Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “implicit”

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 865 records · Page 48
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

First-principles and cluster expansion study of the effect of magnetism on short-range order in Fe–Ni–Cr austenitic stainless steels

Short-range order (SRO), the regular and predictable arrangement of atoms over short distances, alters the mechanical properties of technologically relevant structural materials such as medium/high entropy alloys and austenitic stainless steels. In this study, we present a generalized spin cluster expansion (CE) model and show that magnetism is a primary factor influencing the level of SRO present in austenitic Fe-Ni-Cr alloys. The spin CE consists of a chemical cluster expansion combined with an Ising model for Fe-Ni-Cr austenitic alloys. It explicitly accounts for local magnetic exchange interactions, thereby capturing the effects of finite temperature magnetism on SRO. Model parameters are obtained by fitting to a first-principles data set comprising both chemically and magnetically diverse FCC configurations. The magnitude of the magnetic exchange interactions are found to be comparable to the chemical interactions. Compared to a conventional implicit magnetism CE built from only magnetic ground state configurations, the spin CE shows improved performance on several experimental benchmarks over a broad spectrum of compositions, particularly at higher temperatures due to the explicit treatment of magnetic disorder. We find that SRO is strongly influenced by alloy Cr content, since Cr atoms prefer to align antiferromagnetically with nearest neighbors but become magnetically frustrated with increasing Cr concentration. Using the spin CE, we predict that increasing the Cr concentration in typical austenitic stainless steels promotes the formation of SRO and increases order-disorder transition temperatures. Furthermore, this study underscores the significance of considering magnetic interactions explicitly when exploring the thermodynamic properties of complex transition metal alloys. It also highlights guidelines for customizing SRO through adjustments of alloy composition.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Effect of the scanning strategy on the formation of residual stresses in additively manufactured Ti-6Al-4V

During the laser-powder bed fusion (L-PBF) process, high laser intensities, short interaction times and highly localized heat input drive large thermal gradients that result in a state of high residual stresses. Generally, the residual stresses that develop during the L-PBF process can compromise the performance of the component. Up to now, the literature has indicated that the magnitude of the residual stresses can be affected by various process parameters. In this study, all process parameters such as laser power and speed are held fixed and the focus is solely on the effect of the laser scan strategy on the three-dimensional residual stress state of L-PBF metallic components. Four Ti-6Al-4V bridge shaped components were built using island and continuous scanning patterns parallel and offset 45° from the sample axes. High-energy X-ray diffraction was used to determine the residual stress field in each of the components. Two of them were re-measured after being partially removed from the build plate. The assumptions implicit in diffraction measurements of stress are reviewed and discussed in depth because the unique microstructure associated with L-PBF Ti-6Al-4V renders the validity of those assumptions uncertain. Specifically, additional data was collected and analyzed to evaluate the relationship between grain scale and macroscopic scale stresses. The observed residual stresses were large, ½ to ¾ of the yield strength, particularly the build direction stresses near the lateral edges of the bridges. Here in this work, the higher stresses were observed in the bridges built via the island scan strategies, chiefly near the edges of the parts.

36 MATERIALS SCIENCE↗
DOE OSTI2023

An assessment of the utility of multirate time integration for the modeling of laser powder bed fusion

Finite element simulation of the laser powder bed fusion process is made challenging by the inherently multiscale nature of the process. When using the typical global time stepping techniques, slowly-evolving regions of the domain receive the same numerical treatment as the regions with the highest temperature rates. The current work details the implementation and evaluation of an implicit multirate method which is able to advance different regions of the domain with distinct time steps, depending on their current solution rate. Previous work indicates that this representation of the temporal scales of the problem can lead to significant reductions in wall clock run time, and it is shown herein that multirate time integration, when used with a uniform process-scale mesh, can result in speedups of approximately 19, 42, and 87 times, for domains with edge lengths of approximately 1 mm, 2 mm, and 5 mm, respectively. When used in conjunction with $\ h$-refinement (limited to two levels of refinement), the resulting speedups (taken relative to the uniform mesh) are around 28, 85, and 665 times. The method is demonstrated to converge as indicated by the literature, and its use with an AM-Bench domain is demonstrated.

42 ENGINEERING↗
DOE OSTI2021

Linear and Nonlinear Solvers for Simulating Multiphase Flow within Large-Scale Engineered Subsurface Systems

Simulation of multiphase flow in the subsurface is well-known to be computationally challenging. While there have been many studies that have explored approaches to overcoming these challenges, they often utilize relatively simple case studies. In this paper, we focus on the unique numerical challenges posed by modeling large-scale engineered subsurface systems, characterized by discrete features embedded in a heterogeneous natural subsurface setting. The man-made features such as shafts, tunnels, and barriers often cause multiple challenges in modeling the domain for multiphase porous media flow. This flow scenario can have a wide range of applications such as nuclear waste repositories, enhanced recovery of a petroleum reservoir, geothermal engineering, and carbon sequestration. An example of these severe numerical challenges is the case of performance assessment (PA) for Waste Isolation Pilot Plant (WIPP), the only operating deep geological repository in the US, which simulates extreme material properties of bedded salt rock formation and extreme contrast due to open excavation next to the formation. The models have extremes not only of permeability and porosity but also of the constitutive models needed for multiphase flow; additionally, they have process models like salt creep closure reducing porosity over time, fracturing in clay and anhydrite interbeds of the bedded salt, gas generation from the waste materials, and unintentional human borehole intrusions in some scenarios. Numerical simulations require the solution of coupled systems of nonlinear PDEs; in our work, we use the open-source simulator PFLOTRAN which is based on Finite Volume discretization. The solution of the nonlinear equations requires use of the Newton-Raphson iteration at each time step, which entails the solution of the linearized Jacobian system at each iteration. The effects of all the processes (i.e., large number of unknowns, highly nonlinear constitutive relations, large contrasts in material properties in short distances) lead to an ill-conditioned Jacobian matrix that severely challenges traditional linear solver, i.e., stabilized biconjugate gradient with block Jacobi incomplete LU preconditioner (BCGS-ILU) leading to non-convergence for traditional Newton-Raphson nonlinear solver causing unacceptably long computation time for each model. This paper presents linear solvers such as constrained pressure residual (CPR) two-stage preconditioner with alternate-block-factorization (ABF) and quasi- implicit pressure and explicit saturation (QIMPES) decouplers and flexible generalized residual solver (FGMRES). The new general-purpose nonlinear solver, Newton trust-region dogleg Cauchy (NTRDC), is also introduced to resolve extreme nonlinearities in the models. We demonstrate the effectiveness of each method relative to the default BCGS-Newton solver. The two best cases had nearly 50 times speed-up and achieved completion of a simulation in 14 hours that never completed due to non-convergence with the default solver. We also investigate the strong scalability of each method and discuss some of the deficiencies found for Block Jacobi preconditioner using parallel domain decomposition, and node packing effects of modern processor architecture.

Preconditioner, Nonlinear, Porous media, Multiphas↗
DOE OSTI2019

From plot to scale: ex-ante assessment of conservation agriculture in Zambia

This study combined bottom-up and top-down approaches to assess the ex-ante effects of conservation agriculture (CA)-based systems in Zambia considering both biophysical and economic factors and prevailing farm systems characteristics. For continuous maize cropping we compared a CA-based system of no-tillage with crop residue retention to a control system of conventional tillage with crop residue removal. First, we simulated yield effects that were calibrated and evaluated against multiple datasets, including on-farm agronomic trials from two seasons and six sites. Next, we extrapolated our simulations to all maize-growing areas in Zambia using gridded climate and soil datasets. Then simulated yields (in kg ha( -1 )) were combined with economic data from a nationally-representative household survey to construct economic indicators including benefit-cost ratios (based on gross benefits and variable costs both in $ ha( -1 )) that captured the implicit value of crop residues and labor demands. The field scale (per ha) indicators were scaled out using harvested areas as an expansion factor. All indicators were calculated over 3-, 10-, and 20-year simulation periods using an interpolated sequence of historical climate data. Finally, we conducted a spatial farm typology analysis to help understand the spatial variation in our field-scale indicators and provide insights into trade-offs and the suitability of CA-based systems for farmers. Average changes in yield from using CA-based systems (compared with the control) at the district scale ranged from -37% to 70% (average 33%), with a similar range of changes in benefit-cost ratios once economic factors were included, in addition to intra-district yield variability. Combining the changes in benefit cost ratios with maize harvested area resulted in an average annual change in district-scale net benefit ranging from US $ - 3.9 to US $9.9 million (with an average of US $1.1 million). The heterogeneity in biophysical and economic factors gave a ranking of provinces different according to biophysical or economic indicators, reinforcing the importance of coupling biophysical and economic approaches. The spatial farm typology analysis highlighted the specific contexts of farmers relevant to the suitability of CA, such as their mineral fertilizer applications rates, ownership of livestock, and prevailing soil texture and rainfall.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

Numerical implementation, verification and validation of two-phase flow four-equation drift flux model with Jacobian-free Newton–Krylov method

This study presents a numerical investigation on using the Jacobian-free Newton–Krylov (JFNK) method to solve the two-phase flow four-equation drift flux model with realistic constitutive correlations (‘closure models’). The drift flux model is based on Isshi and his collaborators’ work. Additional constitutive correlations for vertical channel flow, such as two-phase flow pressure drop, flow regime map, wall boiling and interfacial heat transfer models, were taken from the RELAP5-3D Code Manual and included to complete the model. The staggered grid finite volume method and fully implicit backward Euler method was used for the spatial discretization and time integration schemes, respectively. The Jacobian-free Newton–Krylov method shows no difficulty in solving the two-phase flow drift flux model with a discrete flow regime map. In addition to the Jacobian-free approach, the preconditioning matrix is obtained by using the default finite differencing method provided in the PETSc package, and consequently the labor-intensive implementation of complex analytical Jacobian matrix is avoided. Extensive and successful numerical verification and validation have been performed to prove the correct implementation of the models and methods. Code-to-code comparison with RELAP5-3D has further demonstrated the successful implementation of the drift flux model.

42 ENGINEERING↗
DOE OSTI2017

Newton-Krylov method in solving drift-flux two-phase flow problems for both pre-CHF and post-CHF conditions at steady state

Furthermore, this paper presents numerical simulations of two-phase flow heat transfer for both pre-CHF and post-CHF conditions typical in light water nuclear reactors. The conjugate heat transfer problem is modeled with one-dimensional drift-flux two-phase flow model for coolant flow and two-dimensional heat conduction equation in solid walls. Fully implicit time integration schemes were employed, and the resulted non-linear equations were solved with a Newton-Krylov method. For the drift-flux two-phase flow model, the EPRI drift-flux closure correlation is used to model the relative motion between the two phases. Additional closure correlations were adopted from REALP5-3D to determine two-phase flow regime, wall boiling heat and mass transfer, interfacial heat and mass transfer, and two-phase flow frictional pressure drop. Three sets of experiments were used for code validation, including Bartolomei subcooled flow boiling in vertical pipes, FRIGG boiling tests in vertical bundles, and Bennett heated tube tests. RELAP5-3D simulation results were also provided to perform code-to-code benchmark. Overall, numerical results of this work showed good agreements with both experimental data and RELAP5-3D simulation results. Discrepancy between them were also identified in post-CHF region, which suggests necessary further improvement.

42 ENGINEERING↗
DOE OSTI2018

Verification of iterative matrix solutions for multipoint kinetics equations

Multipoint kinetic equation systems have been solved numerically using matrix algebra software and 1st to 4th order implicit schemes based on single-step matrix propagators. These matrix schemes have been validated successfully on demanding point kinetics benchmarks with various prescribed reactivity insertions. Verification tests have also been performed on a simple 3-region fast reactor core model with asymmetric step or ramp reactivity insertions and cross-checked with the multipoint kinetics SACRE code developed at INL and based on existing and validated stiff ODE solver packages. Accurate results can be obtained at a limited time expense. The reason for intriguing results obtained in some transients has been elucidated and linked to the multipoint matrix coefficient interpolation method during the transient.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2019

An a posteriori residual-based spatial discretization error estimator for S N neutron transport

The “residual source estimator”, an implicit residual-based spatial discretization error estimator for S N neutron transport methods, is introduced. The estimator uses an approximation of the residual as a fixed source for an analogous transport problem whose solution is the error estimate, using the same transport operator as the original numerical solution. The complete derivation of the residual source estimator, the approximation of the residual, and higher-order derivatives is included. The performance of the residual source estimator for 0-order DGFEM is tested against reference solutions. For problems with true solutions discontinuous in the first derivative across the singular characteristics, the residual source estimator is generally accurate, precise, and computationally affordable compared to similar estimators. It suffers in problems where solutions are discontinuous, particularly when the discontinuity inflicts significant inaccuracies on the discrete solution; however, compared to other estimators, which suffer similarly, it remains a competitive option.

42 ENGINEERING↗
DOE OSTI2016

Microscopically derived potential energy surfaces from mostly structural considerations

A simple procedure to estimate the quadrupole Potential-Energy-Surface (PES) is presented, using mainly structural information, namely the content of the shell model space and the Pauli exclusion principle. Further microscopic properties are implicitly contained through the use of results from the Möller and Nix tables or experimental information. A mapping to the geometric potential is performed yielding the PES. The General Collective Model is used in order to obtain an estimate on the spectrum and quadrupole transitions, adjusting only the mass parameter. First, we test the conjecture on known nuclei, deriving the PES and compare them to known data. We will see that the PES approximates very well the structure expected. Having acquired a certain confidence, we predict the PES of several chain of isotopes of heavy and super-heavy nuclei and at the end we investigate the structure of nuclei in the supposed island of stability. One of the main points to show is that simple assumptions can provide already important information on the structure of nuclei outside known regions and that spectra and electromagnetic transitions can be estimated without using involved calculations and assumptions. The procedure does not allow to calculate binding energies. The method presented can be viewed as a starting point for further improvements.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2018

Two patterns of PT-symmetry breakdown in a non-numerical six-state simulation

Highlights: • Hot topic (PT symmetry breakdown in quantum theory) studied. • Next to elementary toy model considered. • Characteristic features (like quantum phase transitions) sampled. • Surprisingly, the results are non-numerical. • The method (inverse-function treatment) is brand new. - Abstract: Three-parametric family of non-Hermitian but PT-symmetric six-by-six matrix Hamiltonians H{sup (6)}(x,y,z) is considered. The PT-symmetry remains spontaneously unbroken (i.e., the spectrum of the bound-state energies remains real so that the unitary-evolution stability of the quantum system in question is shown guaranteed) in a non-empty domain D{sup (physical)} of parameters x,y,z. The construction of the exceptional-point (EP) boundary ∂D{sup (physical)} of the physical domain is preformed using an innovative non-numerical implicit-function-construction strategy. The topology of the resulting EP boundary of the spontaneous PT-symmetry breakdown (i.e., of the physical “horizon of stability”) is shown similar to its much more elementary N=4 predecessor. Again, it is shown to consist of two components, viz., of the region of the quantum phase transitions of the first kind (during which at least some of the energies become complex) and of the quantum phase transitions of the second kind (during which some of the level pairs only cross but remain real).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Absence of cosmological constant problem in special relativistic field theory of gravity

The principles of quantum field theory in flat spacetime suggest that gravity is mediated by a massless particle with helicity ±2, the so-called graviton. It is regarded as textbook knowledge that, when the self-coupling of a particle with these properties is considered, the long-wavelength structure of such a nonlinear theory is fixed to be that of general relativity. However, here we indicate that these arguments conceal an implicit assumption which is surreptitiously motivated by the very knowledge of general relativity. This is shown by providing a counterexample: we revisit a nonlinear theory of gravity which is not structurally equivalent to general relativity and that, in the non-interacting limit, describes a free helicity ±2 graviton. We explicitly prove that this theory, known as Weyl-transverse gravity (unimodular gravity with explicit Weyl invariance), can be understood as the result of self-coupling in complete parallelism to the well-known case of general relativity. We discuss the absence of cosmological constant problem in this theory, highlighting that it provides a particular realization of previous arguments formulated in studies of the emergence of the gravitational interaction from condensed-matter-like models. Overall, we conclude that the consideration that gravity is mediated by a massless particle with helicity ±2 does not inextricably lead to the cosmological constant problem.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Precipitation of calcium carbonate and calcium phosphate under diffusion controlled mixing

Multi-component mineral precipitation in porous, subsurface environments is challenging to simulate or engineer when in situ reactant mixing is controlled by diffusion. In contrast to well-mixed systems, the conditions that favor mineral precipitation in porous media are distributed along chemical gradients, which evolve spatially due to concurrent mineral precipitation and modification of solute transport in the media. The resulting physical and chemical characteristics of a mixing/precipitation zone are a consequence of coupling between transport and chemical processes, and the distinctive properties of individual chemical systems. We examined the spatial distribution of precipitates formed in “double diffusion” columns for two chemical systems, calcium carbonate and calcium phosphate. Polyacrylamide hydrogel was used as a low permeability, high porosity medium to maximize diffusive mixing and minimize pressure- and density-driven flow between reactant solutions. In the calcium phosphate system, multiple, visually dense and narrow bands of precipitates were observed that were reminiscent of previously reported Liesegang patterns. In the calcium carbonate system, wider precipitation zones characterized by more sparse distributions of precipitates and a more open channel structure were observed. In both cases, formation of precipitates inhibited, but did not necessarily eliminate, continued transport and mixing of the reactants. A reactive transport model with fully implicit coupling between diffusion, chemical speciation and precipitation kinetics, but where explicit details of nucleation processes were neglected, was able to qualitatively simulate properties of the precipitation zones. The results help to illustrate how changes in the physical properties of a precipitation zone depend on coupling between diffusion-controlled reactant mixing and chemistry-specific details of precipitation kinetics.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Comparison of exponential integrators and traditional time integration schemes for the shallow water equations

We report the time integration scheme is probably one of the most fundamental choices in the development of an ocean model. In this paper, we investigate several time integration schemes when applied to the shallow water equations. This set of equations is accurate enough for the modeling of a shallow ocean and is also relevant to study as it is the one solved for the barotropic (i.e. vertically averaged) component of a three dimensional ocean model. We analyze different time stepping algorithms for the linearized shallow water equations. High order explicit schemes are accurate but the time step is constrained by the Courant-Friedrichs-Lewy stability condition. Implicit schemes can be unconditionally stable but, in practice lack accuracy when used with large time steps. In this paper we propose a detailed comparison of such classical schemes with exponential integrators. The accuracy and the computational costs are analyzed in different configurations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

The Mycobacterium tuberculosis desaturase DesA1 (Rv0824c) is a Ca{sup 2+} binding protein

The hallmark feature of Mycobacterium tuberculosis (M.tb) the causative agent of human tuberculosis, is its complex lipid rich cell wall comprised primarily of mycolic acids, long chain fatty acids that play a key role in structural stability and permeability of the cell wall. In addition, they are involved in inhibiting phagosome-lysosome fusion and aid in granuloma formation during the pathogenic process. M.tb DesA1 is an essential acyl-acyl carrier protein desaturase predicted to catalyze the introduction of position specific double bonds during the biosynthesis of mycolic acids. This protein is one among three annotated desaturases (DesA1-3) in the M.tb genome but is unique in containing a βγ-crystallin Greek key signature motif, a well-characterized fold known to mediate Ca{sup 2+} binding in both prokaryotic and eukaryotic organisms. Using Isothermal Titration Calorimetry and {sup 45}CaCl{sub 2} overlay, we demonstrate that Ca{sup 2+} binds to DesA1. Spectroscopic measurements suggested that this binding induces changes in protein conformation but does not lead to significant alterations in the secondary structure of the protein, a feature common to several βγ-crystallins. An M. smegmatis strain over-expressing M.tb desA1 showed a Ca{sup 2+} dependent variation in surface phenotype, revealing a functional role for Ca{sup 2+}in DesA1 activity. This study represents the first identification of a Ca{sup 2+} binding βγ-crystallin in M.tb, emphasizing the implicit role of Ca{sup 2+} in the pathogenesis of M.tb. - Highlights: • Mycobacterium tuberculosis DesA1 is an essential acyl-ACP desaturase. • DesA1 was identified to contain a βγ-crystallin Greek key signature motif. • Ca{sup 2+} binds to DesA1 with an affinity of 53 μM and induces changes in its conformation. • M. smegmatis overexpressing M.tb DesA1 shows a Ca{sup 2+} dependent phenotype. • Targetting the Ca{sup 2+} dependent function of DesA1 could be of therapeutic value.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2023

Multiscale simulations reveal TDP-43 molecular-level interactions driving condensation

The RNA-binding protein TDP-43 is associated with mRNA processing and transport from the nucleus to the cytoplasm. TDP-43 localizes in the nucleus as well as accumulating in cytoplasmic condensates such as stress granules. Aggregation and formation of amyloid-like fibrils of cytoplasmic TDP-43 are hallmarks of numerous neurodegenerative diseases, most strikingly present in >90% of amyotrophic lateral sclerosis (ALS) patients. If excessive accumulation of cytoplasmic TDP-43 causes, or is caused by, neurodegeneration is presently not known. In this work, we use molecular dynamics simulations at multiple resolutions to explore TDP-43 self- and cross-interaction dynamics. A full-length molecular model of TDP-43, all 414 amino acids, was constructed from select structures of the protein functional domains (N-terminal domain, and two RNA recognition motifs, RRM1 and RRM2) and modeling of disordered connecting loops and the low complexity glycine-rich C-terminus domain. All-atom CHARMM36m simulations of single TDP-43 proteins served as guides to construct a coarse-grained Martini 3 model of TDP-43. The Martini model and a coarser implicit solvent Cα model, optimized for disordered proteins, were subsequently used to probe TDP-43 interactions; self-interactions from single-chain full-length TDP-43 simulations, cross-interactions from simulations with two proteins and simulations with assemblies of dozens to hundreds of proteins. Our findings illustrate the utility of different modeling scales for accessing TDP-43 molecular-level interactions and suggest that TDP-43 has numerous interaction preferences or patterns, exhibiting an overall strong, but dynamic, association and driving the formation of biomolecular condensates.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

An international review of occupant-related aspects of building energy codes and standards

In light of recent research, it is evident that occupants are playing an increasingly important role in building energy performance. Furthermore, despite the important role of building energy codes and standards in design, the occupant-related aspects are typically simple and have not kept up with the leading research. This paper reviews 23 regions’ building energy codes and standards by first comparing their quantitative aspects and then analyzing their mandated rules and approaches. While the present paper focuses on offices, general recommendations are applicable to other building types as well. The review revealed a wide range of occupant-related values, approaches, and attitudes. For example, code-specified occupant density varies by nearly a factor of three between different codes. This underlines the need for development of advancement in occupant behavior modeling approaches for future occupant-centric building performance codes and standards. Moreover, occupants are often referred to only implicitly; underlying expectations about energy-saving occupant behavior from building occupants varies greatly; and, only a few codes address occupant feedback and system usability. Based on the findings of the review, a set of initial recommendations for future building energy codes is proposed.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2017

Performance of fully-coupled algebraic multigrid preconditioners for large-scale VMS resistive MHD

Here, we explore the current performance and scaling of a fully-implicit stabilized unstructured finite element (FE) variational multiscale (VMS) capability for large-scale simulations of 3D incompressible resistive magnetohydrodynamics (MHD). The large-scale linear systems that are generated by a Newton nonlinear solver approach are iteratively solved by preconditioned Krylov subspace methods. The efficiency of this approach is critically dependent on the scalability and performance of the algebraic multigrid preconditioner. Our study considers the performance of the numerical methods as recently implemented in the second-generation Trilinos implementation that is 64-bit compliant and is not limited by the 32-bit global identifiers of the original Epetra-based Trilinos. The study presents representative results for a Poisson problem on 1.6 million cores of an IBM Blue Gene/Q platform to demonstrate very large-scale parallel execution. Additionally, results for a more challenging steady-state MHD generator and a transient solution of a benchmark MHD turbulence calculation for the full resistive MHD system are also presented. These results are obtained on up to 131,000 cores of a Cray XC40 and one million cores of a BG/Q system.

97 MATHEMATICS AND COMPUTING↗