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Measurement and analysis of GPU-accelerated applications with HPCToolkit

To address the challenge of performance analysis on the US DOE’s forthcoming exascale supercomputers, Rice University has been extending its HPCToolkit performance tools to support measurement and analysis of GPU-accelerated applications. To help developers understand the performance of accelerated applications as a whole, HPCToolkit’s measurement and analysis tools attribute metrics to calling contexts that span both CPUs and GPUs. To measure GPU-accelerated applications efficiently, HPCToolkit employs a novel wait-free data structure to coordinate monitoring and attribution of GPU performance. To help developers understand the performance of complex GPU code generated from high-level programming models, HPCToolkit constructs sophisticated approximations of call path profiles for GPU computations. To support fine-grained analysis and tuning, HPCToolkit uses PC sampling and instrumentation to measure and attribute GPU performance metrics to source lines, loops, and inlined code. To supplement fine-grained measurements, HPCToolkit can measure GPU kernel executions using hardware performance counters. To provide a view of how an execution evolves over time, HPCToolkit can collect, analyze, and visualize call path traces within and across nodes. Finally, on NVIDIA GPUs, HPCToolkit can derive and attribute a collection of useful performance metrics based on measurements using GPU PC samples. Here, we illustrate HPCToolkit’s new capabilities for analyzing GPU-accelerated applications with several codes developed as part of the Exascale Computing Project.

97 MATHEMATICS AND COMPUTING↗

Computer Codes V and V Tests with a Large-Scale Sodium Thermal-Hydraulic Test Facility (STELLA)

The Korea Atomic Energy Research Institute (KAERI) is carrying out the design of a 'Prototype Generation IV Sodium-cooled Fast Reactor (PGSFR)' in cooperation with Argonne National Laboratory (ANL) in the US. In regard to computer codes V and V, a large-scale sodium thermal-hydraulic test program is currently being progressed in parallel with the PGSFR design, which is called STELLA (Sodium Test Loop for Safety Simulation and Assessment). The final objective of this program is to collect a separate and integral effect test database to validate the safety analysis codes and other thermal hydraulic design codes. In the first phase of the STELLA program, the sodium component test loop (hereafter called STELLA-1) was constructed at the KAERI site, and it has been used for performance tests of key sodium heat exchangers in PGSFR. Since this sodium test loop is basically for separate effects tests to verify the performance of key sodium components, the test database obtained from STELLA-1 has been used for the V and V of safety codes as well as heat exchanger design codes. The second phase of the program aiming at an integral effect test is called STELLA-2, which will be used for synthetic review of the key safety issues of PGSFR. The basic and detailed design phases of the STELLA-2 test facility are underway in accordance with the specific design requirements reflecting the whole design features of PGSFR. The facility installation is scheduled to be completed by 2018. Then the main experiments including the start-up tests will begin and the first integral effect test database will be constructed by the end of 2019. Based on the STELLA-2 platform, a simulation of the PGSFR transient will be made to evaluate the plant dynamic behaviors and demonstrate the decay heat removal performance. Multi-dimensional effects coming from a large sodium pool system will be identified as well. The test database obtained from the STELLA-2 experiment will be used for the validation of the safety analysis codes and other thermal hydraulics codes, and this project finally contributes to the specific design phase of PGSFR. This paper presents both the results of heat transfer tests for the key sodium heat exchangers using STELLA-1 and the first results of heat exchanger design codes V and V. The recent progress of the engineering design for the STELLA-2 test section is introduced and its specific design parameters are also presented in this paper with detailed evaluation results of their scaling distortions. A large-scale sodium thermal-hydraulic test program (STELLA) was introduced with the specific activities for separate and integral effects tests. The test database obtained from STELLA-1 was successfully used to validate both the heat exchanger design and safety analysis codes. Specific design features of the integral effects test facility (STELLA- 2) with a scaling ratio of 1/5 in length and 1/125 in volume were also presented. Validation of the STELLA-2 facility design is underway using system codes and CFD tools. Dedicated water-mockup experiments to verify the scaling design of key subsystems are currently being conducted as well. (authors)

42 ENGINEERING↗

GronOR: Massively Parallel and GPU-Accelerated Non-Orthogonal Configuration Interaction for Large Molecular Systems

GronOR is a program package for non-orthogonal configuration interaction calculations for an electronic wave function built in terms of anti-symmetrized products of multi-configuration molecular fragment wave functions. The two-electron integrals that have to be processed may be expressed in terms of atomic orbitals or in terms of an orbital basis determined from the molecular orbitals of the fragments. The code has been specifically designed for execution on distributed memory massively parallel and Graphics Processing Unit (GPU)-accelerated computer architectures, using an MPI+OpenACC/OpenMP programming approach. The task-based execution model used in the implementation allows for linear scaling with the number of nodes on the largest pre-exascale architectures available, provides hardware fault resiliency, and enables effective execution on systems with distinct central processing unit-only and GPU-accelerated partitions. The code interfaces with existing multi-configuration electronic structure codes that provide optimized molecular fragment orbitals, configuration interaction coefficients, and the required integrals. Algorithm and implementation details, parallel and accelerated performance benchmarks, and an analysis of the sensitivity of the accuracy of results and computational performance to thresholds used in the calculations are presented.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Developing MiniApps on Modern Platforms Using Multiple Programming Models, In: 2015 IEEE International Conference on Cluster Computing

We have developed a set of reduced, proxy applications ("MiniApps") based on large-scale application codes supported at the Oak Ridge Leadership Computing Facility (OLCF). The MiniApps are designed to encapsulate the details of the most important (i.e. the most time-consuming and/or unique) facets of the applications that run in production mode on the OLCF. In each case, we have produced or plan to produce individual versions of the MiniApps using different specific programming models (e.g., OpenACC, CUDA, OpenMP). We describe some of our initial observations regarding these different implementations along with estimates of how closely the MiniApps track the actual performance characteristics (in particular, the overall scalability) of the large-scale applications from which they are derived.

Computer Science↗

Assessment of ion kinetic effects in shock-driven inertial confinement fusion implosions using fusion burn imaging

The significance and nature of ion kinetic effects in D{sup 3}He-filled, shock-driven inertial confinement fusion implosions are assessed through measurements of fusion burn profiles. Over this series of experiments, the ratio of ion-ion mean free path to minimum shell radius (the Knudsen number, N{sub K}) was varied from 0.3 to 9 in order to probe hydrodynamic-like to strongly kinetic plasma conditions; as the Knudsen number increased, hydrodynamic models increasingly failed to match measured yields, while an empirically-tuned, first-step model of ion kinetic effects better captured the observed yield trends [Rosenberg et al., Phys. Rev. Lett. 112, 185001 (2014)]. Here, spatially resolved measurements of the fusion burn are used to examine kinetic ion transport effects in greater detail, adding an additional dimension of understanding that goes beyond zero-dimensional integrated quantities to one-dimensional profiles. In agreement with the previous findings, a comparison of measured and simulated burn profiles shows that models including ion transport effects are able to better match the experimental results. In implosions characterized by large Knudsen numbers (N{sub K} ∼ 3), the fusion burn profiles predicted by hydrodynamics simulations that exclude ion mean free path effects are peaked far from the origin, in stark disagreement with the experimentally observed profiles, which are centrally peaked. In contrast, a hydrodynamics simulation that includes a model of ion diffusion is able to qualitatively match the measured profile shapes. Therefore, ion diffusion or diffusion-like processes are identified as a plausible explanation of the observed trends, though further refinement of the models is needed for a more complete and quantitative understanding of ion kinetic effects.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Monte Carlo simulation of TrueBeam flattening-filter-free beams using Varian phase-space files: Comparison with experimental data

Purpose: Phase-space files for Monte Carlo simulation of the Varian TrueBeam beams have been made available by Varian. The aim of this study is to evaluate the accuracy of the distributed phase-space files for flattening filter free (FFF) beams, against experimental measurements from ten TrueBeam Linacs. Methods: The phase-space files have been used as input in PRIMO, a recently released Monte Carlo program based on thePENELOPE code. Simulations of 6 and 10 MV FFF were computed in a virtual water phantom for field sizes 3 × 3, 6 × 6, and 10 × 10 cm{sup 2} using 1 × 1 × 1 mm{sup 3} voxels and for 20 × 20 and 40 × 40 cm{sup 2} with 2 × 2 × 2 mm{sup 3} voxels. The particles contained in the initial phase-space files were transported downstream to a plane just above the phantom surface, where a subsequent phase-space file was tallied. Particles were transported downstream this second phase-space file to the water phantom. Experimental data consisted of depth doses and profiles at five different depths acquired at SSD = 100 cm (seven datasets) and SSD = 90 cm (three datasets). Simulations and experimental data were compared in terms of dose difference. Gamma analysis was also performed using 1%, 1 mm and 2%, 2 mm criteria of dose-difference and distance-to-agreement, respectively. Additionally, the parameters characterizing the dose profiles of unflattened beams were evaluated for both measurements and simulations. Results: Analysis of depth dose curves showed that dose differences increased with increasing field size and depth; this effect might be partly motivated due to an underestimation of the primary beam energy used to compute the phase-space files. Average dose differences reached 1% for the largest field size. Lateral profiles presented dose differences well within 1% for fields up to 20 × 20 cm{sup 2}, while the discrepancy increased toward 2% in the 40 × 40 cm{sup 2} cases. Gamma analysis resulted in an agreement of 100% when a 2%, 2 mm criterion was used, with the only exception of the 40 × 40 cm{sup 2} field (∼95% agreement). With the more stringent criteria of 1%, 1 mm, the agreement reduced to almost 95% for field sizes up to 10 × 10 cm{sup 2}, worse for larger fields. Unflatness and slope FFF-specific parameters are in line with the possible energy underestimation of the simulated results relative to experimental data. Conclusions: The agreement between Monte Carlo simulations and experimental data proved that the evaluated Varian phase-space files for FFF beams from TrueBeam can be used as radiation sources for accurate Monte Carlo dose estimation, especially for field sizes up to 10 × 10 cm{sup 2}, that is the range of field sizes mostly used in combination to the FFF, high dose rate beams.

61 RADIATION PROTECTION AND DOSIMETRY↗

Benchmark Specification for FFTF LOFWOS Test #13

The Fast Flux Test Facility (FFTF) at the Hanford site in Washington was designed by the Westinghouse Electric Corporation for the U.S. Department of Energy. FFTF was a 400 MW thermal, oxide-fueled, liquid sodium cooled test reactor, built to assist development and testing of advanced fuels and materials for fast breeder reactors. After reaching criticality in 1980, FFTF operated until 1992, providing the U.S. Department of Energy (DOE) with the means to test fuels, materials, and other components in a fast neutron flux environment. In July 1986, a series of unprotected transients (with the plant protection system intentionally disabled) were performed in FFTF as part of the passive safety demonstration program. Among these were thirteen loss of flow without scram (LOFWOS) tests. The goals of this program included confirming the liquid metal reactor safety margins, providing data for computer code validation, and demonstrating the inherent and passive safety benefits of specific design features. The test defined in this benchmark is LOFWOS Test #13, which was initiated at 50% power and 100% flow with the pump pony motors turned off. This benchmark specification is intended to support collaborative efforts within international partnerships on the validation of simulation tools and models in the area of Sodium-cooled Fast Reactor (SFR) safety. Validated tools and models are needed to evaluate SFR inherent safety characteristics and assess the impact of passive design features in response to accident initiators. Comparisons with experimental data and the results of safety analyses from other groups create unique opportunities to improve predictive capabilities of computational codes and methods for SFR modeling and simulation. The conditions of the LOFWOS test along with the feedback from FFTF’s limited free bow core restraint system and the novel passive reactivity control Gas-Expansion Modules (GEMs) pose a very challenging and uniquely valuable benchmark exercise.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

System, methods and apparatus for program optimization for multi-threaded processor architectures

Methods, apparatus and computer software product for source code optimization are provided. In an exemplary embodiment, a first custom computing apparatus is used to optimize the execution of source code on a second computing apparatus. In this embodiment, the first custom computing apparatus contains a memory, a storage medium and at least one processor with at least one multi-stage execution unit. The second computing apparatus contains at least two multi-stage execution units that allow for parallel execution of tasks. The first custom computing apparatus optimizes the code for parallelism, locality of operations and contiguity of memory accesses on the second computing apparatus. This Abstract is provided for the sole purpose of complying with the Abstract requirement rules. This Abstract is submitted with the explicit understanding that it will not be used to interpret or to limit the scope or the meaning of the claims.

42 ENGINEERING↗

Summer Proceedings 2019

The Computer Science Research Institute (CSRI) brings university faculty and students to Sandia for focused collaborative research on Department of Energy (DOE) computer and computational science problems. The institute provides an opportunity for university researchers to learn about problems in computer and computational science at DOE laboratories. Participants conduct leading-edge research, interact with scientists and engineers at the laboratories, and help transfer results of their research to programs at the labs. Some specific CSRI research interest areas are: scalable solvers, optimization, adaptivity and mesh refinement, graph-based, discrete, and combinatorial algorithms, uncertainty estimation, mesh generation, dynamic load-balancing, virus and other malicious-code defense, visualization, scalable cluster computers and heterogeneous computers, data-intensive computing, environments for scalable computing, parallel input/output, advanced architectures, and theoretical computer science. The CSRI Summer Program includes the organization of a weekly seminar series and the publication of this summer proceedings.

97 MATHEMATICS AND COMPUTING↗

Evaluation of Low Power ARM Processors for Monte Carlo Particle Transport: MCNP6 on the ARM Cortex-A8 - Paper 83

In the push towards exascale computing, the limiting factors are power requirements and heat dissipation. Using current technology, the power required to drive an exascale supercomputer would near 400-MW. Clearly, future computing hardware will have to be more energy efficient in order to achieve exascale performance. Most of the current research in advanced computing architectures is in the use of standard CPUs with accelerators. However, these accelerators are not generally supported by the traditional scientific programming languages (C, C++, and Fortran) and the scientific software must be tailored specifically to take advantage of the accelerators. Large scale scientific software (hundreds-of-thousand to millions of lines of code) can not be easily ported to the computing platform du jour. The widespread use of low power ARM based processors in the mobile computing market offer a low power alternative to accelerators that are also supported by the traditional scientific programming languages and programming paradigms such as MPI and OpenMP. Computing architectures for scientific computing are often assessed using standard benchmarks such as LINPACK benchmark or using suites of mini-applications that are greatly simplified stand-ins for scientific software. Often the real applications that will deployed on the scientific supercomputers are not ported or tested until delivery of the machines. In order to evaluate the use of ARM processors for scientific computing the Monte Carlo particle transport code, MCNP version 6 was compiled on the ARM Cortex-A8 and a set of benchmark problems were used to assess performance in comparison to an Intel Xeon E5-2670 and the low power Intel Atom N270. MCNP is a continuous energy Monte Carlo particle transport code in development at Los Alamos National Laboratory since 1977. MCNP is used to transport neutrons, photon, electrons, and charged particles using continuous energy interaction data. It is commonly used in fields of nuclear power, nuclear medicine, radiation protection, and high-energy physics through-out the world. MCNP version 6 is approximately 450 thousand lines of code, written primary in Fortran90, with some C and C++. MCNP supports distributed multiprocessing using MPI and threading with OpenMP. The ARM Cortex-A8 executes MCNP6 using about twice as much power as the Intel Xeon E5-2670 and about the same amount of power as the Intel Atom N270. However, these results are encouraging for the use of low-power ARM chips in future supercomputers. The ARM Cortex-A8 is a 32-bit CPU and it's NEON general-purpose SIMD (single-instruction multiple data) engine does not support double-precision floating-point arithmetic. More recent ARM processors (ARM Cortex-A53 and Cortex-A57) support 64-bit addressing and have NEON co-processors that support double-precision floating-point arithmetic. ARM claims that the A50 series delivers a performance increase of 15 times the Cortex-A8 performance for similar power usage. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗

Evaluation of anticipatory signal to steam generator pressure control program for 700 MWe Indian pressurized heavy water reactor

700 MWe Indian Pressurized Heavy Water Reactor (IPHWR) is horizontal channel type reactor with partial boiling at channel outlet. Due to boiling, it has a large volume of vapor present in the primary loops. It has two primary loops connected with the help of pressurizer surge line. The pressurizer has a large capacity and is partly filled by liquid and partly by vapor. Large vapor volume improves compressibility of the system. During turbine trip or load rejection, pressure builds up in Steam Generator (SG). This leads to pressurization of Primary Heat Transport System (PHTS). To control pressurization of SG and PHTS, around 70% of the steam generated in SG is dumped into the condenser by opening Condenser Steam Dump Valves (CSDVs) and rest of the steam is released to the atmosphere by opening Atmospheric Steam Discharge Valves (ASDVs) immediately after sensing the event. This is accomplished by adding anticipatory signal to the output of SG pressure controller. Anticipatory signal is proportional to the thermal power of reactor and the proportionality constant is set so that SG pressure controller's output jacks up to ASDV opening range when operating at 100% FP. To simulate this behavior for 700 MWe IPHWR, Primary and secondary heat transport system is modeled. SG pressure control and other process control program have also been modeled to capture overall plant dynamics. Analysis has been carried out with 3-D neutron kinetics coupled thermal hydraulic computer code ATMIKA.T to evaluate the effect of the anticipatory signal on PHT pressure and over all plant dynamics during turbine trip in 700 MWe IPHWR. This paper brings out the results of the analysis with and without considering anticipatory signal in SG pressure control program during turbine trip. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Scalable Triadic Analysis of Large-Scale Graphs: Multi-Core vs. Multi-Processor vs. Multi-Threaded Shared Memory Architectures

Triadic analysis encompasses a useful set of graph mining methods that is centered on the concept of a triad, which is a subgraph of three nodes and the configuration of directed edges across the nodes. Such methods are often applied in the social sciences as well as many other diverse fields. Triadic methods commonly operate on a triad census that counts the number of triads of every possible edge configuration in a graph. Like other graph algorithms, triadic census algorithms do not scale well when graphs reach tens of millions to billions of nodes. To enable the triadic analysis of large-scale graphs, we developed and optimized a triad census algorithm to efficiently execute on shared memory architectures. We will retrace the development and evolution of a parallel triad census algorithm. Over the course of several versions, we continually adapted the code’s data structures and program logic to expose more opportunities to exploit parallelism on shared memory that would translate into improved computational performance. We will recall the critical steps and modifications that occurred during code development and optimization. Furthermore, we will compare the performances of triad census algorithm versions on three specific systems: Cray XMT, HP Superdome, and AMD multi-core NUMA machine. These three systems have shared memory architectures but with markedly different hardware capabilities to manage parallelism.

Triadic analysis, triads, triad census, large-scal↗

Management of Digital Equipment in Preproduction by Means of Uniform Numeric Control Language

The requirements on preproduction and the control software for various digital machining systems (numerically controlled machine tools, robot manipulators, additive manufacturing equipment) in flexible production are considered. By analysis of existing programming languages for digital equipment, UNCL (Uniform Numeric Control Language) has been developed for standard representation of control commands. The use of UNCL in verifying program operation on a machining simulator is considered. Software for the translation of control programs (specified in CLDATA formats and in ISO code) to the invariant format of the universal language is described. The postprocessing of control software from the universal language into programs in commonly used digital control systems is also considered.

42 ENGINEERING↗

FY2012 Report on Fast Reactor Toolset Work (PROTEUS-Fast)

As part of the NEAMS activity in DOE, a fast reactor simulation program was launched in April 2007, termed SHARP. The initial goal of SHARP was to develop a suite of modern simulation tools specifically for the analysis and design of sodium cooled fast reactors, and this goal has since been extended to consider all reactor types of interest. As part of that work, a high‐fidelity deterministic neutron transport code named UNIC was started, providing a common framework for fast reactor neutronics tools. Focusing on UNIC, spatial de‐homogenization increased the typical neutronics problem with a few hundred million degrees of freedom (DOF) into ones with hundreds of trillions of DOF. Such problems are beyond the capabilities of existing supercomputers. With the advent of future computer hardware, these high‐fidelity problems can be solved but only after a multiyear development program to adapt codes such as UNIC to that technology. UNIC can presently be used on smaller problems (single assembly, multiple assemblies) with today’s hardware, but it is also necessary to provide tools to solve the larger problems of interest, albeit without the aforementioned level of spatial de‐homogenization. To address the desire to demonstrate the coupling capability of NEAMS, part of the FY12 funding was focused on preparing the legacy codes, termed PROTEUS‐Fast, which are fully capable of solving full‐scale fast reactor problems. A bulk of the work this year was focused on preparing and distributing the PROTEUS‐Fast codes for use by all NEAMS users. The demonstration of a full coupling capability will require more follow on work, but significant progress was made this year preparing the interface coupling routines and preparing PROTEUS‐Fast for use. The primary targets of interest in PROTEUS‐Fast are DIF3D, DIF3D‐K (kinetics), and VARI3D (reactivity coefficients), with REBUS (fuel cycle) being an auxiliary component updated for convenience. All codes in PROTEUS‐Fast were verified and added to the BuildBot regression test. Unfortunately, all of the older codes suffered significant problems from the deprecated coding practices used within them and resulting conflicts with modern compilers. After some work, all of these issues were resolved and we feel confident in releasing them for use by others NEAMS members. With regard to specific upgrades, DIF3D‐VARIANT was upgraded with a few months of effort to allow the large scale problems of interest to be executed. After significant study, we choose not to modify VARI3D to include a transport option, but to develop a new code, PERSENT (partially funded by an external project) which uses the DIF3D‐VARIANT transport solution option. The outstanding features missing from MC 2 ‐3 were added, and MC 2 ‐3 has been released to RSICC. All of the remaining PROTEUS‐Fast codes are either finished with the copyright and licensing procedure or are actively going through it. While that process will delay the targeted August 2012 release to RSICC for a few more months, the codes are ready for immediate use and can be connected to the framework either by us or by others as the interface readers and documentation will be released with the PROTEUS‐Fast codes.

Wolters, E. R.↗

SIERRA Multimechanics Module: Aria Thermal Theory Manual - Version 4.50.

This document describes the theoretical foundation of thermal analysis in Sierra Mechanics. The SIERRA Multimechanics Module: Aria, henceforth referred to as Aria for brevity, was developed at Sandia National Laboratories under the ASC program, and approximates linear and nonlinear continuum models of heat transfer. Aria uses the SIERRA Framework, which provides data management services commonly required by computational mechanics software, and facilitates the development of coupled, multi-mechanics applications for massively parallel computers. The mathematical models in Aria are based heavily on those of COYOTE, a well-established thermal analysis program that was also developed at Sandia and its ASC code predecessor, Calore. Aria, Calore and COYOTE share a significant body of numerical methods, which are described in detail by Reddy and Gartling. Throughout this document, the terms software and implementation are synonymous with the Aria thermal-fluid analysis computer program. Whether one uses Aria to perform heat transfer analysis, or in developing a new capability for the Aria application, this document provides the information needed understand the existing numerical algorithm implementations. Justification for the fundamental assumptions of heat transfer, nor derivation of the energy conservation equations are included in this document. For a more thorough theoretical background, one is referred to one of the many available textbooks, e.g. Another reference, which is freely available in downloadable electronic form, is Lienhard and Lienhard.

97 MATHEMATICS AND COMPUTING↗

SIERRA Multimechanics Module: Aria Thermal Theory Manual (Version 4.46)

This document describes the theoretical foundation of thermal analysis in Sierra Mechanics. The SIERRA Multimechanics Module: Aria, henceforth referred to as Aria for brevity, was developed at Sandia National Laboratories under the ASC program, and approximates linear and nonlinear continuum models of heat transfer. Aria uses the SIERRA Framework, which provides data management services commonly required by computational mechanics software, and facilitates the development of coupled, multi-mechanics applications for massively parallel computers. The mathematical models in Aria are based heavily on those of COYOTE, a well-established thermal analysis program that was also developed at Sandia and its ASC code predecessor, Calore. Aria, Calore and COYOTE share a significant body of numerical methods, which are described in detail by Reddy and Gartling. Throughout this document, the terms software and implementation are synonymous with the Aria thermal-fluid analysis computer program.

97 MATHEMATICS AND COMPUTING↗

SIERRA Multimechanics Module: Aria Thermal Theory Manual (Version 4.44)

This document describes the theoretical foundation of thermal analysis in Sierra Mechanics. The SIERRA Multimechanics Module: Aria, henceforth referred to as Aria for brevity, was developed at Sandia National Laboratories under the ASC program, and approximates linear and nonlinear continuum models of heat transfer. Aria uses the SIERRA Framework, which provides data management services commonly required by computational mechanics software, and facilitates the development of coupled, multi-mechanics applications for massively parallel computers. The mathematical models in Aria are based heavily on those of COYOTE, a well-established thermal analysis program that was also developed at Sandia and its ASC code predecessor, Calore. Aria, Calore and COYOTE share a significant body of numerical methods, which are described in detail by Reddy and Gartling. Throughout this document, the terms software and implementation are synonymous with the Aria thermal-fluid analysis computer program.

97 MATHEMATICS AND COMPUTING↗

SIERRA Multimechanics Module: Aria Thermal Theory Manual (Version 4.42)

This document describes the theoretical foundation of thermal analysis in Sierra Mechanics. The SIERRA Multimechanics Module: Aria, henceforth referred to as Aria for brevity, was developed at Sandia National Laboratories under the ASC program, and approximates linear and nonlinear continuum models of heat transfer. Aria uses the SIERRA Framework, which provides data management services commonly required by computational mechanics software, and facilitates the development of coupled, multi-mechanics applications for massively parallel computers. The mathematical models in Aria are based heavily on those of COYOTE, a well-established thermal analysis program that was also developed at Sandia and its ASC code predecessor, Calore. Aria, Calore and COYOTE share a significant body of numerical methods, which are described in detail by Reddy and Gartling. Throughout this document, the terms software and implementation are synonymous with the Aria thermal-fluid analysis computer program.

97 MATHEMATICS AND COMPUTING↗