Search NASA⌕ Search

SEARCH · Search NASA

Results for “multilevel methods”

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 343 records · Page 19

On ParELAG's Parallel Element-based Algebraic Multigrid and its MFEM Miniapps for H(curl) and H(div) Problems: a report including lowest and next to the lowest order numerical results

This paper presents the utilization of element-based algebraic multigrid (AMGe) hierarchies, implemented in the ParELAG (Parallel Element Agglomeration Algebraic Multigrid Upscaling and Solvers) library, to produce multilevel preconditioners and solvers for H(curl) and H(div) formulations. This involves the construction of hierarchies of compatible nested spaces, forming an exact de Rham sequence on each level. This allows the application of hybrid smoothers on all levels and AMS (Auxiliary-space Maxwell Solver) or ADS (Auxiliary-space Divergence Solver) on the coarsest levels, obtaining complete multigrid cycles. Numerical results are presented, showing the parallel performance of the proposed methods. As a part of the exposition, this paper demonstrates some of the capabilities of ParELAG and outlines some of the components and procedures within the library.

97 MATHEMATICS AND COMPUTING↗

Modeling and control of cascaded bridgeless multilevel rectifier under unbalanced load conditions

The goal of this project is to model and control a novel unidirectional cascaded multilevel bridgeless rectifier as an active front end in medium and high voltage applications. This topology has many advantages over a conventional cascaded H-bridge rectifier, such as lower implementation cost, higher reliability, and greater flexibility with similar power quality. The complete design process of the proposed converter is developed step by step in order to meet all the desired objectives. The steady-state mathematical model is used to develop a method for the voltage balancing of dc cells. Power factor analysis is discussed to mathematically derive requirements for the number of partially controlled and fully controlled H-bridges in the proposed H-bridge converter. Power loss, efficiency, and cost comparison studies between the traditional cascaded H-Bridge converter and the proposed bridgeless converter demonstrate the advantages. After exploring various well-established control methods, a novel control strategy is proposed to achieve dc voltage balancing, fast and robust grid synchronization, power factor correction, and elimination of zero crossing current distortion under both balanced and unbalanced load conditions. The converter can also be used for reactive power compensation in a grid tied power system if a sufficient number of fully controlled H-bridge modules are included. Processor-In-the-Loop (PIL) simulation has been the utilized to validate the performance of discrete control structure. Simulation and experimental results validate the models and control method.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Multilevel Morphology of Complex Nanoporous Materials

This work exploits gas adsorption and small-angle X-ray scattering (SAXS) to determine the morphology of complex nanoporous materials. We resolve multiple classes of porosity including previously undetected large-scale texture that significantly compromises the canonical interpretation of gas adsorption. Specifically, a UVM-7 class mesoporous silica was synthesized that has morphological features on three length scales: macropores due to packing of 150 nm globules, 1.9 nm radius spherical mesopores inside the globules, and >7 nm pockets on and between the globules. The total and external surface areas, as well as the mesopore volume, were determined using gas adsorption (α s -plot) and SAXS. A new approach was applied to the SAXS data using multilevel fitting to determine the surface areas on multiple length scales. The SAXS analysis code is applicable to any two-phase system and is freely available to the public. The total surface area determined by SAXS was 12% greater than that obtained by gas adsorption. The macropore interfacial area, however, is only 30% of the external surface area determined by the α s -plot. The overestimation of the external surface area by the αs-plot method is attributed to capillary condensation in nanoscale surface irregularities. Here, the discrepancy is resolved assuming that the macropore–globule interfaces harbor fractally distributed nooks and crannies, which lead to gas adsorption at pressures above the mesopore filling pressure.

36 MATERIALS SCIENCE↗

Fundamental-Frequency Reactive Circulating Current Injection for Capacitor Voltage Balancing in Hybrid-MMC HVDC Systems During Riding Through PTG Faults

Here, this article presents a comprehensive analysis and a novel solution for the discharge problem on the half-bridge submodules' (HBSMs') capacitors in the hybrid modular multilevel converter (MMC)-based high-voltage direct current transmission systems under a long-term (e.g., several minutes or longer) pole-to-ground fault condition. The mechanism of this issue is analyzed, and then a solution based on fundamental-frequency reactive circulating current (FFRCC) injection is proposed. The influence of FFRCC injection is analyzed in terms of the fluctuated arm capacitor energy and the current stress of semiconductors. Moreover, an enhanced arm voltage modulation method based on HBSMs and full-bridge submodules coordinate control is proposed to accelerate the capacitor voltage balance of HBSMs. Finally, the performance of the proposed control strategy is verified by the simulation results.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Hybrid concatenated codes and iterative decoding

Several improved turbo code apparatuses and methods. The invention encompasses several classes: (1) A data source is applied to two or more encoders with an interleaver between the source and each of the second and subsequent encoders. Each encoder outputs a code element which may be transmitted or stored. A parallel decoder provides the ability to decode the code elements to derive the original source information d without use of a received data signal corresponding to d. The output may be coupled to a multilevel trellis-coded modulator (TCM). (2) A data source d is applied to two or more encoders with an interleaver between the source and each of the second and subsequent encoders. Each of the encoders outputs a code element. In addition, the original data source d is output from the encoder. All of the output elements are coupled to a TCM. (3) At least two data sources are applied to two or more encoders with an interleaver between each source and each of the second and subsequent encoders. The output may be coupled to a TCM. (4) At least two data sources are applied to two or more encoders with at least two interleavers between each source and each of the second and subsequent encoders. (5) At least one data source is applied to one or more serially linked encoders through at least one interleaver. The output may be coupled to a TCM. The invention includes a novel way of terminating a turbo coder.

Divsalar, Dariush↗

An approximation concepts method for space frame synthesis

A method is presented for the minimum mass design of three dimensional space frames constructed of thin walled rectangular cross-section members. Constraints on nodal displacements and rotations, material stress, local buckling, and cross sectional dimensions are included. A high quality separable approximate problem is formed in terms of the reciprocals of the four section properties of the frame element cross section, replacing all implicit functions with simplified explicit relations. The cross sectional dimensions are efficiently calculated without using multilevel techniques. Several test problems are solved, demonstrating that a series of approximate problem solutions converge rapidly to an optimal design.

Mills-Curran, W. C.↗

Multi-level adaptive finite element methods. 1: Variation problems

A general numerical strategy for solving partial differential equations and other functional problems by cycling between coarser and finer levels of discretization is described. Optimal discretization schemes are provided together with very fast general solvers. It is described in terms of finite element discretizations of general nonlinear minimization problems. The basic processes (relaxation sweeps, fine-grid-to-coarse-grid transfers of residuals, coarse-to-fine interpolations of corrections) are directly and naturally determined by the objective functional and the sequence of approximation spaces. The natural processes, however, are not always optimal. Concrete examples are given and some new techniques are reviewed. Including the local truncation extrapolation and a multilevel procedure for inexpensively solving chains of many boundary value problems, such as those arising in the solution of time-dependent problems.

Brandt, A.↗

Parallel Element Agglomeration Multilevel Monte Carlo Library (ParELAGMC)

ParELAGMC is a parallel distributed memory C++ library for multilevel Monte Carlo (MLMC) simulations with algebraically constructed coarse spaces for estimating statistical moments of a quantity of interest involving solutions of partial differential equations with uncertain coefficients. A primary focus of the library is the scalable generation of Gaussian random fields using a novel stochastic PDE (SPDE) sampling technique for large-scale simulations. A key feature in the SPDE sampling technique is a novel non-matching mesh embedding technique to mitigate artificial boundary artifacts that are inherent in the method. Example applications to uncertainty quantification of subsurface flow simulations in the mixed finite element setting are provided as well.

Osborn, SarahV.↗

Low Interrater Reliability in Grading of Rectal Bleeding Using National Cancer Institute Common Toxicity Criteria and Radiation Therapy Oncology Group Toxicity Scales: A Survey of Radiation Oncologists

Purpose: To measure concordance among genitourinary radiation oncologists in using the National Cancer Institute Common Toxicity Criteria (NCI CTC) and Radiation Therapy Oncology Group (RTOG) grading scales to grade rectal bleeding. Methods and Materials: From June 2013 to January 2014, a Web-based survey was sent to 250 American and Canadian academic radiation oncologists who treat prostate cancer. Participants were provided 4 case vignettes in which patients received radiation therapy and developed rectal bleeding and were asked for management plans and to rate the bleeding according to NCI CTC v.4 and RTOG late toxicity grading (scales provided). In 2 cases, participants were also asked whether they would send the patient for colonoscopy. A multilevel, random intercept modeling approach was used to assess sources of variation (case, respondent) in toxicity grading to calculate the intraclass correlation coefficient (ICC). Agreement on a dichotomous grading scale (low grades 1-2 vs high grades 3-4) was also assessed, using the κ statistic for multiple respondents. Results: Seventy-two radiation oncologists (28%) completed the survey. Forty-seven (65%) reported having either written or been principal investigator on a study using these scales. Agreement between respondents was moderate (ICC 0.52, 95% confidence interval [CI] 0.47-0.58) when using NCI CTC and fair using the RTOG scale (ICC 0.28, 95% CI 0.20-0.40). Respondents who chose an invasive management were more likely to select a higher toxicity grade (P<.0001). Using the dichotomous scale, we observed moderate agreement (κ = 0.42, 95% CI 0.40-0.44) with the NCI CTC scale, but only slight agreement with the RTOG scale (κ = 0.19, 95% CI 0.17-0.21). Conclusion: Low interrater reliability was observed among radiation oncologists grading rectal bleeding using 2 common scales. Clearer definitions of late rectal bleeding toxicity should be constructed to reduce this variability and avoid ambiguity in both reporting and interpretation.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Algebraic multigrid

The state of the art in algebraic multgrid (AMG) methods is discussed. The interaction between the relaxation process and the coarse grid correction necessary for proper behavior of the solution probes is discussed in detail. Sufficient conditions on relaxation and interpolation for the convergence of the V-cycle are given. The relaxation used in AMG, what smoothing means in an algebraic setting, and how it relates to the existing theory are considered. Some properties of the coarse grid operator are discussed, and results on the convergence of two-level and multilevel convergence are given. Details of an algorithm particularly studied for problems obtained by discretizing a single elliptic, second order partial differential equation are given. Results of experiments with such problems using both finite difference and finite element discretizations are presented.

Ruge, J. W.↗

Application of the ERTS system to the study of Wyoming resources with emphasis on the use of basic data products

Many potential users of ERTS data products and other aircraft and satellite imagery are limited to visual methods of analyses of these products. Illustrations are presented from Wyoming studies that have employed these standard data products for a variety of geologic and related studies. Possible economic applications of these studies are summarized. Studies include regional geologic mapping for updating and correcting existing maps and to supplement incomplete regional mapping; illustrations of the value of seasonal images in geologic mapping; specialized mapping of such features as sand dunes, playa lakes, lineaments, glacial features, regional facies changes, and their possible economic value; and multilevel sensing as an aid in mineral exploration. Examples of cooperative studies involving botanists, plant scientists, and geologists for the preparation of maps of surface resources that can be used by planners and for environmental impact studies are given.

Houston, R. S.↗

Theoretical and software considerations for nonlinear dynamic analysis

In the finite element method for structural analysis, it is generally necessary to discretize the structural model into a very large number of elements to accurately evaluate displacements, strains, and stresses. As the complexity of the model increases, the number of degrees of freedom can easily exceed the capacity of present-day software system. Improvements of structural analysis software including more efficient use of existing hardware and improved structural modeling techniques are discussed. One modeling technique that is used successfully in static linear and nonlinear analysis is multilevel substructuring. This research extends the use of multilevel substructure modeling to include dynamic analysis and defines the requirements for a general purpose software system capable of efficient nonlinear dynamic analysis. The multilevel substructuring technique is presented, the analytical formulations and computational procedures for dynamic analysis and nonlinear mechanics are reviewed, and an approach to the design and implementation of a general purpose structural software system is presented.

Schmidt, R. J.↗

Multilevel decomposition approach to the preliminary sizing of a transport aircraft wing

A multilevel/multidisciplinary optimization scheme for sizing an aircraft wing structure is described. A methodology using nonlinear programming in application to a very large engineering problem is presented. This capability is due to the decomposition approach. Over 1300 design variables are considered for this nonlinear optimization task. In addition, a mathematical link is established coupling the detail of structural sizing to the overall system performance objective, such as fuel consumption. The scheme is implemented as a three level system analyzing aircraft mission performance at the top level, the total aircraft structure as the middle level, and individual stiffened wing skin cover panels at the bottom level. Numerical show effectiveness of the method and its good convergence characteristics.

Wrenn, Gregory A.↗

Scalable Multiphysics Block Preconditioning for Low Mach Number Compressible Resistive MHD with Application to Magnetic Confinement Fusion

This study investigates multiphysics block preconditioners that are critical in devising scalable Newton–Krylov iterative solvers for longer time-scale fully implicit fluid plasma models. The specific model of interest is the visco-resistive, low Mach number, compressible magnetohydrodynamics (MHD) model. This model describes the dynamics of conducting fluids in the presence of electromagnetic fields and can be used to study aspects of astrophysical phenomena, important science and technology applications, and basic plasma physics. The specific application of interest that motivates this study is the macroscopic simulation of longer time-scale stability and disruptions of magnetic confinement fusion devices, specifically the ITER Tokamak. The computational solution of the governing balance equations for mass, momentum, heat transfer, and magnetic induction for resistive MHD systems can be extremely challenging. These difficulties arise from both the strong nonlinear, nonsymmetric coupling of fluid and electromagnetic phenomena as well as the significant range of time and length scales that the interactions of these physical mechanisms produce. To handle the range of time and spatial scales of interest, a fully implicit unstructured variational multiscale finite element formulation is employed. For the scalable solution of the Newton linearized systems, fully coupled block preconditioners are designed to leverage algebraic multigrid subsolves. In conclusion, results are presented for the strong and weak scaling of the method as well as the robustness of these techniques for a large range of Lundquist numbers.

97 MATHEMATICS AND COMPUTING↗

Downscaling-Based Segmentation for Unresolved Images of Highly Heterogeneous Granular Porous Samples

Numerical simulations of pore-scale flow and transport in natural sediments require the knowledge of pore-space topology. Limited resolution of X-ray tomography is often insufficient to fully characterize pore-space structure within fine-grained regions. Single and multilevel threshold-based segmentation approaches are customarily employed to identify solid, pore and porous-solid regions by means of grey intensity thresholds. While the choice of cutoff thresholds is often arbitrary, it dramatically affects the effective properties and the dynamical response of the reconstructed porous structure. As such, we propose an algorithm of downscaling, i.e., the process of increasing image resolution, followed by segmentation, i.e., the identification of different phases, to reconstruct the unresolved pore-space from XCT images of natural geological porous media. The method, applicable to moderately unresolved, chemically homogeneous granular media, is based on a map between local pixel porosity and pore size that does not rely on the definition of arbitrary thresholds and it allows to generate a high-resolution binary image of the porous medium from poorly resolved grey-scale images. First, we validate the method on synthetic unresolved images and compare their known pore-space distribution with the extracted one. Then, we consider a synthetic porous medium and compare the pore size distribution, conductivity, and tortuosity between the original and the reconstructed structures. Finally, we apply the method to extract the pore-space distribution from unresolved XCT images of two natural sediment columns and use it (i) to parametrize a capillary-bundle model and (ii) to estimate the hydraulic conductivity by matching breakthrough behavior of passive solute transport.

58 GEOSCIENCES↗

Impact of Using Audit Data to Improve the Evidence-Based Use of Single-Fraction Radiation Therapy for Bone Metastases in British Columbia

Purpose: To assess the impact of a population-based intervention to increase the consistency and use of single-fraction radiation therapy (SFRT) for bone metastases. Methods and Materials: In 2012, an audit of radiation therapy prescriptions for bone metastases in British Columbia identified significant interphysician and -center (26%-73%) variation in the use of SFRT. Anonymous physician-level and identifiable regional cancer center SFRT use data were presented to all radiation oncologists, together with published guidelines, meta-analyses, and recommendations from practice leaders. The use of SFRT for bone metastases from 2007 through 2011 was compared with use of SFRT in 2013, to assess the impact of the audit and educational intervention. Multilevel logistic regression was used to assess the relationship between the usage of SFRT and the timing of the radiation while controlling for potentially confounding variables. Physician and center were included as group effects to account for the clustered structure of the data. Results: A total of 16,898 courses of RT were delivered from 2007 through 2011, and 3200 courses were delivered in 2013. The rates of SFRT use in 2007, 2008, 2009, 2010, 2011, and 2013 were 50.5%, 50.9%, 48.3%, 48.5%, 48.0%, and 59.7%, respectively (P<.001). Use of SFRT increased in each of 5 regional centers: A: 26% to 32%; B: 36% to 56%; C: 39% to 57%; D: 49% to 56%; and E: 73% to 85.0%. Use of SFRT was more consistent; 3 of 5 centers used SFRT for 56% to 57% of bone metastases RT courses. The regression analysis showed strong evidence that the usage of SFRT increased after the 2012 intervention (odds ratio 2.27, 95% confidence interval 2.06-2.50, P<.0001). Conclusion: Assessed on a population basis, an audit-based intervention increased utilization of SFRT for bone metastases. The intervention reversed a trend to decreasing SFRT use, reduced costs, and improved patient convenience. This suggests that dissemination of programmatic quality indicators in oncology can lead to increased utilization of evidence-based practice.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Multigrid Reduction in Time for Nonlinear Parabolic Problems

The need for parallel-in-time is being driven by changes in computer architectures, where future speed-ups will be available through greater concurrency, but not faster clock speeds, which are stagnant.This leads to a bottleneck for sequential time marching schemes, because they lack parallelism in the time dimension. Multigrid Reduction in Time (MGRIT) is an iterative procedure that allows for temporal parallelism by utilizing multigrid reduction techniques and a multilevel hierarchy of coarse time grids. MGRIT has been shown to be effective for linear problems, with speedups of up to 50 times. The goal of this work is the efficient solution of nonlinear problems with MGRIT, where efficient is defined as achieving similar performance when compared to a corresponding linear problem. As our benchmark, we use the p-Laplacian, where p = 4 corresponds to a well-known nonlinear diffusion equation and p = 2 corresponds to our benchmark linear diffusion problem. When considering linear problems and implicit methods, the use of optimal spatial solvers such as spatial multigrid imply that the cost of one time step evaluation is fixed across temporal levels, which have a large variation in time step sizes. This is not the case for nonlinear problems, where the work required increases dramatically on coarser time grids, where relatively large time steps lead to worse conditioned nonlinear solves and increased nonlinear iteration counts per time step evaluation. This is the key difficulty explored by this paper. We show that by using a variety of strategies, most importantly, spatial coarsening and an alternate initial guess to the nonlinear time-step solver, we can reduce the work per time step evaluation over all temporal levels to a range similar with the corresponding linear problem. This allows for parallel scaling behavior comparable to the corresponding linear problem.

97 MATHEMATICS AND COMPUTING↗

Albany/FELIX: A parallel, scalable and robust, finite element, first-order Stokes approximation ice sheet solver built for advanced analysis

This paper describes a new parallel, scalable and robust finite element based solver for the first-order Stokes momentum balance equations for ice flow. The solver, known as Albany/FELIX , is constructed using the component-based approach to building application codes, in which mature, modular libraries developed as a part of the Trilinos project are combined using abstract interfaces and template-based generic programming, resulting in a final code with access to dozens of algorithmic and advanced analysis capabilities. Following an overview of the relevant partial differential equations and boundary conditions, the numerical methods chosen to discretize the ice flow equations are described, along with their implementation. The results of several verification studies of the model accuracy are presented using (1) new test cases for simplified two-dimensional (2-D) versions of the governing equations derived using the method of manufactured solutions, and (2) canonical ice sheet modeling benchmarks. Model accuracy and convergence with respect to mesh resolution are then studied on problems involving a realistic Greenland ice sheet geometry discretized using hexahedral and tetrahedral meshes. Also explored as a part of this study is the effect of vertical mesh resolution on the solution accuracy and solver performance. The robustness and scalability of our solver on these problems is demonstrated. Lastly, we show that good scalability can be achieved by preconditioning the iterative linear solver using a new algebraic multilevel preconditioner, constructed based on the idea of semi-coarsening.

54 ENVIRONMENTAL SCIENCES↗