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Results for “explicit and implicit methods”

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DOE OSTI2016

A NUMERICAL SCHEME FOR SPECIAL RELATIVISTIC RADIATION MAGNETOHYDRODYNAMICS BASED ON SOLVING THE TIME-DEPENDENT RADIATIVE TRANSFER EQUATION

We develop a numerical scheme for solving the equations of fully special relativistic, radiation magnetohydrodynamics (MHDs), in which the frequency-integrated, time-dependent radiation transfer equation is solved to calculate the specific intensity. The radiation energy density, the radiation flux, and the radiation stress tensor are obtained by the angular quadrature of the intensity. In the present method, conservation of total mass, momentum, and energy of the radiation magnetofluids is guaranteed. We treat not only the isotropic scattering but also the Thomson scattering. The numerical method of MHDs is the same as that of our previous work. The advection terms are explicitly solved, and the source terms, which describe the gas–radiation interaction, are implicitly integrated. Our code is suitable for massive parallel computing. We present that our code shows reasonable results in some numerical tests for propagating radiation and radiation hydrodynamics. Particularly, the correct solution is given even in the optically very thin or moderately thin regimes, and the special relativistic effects are nicely reproduced.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2018

A Comprehensive Comparison of Relativistic Particle Integrators

We compare relativistic particle integrators commonly used in plasma physics, showing several test cases relevant for astrophysics. Three explicit particle pushers are considered, namely, the Boris, Vay, and Higuera–Cary schemes. We also present a new relativistic fully implicit particle integrator that is energy conserving. Furthermore, a method based on the relativistic guiding center approximation is included. The algorithms are described such that they can be readily implemented in magnetohydrodynamics codes or Particle-in-Cell codes. Here, our comparison focuses on the strengths and key features of the particle integrators. We test the conservation of invariants of motion and the accuracy of particle drift dynamics in highly relativistic, mildly relativistic, and non-relativistic settings. The methods are compared in idealized test cases, i.e., without considering feedback onto the electrodynamic fields, collisions, pair creation, or radiation. The test cases include uniform electric and magnetic fields, ${\boldsymbol{E}}\times {\boldsymbol{B}}$ fields, force-free fields, and setups relevant for high-energy astrophysics, e.g., a magnetic mirror, a magnetic dipole, and a magnetic null. These tests have direct relevance for particle acceleration in shocks and in magnetic reconnection.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

A continuous surface reconstruction method on point cloud captured from a 3D surface photogrammetry system

Purpose: To accurately and efficiently reconstruct a continuous surface from noisy point clouds captured by a surface photogrammetry system (VisionRT). Methods: The authors have developed a level-set based surface reconstruction method on point clouds captured by a surface photogrammetry system (VisionRT). The proposed method reconstructs an implicit and continuous representation of the underlying patient surface by optimizing a regularized fitting energy, offering extra robustness to noise and missing measurements. By contrast to explicit/discrete meshing-type schemes, their continuous representation is particularly advantageous for subsequent surface registration and motion tracking by eliminating the need for maintaining explicit point correspondences as in discrete models. The authors solve the proposed method with an efficient narrowband evolving scheme. The authors evaluated the proposed method on both phantom and human subject data with two sets of complementary experiments. In the first set of experiment, the authors generated a series of surfaces each with different black patches placed on one chest phantom. The resulting VisionRT measurements from the patched area had different degree of noise and missing levels, since VisionRT has difficulties in detecting dark surfaces. The authors applied the proposed method to point clouds acquired under these different configurations, and quantitatively evaluated reconstructed surfaces by comparing against a high-quality reference surface with respect to root mean squared error (RMSE). In the second set of experiment, the authors applied their method to 100 clinical point clouds acquired from one human subject. In the absence of ground-truth, the authors qualitatively validated reconstructed surfaces by comparing the local geometry, specifically mean curvature distributions, against that of the surface extracted from a high-quality CT obtained from the same patient. Results: On phantom point clouds, their method achieved submillimeter reconstruction RMSE under different configurations, demonstrating quantitatively the faith of the proposed method in preserving local structural properties of the underlying surface in the presence of noise and missing measurements, and its robustness toward variations of such characteristics. On point clouds from the human subject, the proposed method successfully reconstructed all patient surfaces, filling regions where raw point coordinate readings were missing. Within two comparable regions of interest in the chest area, similar mean curvature distributions were acquired from both their reconstructed surface and CT surface, with mean and standard deviation of (μ{sub recon} = − 2.7 × 10{sup −3} mm{sup −1}, σ{sub recon} = 7.0 × 10{sup −3} mm{sup −1}) and (μ{sub CT} = − 2.5 × 10{sup −3} mm{sup −1}, σ{sub CT} = 5.3 × 10{sup −3} mm{sup −1}), respectively. The agreement of local geometry properties between the reconstructed surfaces and the CT surface demonstrated the ability of the proposed method in faithfully representing the underlying patient surface. Conclusions: The authors have integrated and developed an accurate level-set based continuous surface reconstruction method on point clouds acquired by a 3D surface photogrammetry system. The proposed method has generated a continuous representation of the underlying phantom and patient surfaces with good robustness against noise and missing measurements. It serves as an important first step for further development of motion tracking methods during radiotherapy.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2017

Extreme Scale Unstructured Adaptive CFD: From Multiphase Flow to Aerodynamic Flow Control

Understanding the flow of fluid, either liquid or gas, through and around solid bodies has challenged man since the dawn of scientific inquiry. Many of the great minds of science and math have progressively built up a hierarchy of fluid models. This report is concerned with the computational modeling of turbulent flow around aerodynamic bodies such as planes and wind turbines. In this case, viscous effects near the solid bodies create very thin boundary layers that yield highly anisotropic (gradients normal to the surface may be 10^6 times larger than gradients along the surface) solutions to the governing non-linear partial differential equations (PDE); the Navier-Stokes equations. Furthermore, turbulent flows develop extremely broad ranges of length and time scales.This disparity motivates the use of discretization methods capable of employing adaptivity and implicit time integration. The combination of these features (non-linear, anisotropy, adaptivity, andimplicit) dramatically raise the complexity of the discretization, posing large challenges to efficient scalable parallel implementation. However, through careful design, the more complex algorithms can provide great reductions in computational cost relative to simpler methods (e.g., Cartesian grids with explicit time integration) that are easier to mate efficiently to hardware. In this report, we not only describe our approach but we also address the fact that while complex algorithms may never be as efficient flop-for-flop as simple methods, in the important measure of science-per-core-hour, they can still win big by making complex features like adaptivity and implicit methods as efficient and scalable as possible.

42 ENGINEERING↗

DOE OSTI2018

Performance analysis and implementation details of the Energy Conserving Semi-Implicit Method code (ECsim)

We present in this work the implementation of the Energy Conserving Semi-Implicit Method in a parallel code called ECsim. This new code is a three-dimensional, fully electromagnetic particle in cell (PIC) code. It is written in C/C++ and uses MPI to allow massive parallelization. ECsim is unconditionally stable in time, eliminates the finite grid instability, and has the same cycle scheme as the explicit code with a computational cost comparable to other semi-implicit PIC codes. All these features make it a very valuable tool to address situations which have not been possible to analyze until now with other PIC codes. In this work, we show the details of the algorithm implementation and we study its performance in different systems. ECsim is compared with another semi-implicit PIC code with different time and spectral resolution, showing its ability to address situations where other codes fail.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Potential improvements in brain dose estimates for internal emitters

Background: Element-specific biokinetic models are used to reconstruct doses to systemic tissues from internal emitters. Typically, a systemic model for a radionuclide explicitly depicts only its dominant repositories. Remaining tissues and fluids are aggregated into a pool called Other tissue in which the radionuclide is assumed to be uniformly distributed. In the systemic biokinetic models used in radiation protection, the brain usually is addressed as an implicit mass fraction of Other tissue rather than an explicitly depicted repository. Additionally, due to increasing interest in radiation effects on the brain, efforts are underway to improve brain dosimetry for internal radiation sources. Methods: We assessed potential improvements in brain dosimetry for internal emitters by explicitly modelling brain kinetics rather than treating the brain as a mass fraction of Other tissue. We selected ten elements for which brain kinetics can be modeled using published biokinetic data. Injection dose coefficients were calculated for a relatively long-lived radioisotope of each element using each of two versions of the ICRP’s latest systemic biokinetic model for each element, the original version and a modified version differing only in the treatment of brain. If the ICRP model contained an explicit brain pool, the modified version depicted brain instead as a mass fraction of Other tissue. If the ICRP model included brain in Other tissue, the modified version included an explicit brain pool with kinetics based on best available brain-specific data.Results: The result for a given radionuclide is expressed as a ratio A:B, where A and B are the dose coefficients based on the versions of the model with and without an explicit brain pool, respectively. The following ratios A:B were obtained for the 10 radionuclides addressed here: 241 Am, 0.13; 207 Bi, 0.57; 234 U, 0.81; 239 Pu, 0.96; 203 Hg (vapor), 1.4; 134 Cs, 1.5; 54 Mn, 1.7; 210 Po, 1.7; 226 Ra, 1.9; 210 Pb, 3.3. These ratios indicate that a dose estimate for brain based on a biokinetic model with brain implicitly contained in Other tissue may substantially underestimate or substantially overestimate a dose estimate that reflects best available brain-specific biokinetic data. Of course, the reliability of the latter estimate depends on the quality of the underlying biokinetic data.Conclusions: Finally, where feasible, the brain should be depicted explicitly in biokinetic models used in epidemiological studies addressing adverse effects of ionizing radiation.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

Data-driven linear time advance operators for the acceleration of plasma physics simulation

In this study, we demonstrate the application of data-driven linear operator construction for time advance with a goal of accelerating plasma physics simulation. We apply dynamic mode decomposition (DMD) to data produced by the nonlinear SOLPS-ITER (Scrape-off Layer Plasma Simulator - International Thermonuclear Experimental Reactor) plasma boundary code suite in order to estimate a series of linear operators and monitor their predictive accuracy via online error analysis. We find that this approach defines when these dynamics can be represented by a sequence of approximate linear operators and is essential for providing consistent projections when compared to an unconstrained application. For linear diffusion and advection–diffusion fluid test problems, we construct and apply operators within explicit and implicit time advance schemes, demonstrating that stability can be robustly guaranteed in each case. We further investigate the use of the linear time advance operators within several integration methods including forward Euler, backward Euler, and the matrix exponential. The application of this method to simulation data from SOLPS-ITER, with varying levels of Markov chain Monte Carlo numerical noise, shows that constrained DMD operators yield a capability to identify, extract, and integrate a (slow) subset of the present timescales. Example applications show that for projected speedup factors of [Formula: see text], and [Formula: see text], a mean relative error of 3%, 5%, and 8% and maximum relative error less than 20% are achievable, which appears acceptable for typical SOLPS-ITER steady-state simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Semi-implicit continuum kinetic modeling of weakly collisional parallel transport in a magnetic mirror

We present implicit-explicit (IMEX) kinetic simulations of weakly collisional parallel plasma transport in magnetic mirror configurations using the continuum code COGENT. The numerical scheme employs a Jacobian-free Newton–Krylov method with algebraic multigrid preconditioning to overcome the severe time step limitations imposed by strong mirror forces in fully explicit schemes. Applied to parameters relevant to the Wisconsin HTS Axisymmetric Mirror experiment, the IMEX approach enables time steps up to 2.5×10 4 times larger than those permitted by explicit methods, resulting in a 2500× speedup in 1D–2V simulations of parallel transport with kinetic ions and Boltzmann electrons. Additionally, a reduced bounce-averaged model for a square mirror is implemented to support the computationally intensive fully kinetic simulations. The bounce-averaged formulation is used to evaluate the numerical convergence of the velocity-space discretization algorithms and to assess the role of the collision model by comparing simulations employing the nonlinear Fokker–Planck and the simplified Lenard–Bernstein–Dougherty collision operators.

Collision theories↗

DOE OSTI2021

Buffered freepointer management memory system

A system and method of buffered freepointer management to handle burst traffic to fixed size structures in an external memory system. A circular queue stores implicitly linked free memory locations, along with an explicitly linked list in memory. The queue is updated at the head with newly released locations, and new locations from memory are added at the tail. When a freed location in the queue is reused, external memory need not be updated. When the queue is full, the system attempts to release some of the freepointers such as by dropping them if they are already linked, updating the linked list in memory only if those dropped are not already linked. Latency can be further reduced by loading new locations from memory when the queue is nearly empty, rather than waiting for empty condition, and by writing unlinked locations to memory when the queue is nearly full.

Jacob, Philip↗

DOE OSTI2024

Improving ADAM through an implicit-explicit (IMEX) time-stepping approach

The ADAM optimizer, often used in machine learning for neural network training, corresponds to an underlying ordinary differential equation (ODE) in the limit of very small learning rates. Here, this work shows that the classical ADAM algorithm is a first-order implicit-explicit (IMEX) Euler discretization of the underlying ODE. Employing the time discretization point of view, we propose new extensions of the ADAM scheme obtained by using higher-order IMEX methods to solve the ODE. Based on this approach, we derive a new optimization algorithm for neural network training that performs better than classical ADAM on several regression and classification problems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

A framework to evaluate IMEX schemes for atmospheric models

We present a new evaluation framework for implicit and explicit (IMEX) Runge–Kutta time-stepping schemes. The new framework uses a linearized nonhydrostatic system of normal modes. We utilize the framework to investigate the stability of IMEX methods and their dispersion and dissipation of gravity, Rossby, and acoustic waves. We test the new framework on a variety of IMEX schemes and use it to develop and analyze a set of second-order low-storage IMEX Runge–Kutta methods with a high Courant–Friedrichs–Lewy (CFL) number. We show that the new framework is more selective than the 2-D acoustic system previously used in the literature. Schemes that are stable for the 2-D acoustic system are not stable for the system of normal modes.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Verification of a fully implicit particle-in-cell method for the  v ∥ -formalism of electromagnetic gyrokinetics in the XGC code

A fully implicit particle-in-cell method for handling the v ∥ -formalism of electromagnetic gyrokinetics has been implemented in XGC. By choosing the v ∥ -formalism, here we avoid introducing the nonphysical skin terms in Ampère's law, which are responsible for the well-known “cancellation problem” in the p ∥ -formalism. The v ∥ -formalism, however, is known to suffer from a numerical instability when explicit time integration schemes are used due to the appearance of a time derivative in the particle equations of motion from the inductive component of the electric field. Here, using the conventional δf scheme, we demonstrate that our implicitly discretized algorithm can provide numerically stable simulation results with accurate dispersive properties. We verify the algorithm using a test case for shear Alfvén wave propagation in addition to a case demonstrating the ion temperature gradient-kinetic ballooning mode (ITG-KBM) transition. The ITG-KBM transition case is compared to results obtained from other δf gyrokinetic codes/schemes, whose verification has already been archived in the literature.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Development of an implicit electromagnetic capability for a hybrid gyrokinetic ion-fluid electron model

Here we report on the development and implementation of a hybrid kinetic ion–fluid electron model for electromagnetic COGENT simulations of edge plasmas. COGENT is a finite-volume gyrokinetic code that employs a locally field-aligned coordinate system combined with a mapped multi-block grid technology to handle strongly anisotropic edge plasma turbulence. The simulation model involves the long-wavelength limit of the ion gyrokinetic equation coupled to the vorticity and Ohm's law equations for the electromagnetic field perturbations. In order to handle the fast Alfvén wave time scales, an implicit-explicit time integration approach with a physics-based preconditioner is used. The model is successfully applied to the simulations of ion-scale resistive-drift ballooning turbulence in a toroidal annulus geometry. Substantial speed-up over a fully explicit time integration approach is observed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2017

Extension of the noise propagation matrix method for higher mode solutions

The noise propagation matrix method (NPMM) has been extended to get higher mode solutions. Previous studies show that the NPMM can be used to compute the dominance ratio of a system. It is essentially the same as the Coarse Mesh Projection Method (CMPM), both of which use the noise propagation matrix (NPM) to determine the dominance ratio, either after finishing the Monte Carlo simulation or on-the-fly during the simulation. Since only the fundamental fission source information is explicitly utilized while the higher mode information is implicitly contained in the statistical noises, the NPMM can usually only give an approximate estimation of the dominance ratio after thousands of cycles. In this study, the NPMM is extended by simulating the higher modes explicitly, so that the dominance ratio estimation can be more accurate and efficient. Besides, the higher mode solutions can be obtained at the same time with good accuracy and efficiency.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

Multi-scale simulation of reaction, transport and deactivation in a SBA-16 supported catalyst for the conversion of ethanol to butadiene

Effective design of heterogeneous catalytic systems requires careful coordination of physiochemical phenomena that span orders or magnitude in length and time scales. Multiscale modelling and simulation tools can provide useful insight for understanding and improving the performance of such systems. Mesoporous silica catalyst support materials present a versatile platform wherein support attributes may be tuned to control transport phenomena throughout the system. In this study we develop an integrated multiscale modelling approach for the conversion of ethanol to butadiene over a SBA-16 mesoporous silica supported catalyst. We use molecular dynamics simulations to calculate domain specific diffusivities of reactants and products in the various domains of SBA-16's nanostructure. This is used to calculate a resultant effective diffusivity through its microstructure using finite element method (FEM) models of the tessellated unit cell. The resultant intraparticle effective diffusivity enables the development of a reduced-order reactor level FEM model that is able to implicitly account for the SBA-16's transport effects without the explicit consideration of its detailed geometry. Experimental bench-scale conversion data for the ethanol to butadiene process over SBA-16 is used to extract intrinsic kinetic rate constants for a simplified reaction mechanism using this reduced order bench-scale reactor FEM model. The model is able to reproduce experimental trends in conversion and activity lifetimes. The impact of varying key support attributes such as pore-size and particle size on catalytic activity lifetimes is then explored. We demonstrate the utility of this multi-scale modelling strategy in guiding catalyst design for the development of rational strategies to improve the performance of heterogeneous supported catalytic systems.

09 BIOMASS FUELS↗

DOE OSTI2020

Time-stepping DPG formulations for the heat equation

For a wide range of PDEs, the discontinuous Petrov–Galerkin (DPG) methodology of Demkowicz and Gopalakrishnan provides discrete stability starting from a coarse mesh and minimization of the residual in a user-controlled norm, among other appealing features. Research on DPG for transient problems has mainly focused on spacetime discretizations, which has theoretical advantages, but practical costs for computations and software implementations. The sole examination of time-stepping DPG formulations was performed by Führer, Heuer, and Gupta, who applied Rothe’s method to an ultraweak formulation of the heat equation to develop an implicit time-stepping scheme; their work emphasized theoretical results, including error estimates in time and space. Here, we follow Führer, Heuer, and Gupta in examining the heat equation; our focus is on numerical experiments, examining the stability and accuracy of several formulations, including primal as well as ultraweak, and explicit as well as implicit and Crank–Nicolson time-stepping schemes. We are additionally interested in communication-avoiding algorithms, and we therefore include a highly experimental formulation that places all the trace terms on the right-hand side of the equation.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Effect of slip on vortex shedding from a circular cylinder in a gas flow

Most studies of vortex shedding from a circular cylinder in a gas flow have explicitly or implicitly assumed that the no-slip condition applies on the cylinder surface. To investigate the effect of slip, vortex shedding is simulated using molecular gas dynamics (the direct simulation Monte Carlo method) and computational fluid dynamics (the incompressible Navier-Stokes equations with a slip boundary condition). A Reynolds number of 100, a Mach number of 0.3, and a corresponding Knudsen number of 0.0048 are examined. For these conditions, compressibility effects are small, and periodic laminar vortex shedding is obtained. Slip on the cylinder is varied using combinations of diffuse and specular molecular reflections with accommodation coefficients from zero (maximum slip) to unity (minimum slip). Although unrealistic, bounce-back molecular reflections are also examined because they approximate the no-slip boundary condition (zero slip). The results from both methods are in reasonable agreement. The shedding frequency increases slightly as the accommodation coefficient is decreased, and shedding ceases at low accommodation coefficients (large slip). The streamwise and transverse forces decrease as the accommodation coefficient is decreased. Based on the good agreement between the two methods, computational fluid dynamics is used to determine the critical accommodation coefficient below which vortex shedding ceases for Reynolds numbers of 60–100 at a Mach number of 0.3. Finally, conditions to observe the effect of slip on vortex shedding appear to be experimentally realizable, although challenging.

42 ENGINEERING↗

DOE OSTI2014

SU-D-16A-07: Photobleaching Predicts Necrosis in Interstitial PDT

Purpose: Dosimetry for PDT has proven to be a challenge thus far, and for prediction of PDT outcome, a singlet oxygen model based on fundamental photophysical parameters has been developed. Previously, the photobleaching effect of photosensitizers was taken into account in the singlet oxygen explicit dosimetry model; here we report of direct measurements of photobleaching in the same model to assess the conditions under which implicit dosimetry using photobleaching can serve as an intermediate surrogate for PDT damage. Methods: Fluorescence spectra were measured interstitially in sensitized mouse tumors prior to after irradiation via a cylindrical diffuser. Photobleaching was determined by the relative decrease in fluorescence amplitude from the initial pre-treatment measurement. Spectra were analyzed by singular value decomposition to determine the photosensitizer concentration. Different photosensitizers were used to see the effect of photobleaching on PDT outcome and the impact of fluence on photobleaching. The drugs used were BPD (at two drug-light intervals), HPPH, and Photofrin. PDT outcome was determined by tumor necrosis radii measured upon sectioning and staining of treated tumors. Results: Post-PDT photosentizer concentrations were compared to initial pre-PDT photosensitizer concentrations, and the decrease was greater with a higher fluence measured during treatment. Furthermore, photobleaching and necrosis radius were found to be positively correlated. The relationship between photobleaching and necrosis radius is sensitizer-dependent, however the differences among sensitizers can be understood in terms of their respective photophysical parameters. Conclusions: Photobleaching is predictive of PDT outcome, but a comprehensive singlet oxygen model, has the potential to further improve the prediction of PDT outcome and the understanding of implicit dosimetry.

60 APPLIED LIFE SCIENCES↗