Search NASA⌕ Search

SEARCH · Search NASA

Results for “Parallelization Strategy”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Data-Driven Optimization of the Processing Window for 316H Components Fabricated Using Laser Powder Bed Fusion

The Advanced Materials and Manufacturing Technologies Program is focused on accelerating the development and deployment of advanced materials and components fabricated via additive manufacturing with a specific focus on laser powder bed fusion (LPBF). As an initial case study, the program has selected 316H stainless steel (SS) as an initial material around which to develop a code case development strategy. This strategy involves two parallel approaches: (1) an equivalency approach whereby round-robin testing across multiple collaborating laboratories demonstrates repeatability in processing and direct comparisons with conventional wrought 316H material and (2) a revolutionary approach to code qualification combining in situ data collection and high-fidelity modeling to capture, predict, and bound the performance of LPBF 316HSS components. As part of this campaign, this work package has initiated an extensive process optimization campaign across three laboratories, each printing variations of LPBF 316HSS using three different LPBF units (Concept Laser, EOS, and Renishaw). In FY23, ORNL has focused on unique experimental designs spanning wide ranges in energy inputs and turning knobs such as scan speed, laser power, hatch spacing, layer thickness, spot size, scan rotation, and more. On the Concept Laser M2, 72 different combinations of processing variables were investigated with duplicate samples and different powder compositions. In total, 252 samples were printed with combined in situ sensing data. A parallel design of experiments was conducted on the Renishaw AM400 with an additional 390 printed specimens for analysis. All 642 miniature specimens, each with unique features included in each print to capture geometry-related heterogeneity, were subjected to high-throughput x-ray computed tomography (XCT) analysis to enable the downselection of specific processing parameters of interest. Then, using electrical discharge machining (EDM), miniature tensile specimens were extracted for mechanical testing and microscopy investigations. From the analysis performed in FY23, it was found that powder composition drastically affects the resulting microstructure and mechanical performance of 316SS. Specifically, changing from 316L to 316HSS powder results in a wide range of grain sizes with varying degrees of preferred grain orientation, which increases as a function of energy density. It was also found that due to stored heat in thin fin–type features, large microstructural differences can be seen within one part printed with one set of processing parameters. These variations in microstructure features, including grain size, the nanoscale dislocation structure, and grain texture, will all affect the irradiation performance and high-temperature mechanical performance of LPBF 316HSS parts. Two sets of concept laser processing parameters, spanning both refined and columnar grain structures, were scaled to print larger 316H builds for campaign testing (high-temperature creep and irradiation). In addition, at least two optimized processing parameter sets were identified for the Renishaw AM400 for round-robin testing in FY24 with Argonne National Laboratory. Future work includes printing samples using identical parameters identified by partner institutions, providing material for corrosion and high-temperature mechanical testing, and continuing evaluations of heterogeneity in larger printed parts.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Data-Driven Optimization of the Processing Window for 316H Components Fabricated Using Laser Powder Bed Fusion

The Advanced Materials and Manufacturing Technologies Program is focused on accelerating the development and deployment of advanced materials and components fabricated via additive manufacturing with a specific focus on laser powder bed fusion (LPBF). As an initial case study, the program has selected 316H stainless steel (SS) as an initial material around which to develop a code case development strategy. This strategy involves two parallel approaches: (1) an equivalency approach whereby round-robin testing across multiple collaborating laboratories demonstrates repeatability in processing and direct comparisons with conventional wrought 316H material and (2) a revolutionary approach to code qualification combining in situ data collection and high-fidelity modeling to capture, predict, and bound the performance of LPBF 316HSS components. As part of this campaign, this work package has initiated an extensive process optimization campaign across three laboratories, each printing variations of LPBF 316HSS using three different LPBF units (Concept Laser, EOS, and Renishaw). In FY23, ORNL has focused on unique experimental designs spanning wide ranges in energy inputs and turning knobs such as scan speed, laser power, hatch spacing, layer thickness, spot size, scan rotation, and more. On the Concept Laser M2, 72 different combinations of processing variables were investigated with duplicate samples and different powder compositions. In total, 252 samples were printed with combined in situ sensing data. A parallel design of experiments was conducted on the Renishaw AM400 with an additional 390 printed specimens for analysis. All 642 miniature specimens, each with unique features included in each print to capture geometry-related heterogeneity, were subjected to high-throughput x-ray computed tomography (XCT) analysis to enable the downselection of specific processing parameters of interest. Then, using electrical discharge machining (EDM), miniature tensile specimens were extracted for mechanical testing and microscopy investigations. From the analysis performed in FY23, it was found that powder composition drastically affects the resulting microstructure and mechanical performance of 316SS. Specifically, changing from 316L to 316HSS powder results in a wide range of grain sizes with varying degrees of preferred grain orientation, which increases as a function of energy density. It was also found that due to stored heat in thin fin–type features, large microstructural differences can be seen within one part printed with one set of processing parameters. These variations in microstructure features, including grain size, the nanoscale dislocation structure, and grain texture, will all affect the irradiation performance and high-temperature mechanical performance of LPBF 316HSS parts. Two sets of concept laser processing parameters, spanning both refined and columnar grain structures, were scaled to print larger 316H builds for campaign testing (high-temperature creep and irradiation). In addition, at least two optimized processing parameter sets were identified for the Renishaw AM400 for round-robin testing in FY24 with Argonne National Laboratory. Future work includes printing samples using identical parameters identified by partner institutions, providing material for corrosion and high-temperature mechanical testing, and continuing evaluations of heterogeneity in larger printed parts.

36 MATERIALS SCIENCE↗
NASA NTRS1995

The Effect of Interrupts on Software Pipeline Execution on Message-Passing Architectures

Pipelining is a common strategy for extracting parallelism from a collection of independent computational tasks, each of which is spread among a number of processors and has an implied data dependence. When implemented on MIMD parallel computers with finite process interrupt times, pipeline algorithms suffer from slowdown--in addition to the expected pipeline fill time--due to a wave-like propagation of delays. This phenomenon, which has been observed experimentally using the performance monitoring system AIMS, is investigated analytically, and an optimal correction is derived to eliminate the wave. Efficiency increase through the correction is verified experimentally.

VanderWijngaart, Rob F.↗
DOE OSTI2019

The Updated DESGW Processing Pipeline for the Third LIGO/VIRGO Observing Run

The DESGW group seeks to identify electromagnetic counterparts of gravitational wave events seen by the LIGO-VIRGO network, such as those expected from binary neutron star mergers or neutron star- black hole mergers. DESGW was active throughout the first two LIGO observing seasons, following up several binary black hole mergers and the first binary neutron star merger, GW170817. We describe the modifications to the observing strategy generation and image processing pipeline between the second (ending in August 2017) and third (beginning in April 2019) LIGO observing seasons. The modifications include a more robust observing strategy generator, further parallelization of the image reduction software and difference imaging processing pipeline, data transfer streamlining, and a public webpage listing identified counterpart candidates that updates in real time. Taken together, the additional parallelization steps enable us to identify potential electromagnetic counterpa rts within fully calibrated search images in less than one hour, compared to the 3-5 hours it would typically take during the first two seasons. These performance improvements are critical to the entire EM followup community, as rapid identification (or rejection) of candidates enables detailed spectroscopic followup by multiple instruments as soon as possible, leading to more information about the environment immediately following such gravitational wave events.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Decentralized Interleaving of Paralleled Dc-Dc Buck Converters

We present a decentralized control strategy that yields switch interleaving among parallel-connected dc-dc buck converters. The proposed method is based on the digital implementation of the dynamics of a nonlinear oscillator circuit as the controller. Each controller is fully decentralized, i.e., it only requires the locally measured output current to synthesize the pulse width modulation (PWM) carrier waveform and no communication between different controllers is needed. By virtue of the intrinsic electrical coupling between converters, the nonlinear oscillator-based controllers converge to an interleaved state with uniform phase-spacing across PWM carriers. To the knowledge of the authors, this work presents the first fully decentralized strategy for switch interleaving in paralleled dc-dc buck converters.

14 SOLAR ENERGY↗
DOE OSTI2023

Parallelized domain decomposition for multi-dimensional Lagrangian random walk mass-transfer particle tracking schemes

Lagrangian particle tracking schemes allow a wide range of flow and transport processes to be simulated accurately, but a major challenge is numerically implementing the inter-particle interactions in an efficient manner. This article develops a multi-dimensional, parallelized domain decomposition (DDC) strategy for mass-transfer particle tracking (MTPT) methods in which particles exchange mass dynamically. We show that this can be efficiently parallelized by employing large numbers of CPU cores to accelerate run times. In order to validate the approach and our theoretical predictions we focus our efforts on a well-known benchmark problem with pure diffusion, where analytical solutions in any number of dimensions are well established. In this work, we investigate different procedures for “tiling” the domain in two and three dimensions (2-D and 3-D), as this type of formal DDC construction is currently limited to 1-D. An optimal tiling is prescribed based on physical problem parameters and the number of available CPU cores, as each tiling provides distinct results in both accuracy and run time. We further extend the most efficient technique to 3-D for comparison, leading to an analytical discussion of the effect of dimensionality on strategies for implementing DDC schemes. Increasing computational resources (cores) within the DDC method produces a trade-off between inter-node communication and on-node work. For an optimally subdivided diffusion problem, the 2-D parallelized algorithm achieves nearly perfect linear speedup in comparison with the serial run-up to around 2700 cores, reducing a 5 h simulation to 8 s, while the 3-D algorithm maintains appreciable speedup up to 1700 cores.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Decentralized Interleaving of Parallel-Connected Buck Converters

We present a decentralized control strategy that yields switch interleaving for parallel-connected dc-dc buck converters. Compared to state-of-the-art methods that are distributed at best, the proposed architecture requires no communication, and hence, presents a variety of advantages with regard to reliability, modularity, and cost. The method is based on the digital implementation of the dynamics of a Lienard-type oscillator circuit as the controller for the converters. Each controller only requires the locally measured output current to synthesize the pulsewidth modulation (PWM) carrier waveform. The intrinsic electrical coupling between converters drives the nonlinear-oscillator-based controllers to converge to an interleaved state with uniform phase spacing across PWM carriers, independent of the number of converters, the load, and initial conditions. We provide analytical guarantees for existence and stability of the interleaved state as well as extensive hardware results for a system of five 120 W 48 V-to-12 V dc-dc buck converters that demonstrate convergence to the interleaved state in the face of a variety of large-signal disturbances.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2016

A patch-based pseudo-CT approach for MRI-only radiotherapy in the pelvis

Purpose: In radiotherapy based only on magnetic resonance imaging (MRI), knowledge about tissue electron densities must be derived from the MRI. This can be achieved by converting the MRI scan to the so-called pseudo-computed tomography (pCT). An obstacle is that the voxel intensities in conventional MRI scans are not uniquely related to electron density. The authors previously demonstrated that a patch-based method could produce accurate pCTs of the brain using conventional T{sub 1}-weighted MRI scans. The method was driven mainly by local patch similarities and relied on simple affine registrations between an atlas database of the co-registered MRI/CT scan pairs and the MRI scan to be converted. In this study, the authors investigate the applicability of the patch-based approach in the pelvis. This region is challenging for a method based on local similarities due to the greater inter-patient variation. The authors benchmark the method against a baseline pCT strategy where all voxels inside the body contour are assigned a water-equivalent bulk density. Furthermore, the authors implement a parallelized approximate patch search strategy to speed up the pCT generation time to a more clinically relevant level. Methods: The data consisted of CT and T{sub 1}-weighted MRI scans of 10 prostate patients. pCTs were generated using an approximate patch search algorithm in a leave-one-out fashion and compared with the CT using frequently described metrics such as the voxel-wise mean absolute error (MAE{sub vox}) and the deviation in water-equivalent path lengths. Furthermore, the dosimetric accuracy was tested for a volumetric modulated arc therapy plan using dose–volume histogram (DVH) point deviations and γ-index analysis. Results: The patch-based approach had an average MAE{sub vox} of 54 HU; median deviations of less than 0.4% in relevant DVH points and a γ-index pass rate of 0.97 using a 1%/1 mm criterion. The patch-based approach showed a significantly better performance than the baseline water pCT in almost all metrics. The approximate patch search strategy was 70x faster than a brute-force search, with an average prediction time of 20.8 min. Conclusions: The authors showed that a patch-based method based on affine registrations and T{sub 1}-weighted MRI could generate accurate pCTs of the pelvis. The main source of differences between pCT and CT was positional changes of air pockets and body outline.

60 APPLIED LIFE SCIENCES↗
NASA NTRS1994

Checkpoint-based forward recovery using lookahead execution and rollback validation in parallel and distributed systems

This thesis studies a forward recovery strategy using checkpointing and optimistic execution in parallel and distributed systems. The approach uses replicated tasks executing on different processors for forwared recovery and checkpoint comparison for error detection. To reduce overall redundancy, this approach employs a lower static redundancy in the common error-free situation to detect error than the standard N Module Redundancy scheme (NMR) does to mask off errors. For the rare occurrence of an error, this approach uses some extra redundancy for recovery. To reduce the run-time recovery overhead, look-ahead processes are used to advance computation speculatively and a rollback process is used to produce a diagnosis for correct look-ahead processes without rollback of the whole system. Both analytical and experimental evaluation have shown that this strategy can provide a nearly error-free execution time even under faults with a lower average redundancy than NMR.

Long, Junsheng↗
DOE OSTI2016

Institute for Sustained Performance, Energy, and Resilience (SuPER)

The University of Tennessee (UTK) and University of Texas at El Paso (UTEP) partnership supported the three main thrusts of the SUPER project---performance, energy, and resilience. The UTK-UTEP effort thus helped advance the main goal of SUPER, which was to ensure that DOE's computational scientists can successfully exploit the emerging generation of high performance computing (HPC) systems. This goal is being met by providing application scientists with strategies and tools to productively maximize performance, conserve energy, and attain resilience. The primary vehicle through which UTK provided performance measurement support to SUPER and the larger HPC community is the Performance Application Programming Interface (PAPI). PAPI is an ongoing project that provides a consistent interface and methodology for collecting hardware performance information from various hardware and software components, including most major CPUs, GPUs and accelerators, interconnects, I/O systems, and power interfaces, as well as virtual cloud environments. The PAPI software is widely used for performance modeling of scientific and engineering applications---for example, the HOMME (High Order Methods Modeling Environment) climate code, and the GAMESS and NWChem computational chemistry codes---on DOE supercomputers. PAPI is widely deployed as middleware for use by higher-level profiling, tracing, and sampling tools (e.g., CrayPat, HPCToolkit, Scalasca, Score-P, TAU, Vampir, PerfExpert), making it the de facto standard for hardware counter analysis. PAPI has established itself as fundamental software infrastructure in every application domain (spanning academia, government, and industry), where improving performance can be mission critical. Ultimately, as more application scientists migrate their applications to HPC platforms, they will benefit from the extended capabilities this grant brought to PAPI to analyze and optimize performance in these environments, whether they use PAPI directly, or via third-party performance tools. Capabilities added to PAPI through this grant include support for new architectures such as the lastest GPU and Xeon Phi accelerators, and advanced power measurement and management features. Another important topic for the UTK team was providing support for a rich ecosystem of different fault management strategies in the context of parallel computing. Our long term efforts have been oriented toward proposing flexible strategies and providing building boxes that application developers can use to build the most efficient fault management technique for their application. These efforts span across the entire software spectrum, from theoretical models of existing strategies to easily assess their performance, to algorithmic modifications to take advantage of specific mathematical properties for data redundancy and to extensions to widely used programming paradigms to empower the application developers to deal with all types of faults. We have also continued our tight collaborations with users to help them adopt these technologies to ensure their application always deliver meaningful scientific data. Large supercomputer systems are becoming more and more power and energy constrained, and future systems and applications running on them will need to be optimized to run under power caps and/or minimize energy consumption. The UTEP team contributed to the SUPER energy thrust by developing power modeling methodologies and investigating power management strategies. Scalability modeling results showed that some applications can scale better with respect to an increasing power budget than with respect to only the number of processors. Power management, in particular shifting power to processors on the critical path of an application execution, can reduce perturbation due to system noise and other sources of runtime variability, which are growing problems on large-scale power-constrained computer systems.

42 ENGINEERING↗
DOE OSTI2016

Optimal Battery Utilization Over Lifetime for Parallel Hybrid Electric Vehicle to Maximize Fuel Economy

This paper presents a control strategy to maximize fuel economy of a parallel hybrid electric vehicle over a target life of the battery. Many approaches to maximizing fuel economy of parallel hybrid electric vehicle do not consider the effect of control strategy on the life of the battery. This leads to an oversized and underutilized battery. There is a trade-off between how aggressively to use and 'consume' the battery versus to use the engine and consume fuel. The proposed approach addresses this trade-off by exploiting the differences in the fast dynamics of vehicle power management and slow dynamics of battery aging. The control strategy is separated into two parts, (1) Predictive Battery Management (PBM), and (2) Predictive Power Management (PPM). PBM is the higher level control with slow update rate, e.g. once per month, responsible for generating optimal set points for PPM. The considered set points in this paper are the battery power limits and State Of Charge (SOC). The problem of finding the optimal set points over the target battery life that minimize engine fuel consumption is solved using dynamic programming. PPM is the lower level control with high update rate, e.g. a second, responsible for generating the optimal HEV energy management controls and is implemented using model predictive control approach. The PPM objective is to find the engine and battery power commands to achieve the best fuel economy given the battery power and SOC constraints imposed by PBM. Simulation results with a medium duty commercial hybrid electric vehicle and the proposed two-level hierarchical control strategy show that the HEV fuel economy is maximized while meeting a specified target battery life. On the other hand, the optimal unconstrained control strategy achieves marginally higher fuel economy, but fails to meet the target battery life.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2024

Plastic Parallel Pathways Platform - 4P Model

Global momentum is building towards a circular economy capable of keeping plastics in use and out of waste streams. Given that 79% of all plastic produced since 1950 has accumulated in landfills or the natural environment,rapid implementation of various end-of-life (EoL) management technologies will be needed to reach this target. However, it can be challenging to develop an effective plastic EoL strategy when the available options - chemical or molecular recycling, energy recovery, upcycling, downcycling, closed-loop (plastic-to-plastic) or open-loop (plastic-to-x) recycling, among others - can generate products ranging from low-grade to virgin-quality plastic and from fuels to value-added chemicals. We present a flexible material flow model capable of analyzing the effects of both plastic-to-plastic and plastic-to-x EoL management strategies on the U.S. PET economy. This Plastic Parallel Pathways Platform (4P) assesses the environmental impacts, costs, and circularity of a PET system in which waste is managed through six potential EoL pathways: landfill, incineration with energy recovery, pyrolysis to fuel oil, upcycling to glass fiber reinforced plastic (GFRP), mechanical recycling to low-grade PET, and chemical recycling (glycolysis) to bottle-grade PET. We compare the pathways across multiple metrics using multi-criteria decision analysis (MCDA) and then use a brute force algorithm to predict an optimal combination of EoL pathways to minimize greenhouse gas (GHG) emissions and costs and maximize circularity. This work highlights the need to implement a diverse portfolio of EoL strategies in parallel to enable a PET economy that meets environmental, economic, and circularity requirements simultaneously.

downcycling↗
DOE OSTI2020

Novel strategies for modal-based structural material identification

Here, we present modal-based methods for model calibration in structural dynamics, and address several key challenges in the solution of gradient-based optimization problems with eigenvalues and eigenvectors, including the solution of singular Helmholtz problems encountered in sensitivity calculations, non-differentiable objective functions caused by mode swapping during optimization, and cases with repeated eigenvalues. Unlike previous literature that relied on direct solution of the eigenvector adjoint equations, we present a parallel iterative domain decomposition strategy (Adjoint Computation via Modal Superposition with Truncation Augmentation) for the solution of the singular Helmholtz problems. For problems with repeated eigenvalues we present a novel Mode Separation via Projection algorithm, and in order to address mode swapping between inverse iterations we present a novel Injective mode ordering metric. We present the implementation of these methods in a massively parallel finite element framework with the ability to use measured modal data to extract unknown structural model parameters from large complex problems. A series of increasingly complex numerical examples are presented that demonstrate the implementation and performance of the methods in a massively parallel finite element framework [7], [5], using gradient-based optimization techniques in the Rapid Optimization Library (ROL) [21].

36 MATERIALS SCIENCE↗
NASA NTRS1987

Parallel processing in finite element structural analysis

A brief review is made of the fundamental concepts and basic issues of parallel processing. Discussion focuses on parallel numerical algorithms, performance evaluation of machines and algorithms, and parallelism in finite element computations. A computational strategy is proposed for maximizing the degree of parallelism at different levels of the finite element analysis process including: 1) formulation level (through the use of mixed finite element models); 2) analysis level (through additive decomposition of the different arrays in the governing equations into the contributions to a symmetrized response plus correction terms); 3) numerical algorithm level (through the use of operator splitting techniques and application of iterative processes); and 4) implementation level (through the effective combination of vectorization, multitasking and microtasking, whenever available).

Noor, Ahmed K.↗
DOE OSTI2014

An efficient parallel implementation of explicit multirate Runge–Kutta schemes for discontinuous Galerkin computations

Although explicit time integration schemes require small computational efforts per time step, their efficiency is severely restricted by their stability limits. Indeed, the multi-scale nature of some physical processes combined with highly unstructured meshes can lead some elements to impose a severely small stable time step for a global problem. Multirate methods offer a way to increase the global efficiency by gathering grid cells in appropriate groups under local stability conditions. These methods are well suited to the discontinuous Galerkin framework. The parallelization of the multirate strategy is challenging because grid cells have different workloads. The computational cost is different for each sub-time step depending on the elements involved and a classical partitioning strategy is not adequate any more. In this paper, we propose a solution that makes use of multi-constraint mesh partitioning. It tends to minimize the inter-processor communications, while ensuring that the workload is almost equally shared by every computer core at every stage of the algorithm. Particular attention is given to the simplicity of the parallel multirate algorithm while minimizing computational and communication overheads. Our implementation makes use of the MeTiS library for mesh partitioning and the Message Passing Interface for inter-processor communication. Performance analyses for two and three-dimensional practical applications confirm that multirate methods preserve important computational advantages of explicit methods up to a significant number of processors.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2009

Porting Gravitational Wave Signal Extraction to Parallel Virtual Machine (PVM)

Laser Interferometer Space Antenna (LISA) is a planned NASA-ESA mission to be launched around 2012. The Gravitational Wave detection is fundamentally the determination of frequency, source parameters, and waveform amplitude derived in a specific order from the interferometric time-series of the rotating LISA spacecrafts. The LISA Science Team has developed a Mock LISA Data Challenge intended to promote the testing of complicated nested search algorithms to detect the 100-1 millihertz frequency signals at amplitudes of 10E-21. However, it has become clear that, sequential search of the parameters is very time consuming and ultra-sensitive; hence, a new strategy has been developed. Parallelization of existing sequential search algorithms of Gravitational Wave signal identification consists of decomposing sequential search loops, beginning with outermost loops and working inward. In this process, the main challenge is to detect interdependencies among loops and partitioning the loops so as to preserve concurrency. Existing parallel programs are based upon either shared memory or distributed memory paradigms. In PVM, master and node programs are used to execute parallelization and process spawning. The PVM can handle process management and process addressing schemes using a virtual machine configuration. The task scheduling and the messaging and signaling can be implemented efficiently for the LISA Gravitational Wave search process using a master and 6 nodes. This approach is accomplished using a server that is available at NASA Ames Research Center, and has been dedicated to the LISA Data Challenge Competition. Historically, gravitational wave and source identification parameters have taken around 7 days in this dedicated single thread Linux based server. Using PVM approach, the parameter extraction problem can be reduced to within a day. The low frequency computation and a proxy signal-to-noise ratio are calculated in separate nodes that are controlled by the master using message and vector of data passing. The message passing among nodes follows a pattern of synchronous and asynchronous send-and-receive protocols. The communication model and the message buffers are allocated dynamically to address rapid search of gravitational wave source information in the Mock LISA data sets.

Thirumalainambi, Rajkumar↗
DOE OSTI2015

A scalable, matrix-free multigrid preconditioner for finite element discretizations of heterogeneous Stokes flow

In this paper we describe a computational methodology that is specifically designed for studying three-dimensional geodynamic processes governed by heterogeneous visco-plastic Stokes flow. The method employs a hybrid spatial discretization consisting of a View the MathML sourceQ2-P1disc mixed finite element formulation for the Stokes problem, coupled to a material-point formulation which is used for representing material state and history-dependent variables. The applicability and practicality of this methodology is realized through the development of an efficient, scalable and robust variable viscosity Stokes preconditioner. In this work, these objectives are achieved through exploiting matrix-free operators and a geometric multigrid preconditioner employing hybrid coarse level operators, Chebyshev smoothers and hybrid Krylov coarse level solvers. The robustness and parallel efficiency of this strategy is demonstrated using an idealized geodynamic model. Lastly, we apply the new methodology to study geodynamic models of continental rifting and break-up in order to understand the diverse range of passive continental margins we observe on Earth today

Geodynamics↗
DOE OSTI2015

Iterative stability analysis of spatial domain decomposition based on block Jacobi algorithm for the diamond-difference scheme

Here, we study convergence of the integral transport matrix method (ITMM) based on a parallel block Jacobi (PBJ) iterative strategy for solving particle transport problems. The ITMM is a spatial domain decomposition method proposed for massively parallel computations. AFourier analysis of the PBJ-based iterations applied to SN diamond-difference equations in 1D slab and 2D Cartesian geometries is performed. It is carried out for infinite-medium problems with homogeneous material properties. To analyze the performance of the ITMM with the PBJ algorithm and evaluate its potential in scalability we consider a limiting case of one spatial cell per subdomain. The analysis shows that in such limit the spectral radius of the iteration method is one without regard to values of the scattering ratio and optical thickness of the spatial cells. This implies lack of convergence in infinite medium. Numerical results of finite-medium problems are presented. They demonstrate effects of finite size of spatial domain on the performance of the iteration algorithm as well as its asymptotic behavior when the extent of the spatial domain increases. Finally, these numerical experiments also show that for finite domains iterative convergence to a finite criterion is achievable in a multiple of the sum of number of cells in each dimension.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗