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Amesh generates discretized grids for numerical modeling of flow and transport problems in which the formulation is based on the integral finite difference method (IFDM). For example, the output of Amesh can be used directly as input to the TOUGH2 or TOUGH3 numerical simulators. Amesh can generate 1D, 2D, or 3D numerical grids for a given set of locations, i.e., the centers of each discrete sub-domain. In the 2D areal plane Voronoi tessellation is used.
Calibr8 provides an application to rapidly prototype and perform material model calibration for complex plasticity models using advanced adjoint or forward sensitivity analyses for execution on massively parallel machines. These techniques can be orders of magnitude faster than traditional finite difference approaches for material model calibration. The underlying technology used in Calibr8 is automatic differentiation, which allows for the rapid implementation and testing of new plasticity models within its framework. Additionally, Calibr8 can perform adjoint-based error estimation to approximate discretization errors for user-implemented plasticity models. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. SAND2021-10630 O
Code for my PhD thesis that creates meshes using gmsh and code I wrote to create high-order hybrid meshes to use for testing a hybrid method between spectral element method and generalized finite differences. It also uses a tetrahedral mesh improvement method called "stellar" to improve mesh quality near a curved boundary.
TReactMech couples geomechanical processes (poroelasticity, failure, and inelastic strain) with multiphase nonisothermal flow (derived from TOUGH2) and reactive geochemical transport. At its core is the reactive-transport code TOUGHREACT v4.13. TReactMech is an efficient hybrid parallel simulator, solving the geomechanics using finite elements and MPI/PetSc, the multiphase flow using integrated finite difference and MPI/PETSc, and the reactive chemistry using OpenMP. The advantages of TReactMech are in its multiphase flow capabilities (e.g., supercritical CO2, supercritical water, air) and parallel geomechanics including full 3-D stress tensor, shear and tensile failure, coupled to porosity and permeability changes. It is backwardly compatible with TOUGH2 and TOUGHREACT v4.13, allowing for easier transitions between the codes. TReactMech can be used to simulate many natural and engineered subsurface systems, including geothermal reservoirs, borehole heat exchangers, geologic carbon sequestration, geologic storage of nuclear waste, groundwater resources, weathering, sediment diagenesis, seafloor hydrothermal circulation, hydrofracturing in unconventional reservoirs, and injection/production-induced surface deformation.
APBuilder is a software tool designed to generate atmospheric profiles for use with AC2Dr by downloading weather model data and transforming it into 1D or 2D binary profiles. These binary profiles serve as required inputs for AC2Dr, an LLNL-developed, open source, two-dimensional numerical solver for the acoustic wave equation based on the finite difference method.
Seismic-H2 is an integrated software package for geological hydrogen reservoir simulation, optimization, and leakage monitoring. The package includes multiple components: (1) code used for modeling seismic wave propagation in 3D heterogeneous elastic media based on finite-difference method to support detection of geological hydrogen storage reservoir leakage; (2) 3D reservoir simulations of leaks from an underground reservoir and 3D simulations of saline aquifers and depleted gas reservoirs; (3) seismic monitoring costs of passive and active seismic monitoring required for UHS; (4) rock physics calculations and interpolations for converting the reservoir simulations from part (2) into the elastic media models in part (1); (5) pre-processing seismic data; and lastly (6), a GUI interface that combines these different components.
SAND2025-14430O Hydrogen Diffusion Through Stainless Steel is a tool that employs a finite difference method algorithm to solve Fick's law and other mass transport models pertinent to the diffusion of hydrogen through stainless steel. Additionally, the software uses particle swarm optimization to determine physical parameters based on experimental data. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.
PIAFS is a finite-difference code to solve the compressible Navier-Stokes equations with chemical heating on Cartesian grids. It models chemical reactions of air (oxygen and carbon dioxide) with ozone subject to radiation. It uses a high-order WENO spatial discretization and explicit Runge-Kutta time integration. It is capable of parallel simulations using MPI. The code is written in C/C++.
Abstract We present a data assimilation package for use with ocean circulation models in analysis, forecasting, and system evaluation applications. The basic functionality of the package is centered on a multivariate linear statistical estimation for a given predicted/background ocean state, observations, and error statistics. Novel features of the package include support for multiple covariance models, and the solution of the least squares normal equations either using the covariance matrix or its inverse—the information matrix. The main focus of this paper, however, is on the solution of the analysis equations using the information matrix, which offers several advantages for solving large problems efficiently. Details of the parameterization of the inverse covariance using Markov random fields are provided and its relationship to finite-difference discretizations of diffusion equations are pointed out. The package can assimilate a variety of observation types from both remote sensing and in situ platforms. The performance of the data assimilation methodology implemented in the package is demonstrated with a yearlong global ocean hindcast with a 1/4° ocean model. The code is implemented in modern Fortran, supports distributed memory, shared memory, multicore architectures, and uses climate and forecasts compliant Network Common Data Form for input/output. The package is freely available with an open source license from www.tendral.com/tsis/ .
Abstract Observations of thermodynamic and kinematic parameters associated with derivatives of the thermodynamics and wind fields, namely, advection, vorticity, divergence, and deformation, can be obtained by applying Green’s theorem to a network of observing sites. The five nodes that comprise the Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) profiling network, spaced 50–80 km apart, are used to obtain measurements of these parameters over a finite region. To demonstrate the applicability of this technique at this location, it is first applied to gridded model output from the High-Resolution Rapid Refresh (HRRR) numerical weather prediction model, using profiles from the locations of ARM network sites, so that values calculated from this method can be directly compared to finite difference calculations. Good agreement is found between both approaches as well as between the model and values calculated from the observations. Uncertainties for the observations are obtained via a Monte Carlo process in which the profiles are randomly perturbed in accordance with their known error characteristics. The existing size of the ARM network is well suited to capturing these parameters, with strong correlations to model values and smaller uncertainties than a more closely spaced network, yet it is small enough that it avoids the tendency for advection to go to zero over a large area.
We present a high-performance coupled electrodynamics–micromagnetics solver for full physical modeling of signals in microelectronic circuitry. The overall strategy couples a finite-difference time-domain approach for Maxwell’s equations to a magnetization model described by the Landau–Lifshitz–Gilbert equation. The algorithm is implemented in the Exascale Computing Project software framework, AMReX, which provides effective scalability on manycore and GPU-based supercomputing architectures. Furthermore, the code leverages ongoing developments of the Exascale Application Code, WarpX, which is primarily being developed for plasma wakefield accelerator modeling. Our temporal coupling scheme provides second-order accuracy in space and time by combining the integration steps for the magnetic field and magnetization into an iterative sub-step that includes a trapezoidal temporal discretization for the magnetization. The performance of the algorithm is demonstrated by the excellent scaling results on NERSC multicore and GPU systems, with a significant (59×) speedup on the GPU using a node-by-node comparison. We demonstrate the utility of our code by performing simulations of an electromagnetic waveguide and a magnetically tunable filter.
HPC trends favor algorithms and implementations that reduce data motion relative to FLOPS. We investigate the use of lossy compressed data arrays in place of traditional IEEE floating point arrays to store the primary data of calculations. Simulation is fundamentally an exercise in controlled approximation, and error introduced by finite-precision arithmetic (or lossy compression) is just one of several sources of error that need to be managed to ensure sufficient accuracy in a computed result. We describe ZFP, a compressed numerical format designed for in-memory storage of multidimensional arrays, and summarize theoretical results that demonstrate that the error of repeated lossy compression can be bounded and controlled. Furthermore, we establish a relationship between grid resolution and compression-induced errors and show that, contrary to conventional floating point, ZFP reduces finite-difference errors with finer grids. We present example calculations that demonstrate data reduction by 4x or more with negligible impact on solution accuracy. Our results further demonstrate several orders-of-magnitude increase in accuracy using ZFP over IEEE floating point and Posits for the same storage budget.
The complex Ginzburg-Landau equation with additive noise is a stochastic partial differential equation that describes a remarkably wide range of physical systems which include coupled non-linear oscillators subject to external noise near a Hopf bifurcation instability and spontaneous structure formation in non-equilibrium systems, e.g., in cyclically competing populations or oscillatory chemical reactions. Here, we employ a finite-difference method to numerically solve the noisy complex Ginzburg-Landau equation on a two-dimensional domain with the goal to investigate its non-equilibrium dynamics when the system is quenched into the “defocusing spiral quadrant”. We observe slow coarsening dynamics as oppositely charged topological defects annihilate each other, and characterize the ensuing aging scaling behavior. We conclude that the physical aging features in this system are governed by non-universal aging scaling exponents. We also investigate systems with control parameters residing in the “focusing quadrant”, and identify slow aging kinetics in that regime as well. Finally, we provide heuristic criteria for the existence of slow coarsening dynamics and physical aging behavior in the complex Ginzburg-Landau equation.
The fluoride-salt-cooled high-temperature reactor (FHR) is one type of the advanced reactors and has been attracting great interest from the research institutes and commercial companies in the recent years. However, currently the technology is relatively immature. To facilitate the design and safety analysis of FHRs, Kairos Power published the generic FHR (gFHR) benchmark. In this paper, a hybrid method combining the stochastic code and deterministic code is developed to simulate the gFHR benchmark. Serpent 2 is employed as a few-group cross section generator and the cross sections are applied to the finite difference neutron diffusion code AGREE. A good consistency with the gFHR benchmark is achieved. The agreement between the Serpent 2 results and the AGREE results shows that the hybrid method is applicable to FHRs. The thermal-hydraulics are coupled to neutronics for the steady-state calculations and good agreement between AGREE and SAM is achieved. (authors)
Laser damage of optical components can be a limiting factor in scaling the energetics of high-peak and average power laser systems. Specifically for optical coatings, damage under nanosecond pulsed irradiation is initiated by pre-existing defects in the coating layers, including those that cause discontinuities in the structure, like craze lines. Crazing or cracking in a multilayer dielectric optical coating is induced when the overall coating stress is sufficiently tensile, and is an occasionally observed issue when employing more porous deposition techniques like electron-beam evaporation. Here, in this study, electron-beam high-reflectors were fabricated utilizing process parameters that are known to induce crazing based on prior processing history to systematically evaluate the impact of crazing on reflector damage performance for 1064 and 355 nm lasers. The crazing that was observed was apparently nucleated at nodular defects. When the cross-section of these nodules was investigated, it was observed that there were cracks into the fused silica substrate of approximately 5 µm in depth. The craze lines were irradiated with 1064 and 355 nm light at fluences slightly above the onset of damage initiation fluence of the coating. The 1064 nm irradiated sub-apertures exhibit laser damage but with no spatial correlation with the craze line, whereas the 355 nm irradiated area exhibited many damage sites along the craze line. Finite-difference time-domain electric-field simulations were conducted, and ∼2× field amplification in hafnia was observed for the 355 nm wavelength case. The laser damage can be attributed to a slight electric-field intensification coincidental with an area where UV damage-prone precursors are known to occur. The 355 nm laser damage in uncoated fused silica substrates has been previously correlated to initiate through localized UV absorption at the broken silica bonds in the tips of fractures.
Recently, our groups have introduced the notion of optical parametric amplification based on non-Hermitian phase matching wherein the incorporation of loss can lead to gain in this nonlinear optical process. Previous simulation results using second-order nonlinear optical coupled-mode theory have demonstrated the potential of this technique as an alternative to the stringent phase-matching condition, which is often difficult to achieve in semiconductor platforms. Here we fortify this notion for the case of third-order nonlinearity by considering parametric amplification in silicon nanowires and illustrate the feasibility of these devices by employing rigorous finite-difference time-domain analysis using realistic materials and geometric parameters. Particularly, we demonstrate that by systematic control of the optical loss of the idler in a four-wave mixing process, we can achieve efficient unidirectional energy conversion from the pump to the signal component even when the typical phase-matching condition is violated. Importantly, our simulations show that a signal gain of ∼ <#comment/> 9 d B for a waveguide length of a few millimeters is possible over a large bandwidth of several hundreds of nanometers ( ∼ <#comment/> 600 n m ). This bandwidth is nearly 2 orders of magnitude larger than what can be achieved in the conventional silicon-photonics-based four-wave mixing process.
Metalenses are composed of nanostructures for focusing light and have been widely explored in many exciting applications. However, their expanding dimensions pose simulation challenges. We propose a method to simulate metalenses in a timely manner using vectorial wave and ray tracing models. We sample the metalens’s radial phase gradient and locally approximate the phase profile by a linear phase response. Each sampling point is modeled as a binary blazed grating, employing the chosen nanostructure, to build a transfer function set. The metalens transmission or reflection is then obtained by applying the corresponding transfer function to the incoming field on the regions surrounding each sampling point. Fourier optics is used to calculate the scattered fields under arbitrary illumination for the vectorial wave method, and a Monte Carlo algorithm is used in the ray tracing formalism. We validated our method against finite-difference time domain simulations at 632 nm, and we were able to simulate metalenses larger than 3000 wavelengths in diameter on a personal computer.
High peak and average power lasers with high wall-plug efficiency, like the Big Aperture Thulium (BAT) laser, have garnered tremendous attention in laser technology. To meet the requirements of the BAT laser, we have developed low-dispersion reflection multilayer dielectric (MLD) gratings suitable for compression of high-energy pulses for operations at 2 micron wavelength. We carried out 10000-on-1 damage tests to investigate the fluence damage thresholds of the designed MLD gratings and mirrors, which were found between 100-230 mJ/cm 2 . An ultrashort pulsed laser (FWHM = 53 fs, λ = 1.9 μ m) operating at 500 Hz was used in the serpentine raster scans. The atomic force microscope images of the damage sites show blister formation of the underlying layers at lower fluences but ablation of the grating pillars at higher fluences. We simulated the dynamic electronic excitation in the MLD optics with a finite-difference in the time domain approach in 2D. The simulation results agree well with the LIDT measurements and the observed blister formation. This model is able to evaluate the absolute LIDT of MLD gratings.