in the high-performance computing arena. However, the increased complexity of heterogeneous architectures demands more generic, high-level programming models. OpenACC is one such attempt to tackle this problem. Although the abstraction provided by OpenACC offers productivity, it raises questions concerning both functional and performance portability. In this article, the authors propose HeteroIR, a high-level, architecture-independent intermediate representation, to map high-level programming models, such as OpenACC, to heterogeneous architectures. They present a compiler approach that translates OpenACC programs into HeteroIR and accelerator kernels to obtain OpenACC functional portability. They then evaluate the performance portability obtained by OpenACC with their approach on 12 OpenACC programs on Nvidia CUDA, AMD GCN, and Intel Xeon Phi architectures. They study the effects of various compiler optimizations and OpenACC program settings on these architectures to provide insights into the achieved performance portability.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Performance Portability of Molecular Docking Miniapp On Leadership Computing Platforms

Rapidly changing computer architectures, such as those found at high-performance computing (HPC) facilities, present the need for mini-applications (miniapps) that capture essential algorithms used in large applications to test program performance and portability, aiding transitions to new systems. The COVID-19 pandemic has fueled a flurry of activity in computational drug discovery, including the use of supercomputers and GPU acceleration for massive virtual screens for therapeutics. Recent work targeting COVID-19 at the Oak Ridge Leadership Computing Facility (OLCF) used the GPU-accelerated program AutoDock-GPU to screen billions of compounds on the Summit supercomputer. In this paper we present the development of a new miniapp, miniAutoDock-GPU, that can be used to evaluate the performance and portability of GPU-accelerated protein-ligand docking programs on different computer architectures. These tests are especially relevant as facilities transition from petascale systems and prepare for upcoming exascale systems that will use a variety of GPU vendors. The key calculations, namely, the Lamarckian genetic algorithm combined with a local search using a Solis-Wets based random optimization algorithm, are implemented. We developed versions of the miniapp using several different programming models for GPU acceleration, including a version using the CUDA runtime API for NVIDIA GPUs, and the Kokkos middle-ware API which is facilitated by C++ template libraries. A third version, currently in progress, uses the HIP programming model. These efforts will help facilitate the transition to exascale systems for this important emerging HPC application, as well as its use on a wide range of heterogeneous platforms.

Thavappiragasam, Mathialakan↗
DOE OSTI2021

Case Study of Using Kokkos and SYCLs Performance-Portable Frameworks for Milc-Dslash Benchmark on NVIDIA, AMD and Intel GPUs

Six of the top ten supercomputers in the TOP500 list from June 2021 rely on NVIDIA GPUs to achieve their peak compute bandwidth. With the announcement of Aurora, Frontier, and El Capitan, Intel and AMD have also entered the domain of providing GPUs for scientific computing. A consequence of the increased diversity in the GPU landscape is the emergence of portable programming models such as Kokkos, SYCL, OpenCL, and OpenMP, which allow application developers to maintain a single-source code across a diverse range of hardware architectures. While the portable frameworks try to optimize the compute resource usage on a given architecture, it is the programmers responsibility to expose parallelism in an application that can take advantage of thousands of processing elements available on GPUs. In this paper, we introduce a GPU-friendly parallel implementation of Milc-Dslash that exposes multiple hierarchies of parallelism in the algorithm. Milc-Dslash was designed to serve as a benchmark with highly optimized matrix-vector multiplications to measure the resource utilization on the GPU systems. The parallel hierarchies in the Milc-Dslash algorithm are mapped onto a target hardware using Kokkos and SYCL programming models. We present the performance achieved by Kokkos and SYCL implementations of Milc-Dslash on NVIDIA A100 GPU, AMD MI100 GPU, and Intel Gen9 GPU. Additionally, we compare the Kokkos and SYCL performances with those obtained from the versions written in CUDA and HIP programming models on NVIDIA A100 GPU and AMD MI100 GPU, respectively.

Dufek, Amanda S↗
DOE OSTI2022

Leveraging Compiler-Based Translation to Evaluate a Diversity of Exascale Platforms

Accelerator-based heterogeneous computing is the de facto standard in current and upcoming exascale machines. These heterogeneous resources empower computational scientists to select a machine or platform well-suited to their domain or applications. However, this diversity of machines also poses challenges related to programming model selection: inconsistent availability of programming models across different exascale systems, lack of performance portability for those programming models that do span several systems, and inconsistent performance between different models on a single platform. We explore these challenges on exascale-similar hardware, including AMD MI100 and NVIDIA A100 GPUs. By extending the sourceto-source compiler OpenARC, we demonstrate the power of automated translation of applications written in a single frontend programming model (OpenACC) into a variety of backend models (OpenMP, OpenCL, CUDA, HIP) that span the upcoming exascale environments. This translation enables us to compare performance within and across devices and to analyze programming model behavior with profiling tools.

Lambert, Jacob↗
DOE OSTI2012

Designing a unified programming model for heterogeneous machines

While high-efficiency machines are increasingly embracing heterogeneous architectures and massive multithreading, contemporary mainstream programming languages reflect a mental model in which processing elements are homogeneous, concurrency is limited, and memory is a flat undifferentiated pool of storage. Moreover, the current state of the art in programming heterogeneous machines tends towards using separate programming models, such as OpenMP and CUDA, for different portions of the machine. Both of these factors make programming emerging heterogeneous machines unnecessarily difficult. We describe the design of the Phalanx programming model, which seeks to provide a unified programming model for heterogeneous machines. It provides constructs for bulk parallelism, synchronization, and data placement which operate across the entire machine. Our prototype implementation is able to launch and coordinate work on both CPU and GPU processors within a single node, and by leveraging the GASNet runtime, is able to run across all the nodes of a distributed-memory machine.

Garland, Michael↗
DOE OSTI2012

Early Evaluation of Directive-Based GPU Programming Models for Productive Exascale Computing

Graphics Processing Unit (GPU)-based parallel computer architectures have shown increased popularity as a building block for high performance computing, and possibly for future Exascale computing. However, their programming complexity remains as a major hurdle for their widespread adoption. To provide better abstractions for programming GPU architectures, researchers and vendors have proposed several directive-based GPU programming models. These directive-based models provide different levels of abstraction, and required different levels of programming effort to port and optimize applications. Understanding these differences among these new models provides valuable insights on their applicability and performance potential. In this paper, we evaluate existing directive-based models by porting thirteen application kernels from various scientific domains to use CUDA GPUs, which, in turn, allows us to identify important issues in the functionality, scalability, tunability, and debuggability of the existing models. Our evaluation shows that directive-based models can achieve reasonable performance, compared to hand-written GPU codes.

Lee, Seyong↗
DOE OSTI2024

Toward Automated Detection of Portability Bugs in Kokkos Parallel Programs

Performance-portable programming frameworks provide abstractions for parallel execution to allow easily porting an application to multiple backend programming models, such as CUDA, HIP, and OpenMP. However, programs may still have portability bugs that manifest only on specific backends. Traditional testing is ineffective in discovering these bugs, as it would require concrete execution on all supported hardware configurations for a potentially infinite set of inputs. To mitigate this issue, we focused on a specific programming framework, Kokkos, and identified several categories of common portability bugs. We then developed Klokkos, a static analysis approach based on symbolic execution that can run on commodity hardware, before execution on supercomputers. As a proof-of-concept, we ran Klokkos on examples encoding the identified bugs. Our results show that Klokkos is effective, efficient, and precise: it detected all the considered bugs, quickly, and without any false positives. Although preliminary, our results motivate further research and development in this direction.

Kale, Vivek↗
DOE OSTI2024

IRIS: A Performance-Portable Framework for Cross-Platform Heterogeneous Computing

From edge to exascale, computer architectures are becoming more heterogeneous and complex. The systems typically have fat nodes, with multicore CPUs and multiple hardware accelerators such as GPUs, FPGAs, and DSPs. This complexity is causing a crisis in programming systems and performance portability. Several programming systems are working to address these challenges, but the increasing architectural diversity is forcing software stacks and applications to be specialized for each architecture. As we show, all of these approaches critically depend on their software framework for discovery, execution, scheduling, and data orchestration. To address this challenge, we believe that a more agile and proactive software framework is essential to increase performance portability and improve user productivity. To this end, we have designed and implemented IRIS: a performance-portable framework for cross-platform heterogeneous computing. IRIS can discover available resources, manage multiple diverse programming platforms (e.g., CUDA, Hexagon, HIP, Level Zero, OpenCL, OpenMP) simultaneously in the same execution, respect data dependencies, orchestrate data movement proactively, and provide for user-configurable scheduling. To simplify data movement, IRIS introduces a shared virtual device memory with relaxed consistency among different heterogeneous devices. IRIS also adds an automatic kernel workload partitioning technique using the polyhedral model so that it can resize kernels for a wide range of devices. Our evaluation on three architectures, ranging from Qualcomm Snapdragon to a Summit supercomputer node, shows that IRIS improves portability across a wide range of diverse heterogeneous architectures with negligible overhead.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Three-dimensional anisotropic adaptive filtering of projection data for noise reduction in cone beam CT

Purpose: The combination of quickly rotating C-arm gantry with digital flat panel has enabled the acquisition of three-dimensional data (3D) in the interventional suite. However, image quality is still somewhat limited since the hardware has not been optimized for CT imaging. Adaptive anisotropic filtering has the ability to improve image quality by reducing the noise level and therewith the radiation dose without introducing noticeable blurring. By applying the filtering prior to 3D reconstruction, noise-induced streak artifacts are reduced as compared to processing in the image domain. Methods: 3D anisotropic adaptive filtering was used to process an ensemble of 2D x-ray views acquired along a circular trajectory around an object. After arranging the input data into a 3D space (2D projections + angle), the orientation of structures was estimated using a set of differently oriented filters. The resulting tensor representation of local orientation was utilized to control the anisotropic filtering. Low-pass filtering is applied only along structures to maintain high spatial frequency components perpendicular to these. The evaluation of the proposed algorithm includes numerical simulations, phantom experiments, and in-vivo data which were acquired using an AXIOM Artis dTA C-arm system (Siemens AG, Healthcare Sector, Forchheim, Germany). Spatial resolution and noise levels were compared with and without adaptive filtering. A human observer study was carried out to evaluate low-contrast detectability. Results: The adaptive anisotropic filtering algorithm was found to significantly improve low-contrast detectability by reducing the noise level by half (reduction of the standard deviation in certain areas from 74 to 30 HU). Virtually no degradation of high contrast spatial resolution was observed in the modulation transfer function (MTF) analysis. Although the algorithm is computationally intensive, hardware acceleration using Nvidia's CUDA Interface provided an 8.9-fold speed-up of the processing (from 1336 to 150 s). Conclusions: Adaptive anisotropic filtering has the potential to substantially improve image quality and/or reduce the radiation dose required for obtaining 3D image data using cone beam CT.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2012

Temporal and spectral imaging with micro-CT

Purpose: Micro-CT is widely used for small animal imaging in preclinical studies of cardiopulmonary disease, but further development is needed to improve spatial resolution, temporal resolution, and material contrast. We present a technique for visualizing the changing distribution of iodine in the cardiac cycle with dual source micro-CT. Methods: The approach entails a retrospectively gated dual energy scan with optimized filters and voltages, and a series of computational operations to reconstruct the data. Projection interpolation and five-dimensional bilateral filtration (three spatial dimensions + time + energy) are used to reduce noise and artifacts associated with retrospective gating. We reconstruct separate volumes corresponding to different cardiac phases and apply a linear transformation to decompose these volumes into components representing concentrations of water and iodine. Since the resulting material images are still compromised by noise, we improve their quality in an iterative process that minimizes the discrepancy between the original acquired projections and the projections predicted by the reconstructed volumes. The values in the voxels of each of the reconstructed volumes represent the coefficients of linear combinations of basis functions over time and energy. We have implemented the reconstruction algorithm on a graphics processing unit (GPU) with CUDA. We tested the utility of the technique in simulations and applied the technique in an in vivo scan of a C57BL/6 mouse injected with blood pool contrast agent at a dose of 0.01 ml/g body weight. Postreconstruction, at each cardiac phase in the iodine images, we segmented the left ventricle and computed its volume. Using the maximum and minimum volumes in the left ventricle, we calculated the stroke volume, the ejection fraction, and the cardiac output. Results: Our proposed method produces five-dimensional volumetric images that distinguish different materials at different points in time, and can be used to segment regions containing iodinated blood and compute measures of cardiac function. Conclusions: We believe this combined spectral and temporal imaging technique will be useful for future studies of cardiopulmonary disease in small animals.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2013

GPU-based relative fuzzy connectedness image segmentation

Purpose:Recently, clinical radiological research and practice are becoming increasingly quantitative. Further, images continue to increase in size and volume. For quantitative radiology to become practical, it is crucial that image segmentation algorithms and their implementations are rapid and yield practical run time on very large data sets. The purpose of this paper is to present a parallel version of an algorithm that belongs to the family of fuzzy connectedness (FC) algorithms, to achieve an interactive speed for segmenting large medical image data sets. Methods: The most common FC segmentations, optimizing an Script-Small-L {sub {infinity}}-based energy, are known as relative fuzzy connectedness (RFC) and iterative relative fuzzy connectedness (IRFC). Both RFC and IRFC objects (of which IRFC contains RFC) can be found via linear time algorithms, linear with respect to the image size. The new algorithm, P-ORFC (for parallel optimal RFC), which is implemented by using NVIDIA's Compute Unified Device Architecture (CUDA) platform, considerably improves the computational speed of the above mentioned CPU based IRFC algorithm. Results: Experiments based on four data sets of small, medium, large, and super data size, achieved speedup factors of 32.8 Multiplication-Sign , 22.9 Multiplication-Sign , 20.9 Multiplication-Sign , and 17.5 Multiplication-Sign , correspondingly, on the NVIDIA Tesla C1060 platform. Although the output of P-ORFC need not precisely match that of IRFC output, it is very close to it and, as the authors prove, always lies between the RFC and IRFC objects. Conclusions: A parallel version of a top-of-the-line algorithm in the family of FC has been developed on the NVIDIA GPUs. An interactive speed of segmentation has been achieved, even for the largest medical image data set. Such GPU implementations may play a crucial role in automatic anatomy recognition in clinical radiology.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

MO-A-BRD-10: A Fast and Accurate GPU-Based Proton Transport Monte Carlo Simulation for Validating Proton Therapy Treatment Plans

Purpose: To build a GPU-based Monte Carlo (MC) simulation of proton transport with detailed modeling of elastic and non-elastic (NE) protonnucleus interactions, for use in a very fast and cost-effective proton therapy treatment plan verification system. Methods: Using the CUDA framework, we implemented kernels for the following tasks: (1) Simulation of beam spots from our possible scanning nozzle configurations, (2) Proton propagation through CT geometry, taking into account nuclear elastic and multiple scattering, as well as energy straggling, (3) Bertini-style modeling of the intranuclear cascade stage of NE interactions, and (4) Simulation of nuclear evaporation. To validate our MC, we performed: (1) Secondary particle yield calculations in NE collisions with therapeutically-relevant nuclei, (2) Pencil-beam dose calculations in homogeneous phantoms, (3) A large number of treatment plan dose recalculations, and compared with Geant4.9.6p2/TOPAS. A workflow was devised for calculating plans from a commercially available treatment planning system, with scripts for reading DICOM files and generating inputs for our MC. Results: Yields, energy and angular distributions of secondaries from NE collisions on various nuclei are in good agreement with the Geant4.9.6p2 Bertini and Binary cascade models. The 3D-gamma pass rate at 2%–2mm for 70–230 MeV pencil-beam dose distributions in water, soft tissue, bone and Ti phantoms is 100%. The pass rate at 2%–2mm for treatment plan calculations is typically above 98%. The net computational time on a NVIDIA GTX680 card, including all CPU-GPU data transfers, is around 20s for 1×10{sup 7} proton histories. Conclusion: Our GPU-based proton transport MC is the first of its kind to include a detailed nuclear model to handle NE interactions on any nucleus. Dosimetric calculations demonstrate very good agreement with Geant4.9.6p2/TOPAS. Our MC is being integrated into a framework to perform fast routine clinical QA of pencil-beam treatment plans. Hardware for such a system will cost under $5000. This work was funded in part by a grant from Varian Medical Systems, Inc.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2014

TH-A-19A-04: Latent Uncertainties and Performance of a GPU-Implemented Pre-Calculated Track Monte Carlo Method

Purpose: Assessing the performance and uncertainty of a pre-calculated Monte Carlo (PMC) algorithm for proton and electron transport running on graphics processing units (GPU). While PMC methods have been described in the past, an explicit quantification of the latent uncertainty arising from recycling a limited number of tracks in the pre-generated track bank is missing from the literature. With a proper uncertainty analysis, an optimal pre-generated track bank size can be selected for a desired dose calculation uncertainty. Methods: Particle tracks were pre-generated for electrons and protons using EGSnrc and GEANT4, respectively. The PMC algorithm for track transport was implemented on the CUDA programming framework. GPU-PMC dose distributions were compared to benchmark dose distributions simulated using general-purpose MC codes in the same conditions. A latent uncertainty analysis was performed by comparing GPUPMC dose values to a “ground truth” benchmark while varying the track bank size and primary particle histories. Results: GPU-PMC dose distributions and benchmark doses were within 1% of each other in voxels with dose greater than 50% of Dmax. In proton calculations, a submillimeter distance-to-agreement error was observed at the Bragg Peak. Latent uncertainty followed a Poisson distribution with the number of tracks per energy (TPE) and a track bank of 20,000 TPE produced a latent uncertainty of approximately 1%. Efficiency analysis showed a 937× and 508× gain over a single processor core running DOSXYZnrc for 16 MeV electrons in water and bone, respectively. Conclusion: The GPU-PMC method can calculate dose distributions for electrons and protons to a statistical uncertainty below 1%. The track bank size necessary to achieve an optimal efficiency can be tuned based on the desired uncertainty. Coupled with a model to calculate dose contributions from uncharged particles, GPU-PMC is a candidate for inverse planning of modulated electron radiotherapy and scanned proton beams. This work was supported in part by FRSQ-MSSS (Grant No. 22090), NSERC RG (Grant No. 432290) and CIHR MOP (Grant No. MOP-211360)

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2014

SU-E-T-107: Development of a GPU-Based Dose Delivery System for Adaptive Pencil Beam Scanning

Purpose: A description of a GPU-based dose delivery system (G-DDS) to integrate a fast forward planning implementing in real-time the prescribed sequence of pencil beams. The system, which is under development, is designed to evaluate the dose distribution deviations due to range variations and interplay effects affecting mobile tumors treatments. Methods: The Dose Delivery System (DDS) in use at the Italian Centro Nazionale di Adroterapia Oncologica (CNAO), is the starting point for the presented system. A fast and partial forward planning (FP) tool has been developed to evaluate in few seconds the delivered dose distributions using the DDS data (on-line measurements of spot properties, i.e. number of particles and positions). The computation is performed during the intervals between synchrotron spills and, made available at the end of each spill. In the interval between two spills, the G-DDS will evaluate the delivered dose distributions taking into account the real-time target positions measured by a tracking system. The sequence of prescribed pencil beams for the following spill will be adapted taking into account the variations with respect to the original plan due to the target motion. In order to speed up the computation required to modify pencil beams distribution (up to 400 times has been reached), the Graphics Processing Units (GPUs) and advanced Field Programmable Gate Arrays (FPGAs) are used. Results: An existing offline forward planning is going to be optimized for the CUDA architecture: the gain in time will be presented. The preliminary performances of the developed GPU-based FP algorithms will be shown. Conclusion: A prototype of a GPU-based dose delivery system is under development and will be presented. The system workflow will be illustrated together with the approach adopted to integrate the three main systems, i.e. CNAO dose delivery system, fast forward planning, and tumor tracking system.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

Latent uncertainties of the precalculated track Monte Carlo method

Purpose: While significant progress has been made in speeding up Monte Carlo (MC) dose calculation methods, they remain too time-consuming for the purpose of inverse planning. To achieve clinically usable calculation speeds, a precalculated Monte Carlo (PMC) algorithm for proton and electron transport was developed to run on graphics processing units (GPUs). The algorithm utilizes pregenerated particle track data from conventional MC codes for different materials such as water, bone, and lung to produce dose distributions in voxelized phantoms. While PMC methods have been described in the past, an explicit quantification of the latent uncertainty arising from the limited number of unique tracks in the pregenerated track bank is missing from the paper. With a proper uncertainty analysis, an optimal number of tracks in the pregenerated track bank can be selected for a desired dose calculation uncertainty. Methods: Particle tracks were pregenerated for electrons and protons using EGSnrc and GEANT4 and saved in a database. The PMC algorithm for track selection, rotation, and transport was implemented on the Compute Unified Device Architecture (CUDA) 4.0 programming framework. PMC dose distributions were calculated in a variety of media and compared to benchmark dose distributions simulated from the corresponding general-purpose MC codes in the same conditions. A latent uncertainty metric was defined and analysis was performed by varying the pregenerated track bank size and the number of simulated primary particle histories and comparing dose values to a “ground truth” benchmark dose distribution calculated to 0.04% average uncertainty in voxels with dose greater than 20% of D{sub max}. Efficiency metrics were calculated against benchmark MC codes on a single CPU core with no variance reduction. Results: Dose distributions generated using PMC and benchmark MC codes were compared and found to be within 2% of each other in voxels with dose values greater than 20% of the maximum dose. In proton calculations, a small (≤1 mm) distance-to-agreement error was observed at the Bragg peak. Latent uncertainty was characterized for electrons and found to follow a Poisson distribution with the number of unique tracks per energy. A track bank of 12 energies and 60000 unique tracks per pregenerated energy in water had a size of 2.4 GB and achieved a latent uncertainty of approximately 1% at an optimal efficiency gain over DOSXYZnrc. Larger track banks produced a lower latent uncertainty at the cost of increased memory consumption. Using an NVIDIA GTX 590, efficiency analysis showed a 807 × efficiency increase over DOSXYZnrc for 16 MeV electrons in water and 508 × for 16 MeV electrons in bone. Conclusions: The PMC method can calculate dose distributions for electrons and protons to a statistical uncertainty of 1% with a large efficiency gain over conventional MC codes. Before performing clinical dose calculations, models to calculate dose contributions from uncharged particles must be implemented. Following the successful implementation of these models, the PMC method will be evaluated as a candidate for inverse planning of modulated electron radiation therapy and scanned proton beams.

07 ISOTOPE AND RADIATION SOURCES↗