Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “iterative solvers”

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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Parallel-in-Time Solution of Scalar Nonlinear Conservation Laws

Here, we consider the parallel-in-time solution of scalar nonlinear conservation laws in one spatial dimension. The equations are discretized in space with a conservative finite-volume method using weighted essentially nonoscillatory (WENO) reconstructions, and in time with high-order explicit Runge–Kutta methods. The solution of the global, discretized space-time problem is sought via a nonlinear iteration that uses a novel linearization strategy in cases of nondifferentiable equations. Under certain choices of discretization and algorithmic parameters, the nonlinear iteration coincides with Newton’s method, although, more generally, it is a preconditioned residual correction scheme. At each nonlinear iteration, the linearized problem takes the form of a certain discretization of a linear conservation law over the space-time domain in question. An approximate parallel-in-time solution of the linearized problem is computed with a single multigrid reduction-in-time (MGRIT) iteration; however, any other effective parallel-in-time method could be used in its place. The MGRIT iteration employs a novel coarse-grid operator that is a modified conservative semi-Lagrangian discretization and generalizes those we have developed previously for nonconservative scalar linear hyperbolic problems. Numerical tests are performed for the inviscid Burgers and Buckley–Leverett equations. For many test problems, the solver converges in just a handful of iterations with a convergence rate independent of mesh resolution, including problems with (interacting) shocks and rarefactions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Scaled ILU Smoothers for Navier-Stokes Pressure Projection

Incomplete LU (ILU) smoothers are effective in the algebraic multigrid (AMG) V-cycle for reducing high-frequency components of the error. However, the requisite direct triangular solves are comparatively slow on GPUs. Previous work has demonstrated the advantages of Jacobi iteration as an alternative to direct solution of these systems. Depending on the threshold and fill-level parameters chosen, the factors can be highly nonnormal and Jacobi is unlikely to converge in a low number of iterations. We demonstrate that row scaling can reduce the departure from normality, allowing us to replace the inherently sequential solve with a rapidly converging Richardson iteration. There are several advantages beyond the lower compute time. Scaling is performed locally for a diagonal block of the global matrix because it is applied directly to the factor. Further, an ILUT Schur complement smoother maintains a constant GMRES iteration count as the number of MPI ranks increases, and thus parallel strong-scaling is improved. Our algorithms have been incorporated into hypre, and we demonstrate improved time to solution for linear systems arising in the Nalu-Wind and PeleLM pressure solvers. For large problem sizes, GMRES+AMG executes at least five times faster when using iterative triangular solves compared with direct solves on massively parallel GPUs.

algebraic multigrid↗
DOE OSTI2025

Parallel-in-Time Solution of Hyperbolic PDE Systems via Characteristic-Variable Block Preconditioning

We consider the parallel-in-time solution of both linear and nonlinear hyperbolic partial differential equation (PDE) systems in one spatial dimension. In the nonlinear setting, the discretized equations are solved with a preconditioned residual iteration based on a global linearization. The linear(ized) equation systems are approximately solved parallel-in-time using a block preconditioner applied in the characteristic variables of the underlying linear(ized) hyperbolic PDE. This change of variables is motivated by the observation that intervariable coupling between characteristic variables is weak, at least locally where spatio-temporal variations in the eigenvectors of the associated flux Jacobian are sufficiently small, while that between the original variables is not. For an ℓ-dimensional system of PDEs, applying the preconditioner consists of solving a sequence of ℓ scalar linear(ized)-advection-like problems, each associated with a different characteristic wave-speed in the underlying linear(ized) PDE. Furthermore, we approximately solve these linear advection problems using multigrid reduction-in-time (MGRIT); however, any other suitable parallel-in-time method could be used. Numerical examples are shown for the (linear) acoustics equations in heterogeneous media and for the (nonlinear) shallow water equations and Euler equations of gas dynamics with shocks and rarefactions. For many test problems, the solver converges in just a handful of iterations and with mesh-independent convergence rates.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Finite Volume Discretization of the Euler Equations in Pronghorn

Modeling flow and heat transfer in high temperature gas reactors (HTGR) requires the ability to model a wide range of flow speeds from slow (natural convection), to intermediate (forced-flow conditions), to supersonic regimes (depressurization) for a wide range of geometries including the pebble bed, upper and lower plenum, and risers. In previous work, Pronghorn has effectively modeled low-to-medium speed flows in scenarios such as the one described in the two-dimensional PBMR-400 benchmark, using its finite-element-based streamline-upwind Petrov-Galerkin (SUPG) stabilized implementation of the Euler equations. However, limitations of this method become apparent when dealing with more complicated geometries (e.g. imposing slip boundary conditions at nodes belonging to two different boundaries) and when gas speeds are fast enough for shocks and supersonic flow to occur. For these problems, the finite-element-based solver lacks robustness and is plagued by slow iterative convergence or even divergence. In order to address these challenges, the Pronghorn code at INL has been updated with new, modified versions of its original equations. The new Pronghorn models are built on the finite volume method with a Harten-Lax-van Leer-Contact (HLLC) Riemann solver based numerical flux method, which (1) allows imposing slip boundary conditions much more robustly and (2) performs well for a wide range of flow speeds. The finite-volume-based flow solver will form the basis for a robust coarse-mesh thermal-hydraulics capability in Pronghorn.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A Code-Agnostic Driver Application for Coupled Neutronics and Thermal-Hydraulic Simulations

While the literature has numerous examples of Monte Carlo and computational fluid dynamics (CFD) coupling, most are hard-wired codes intended primarily for research rather than as standalone, general-purpose applications. In this work, we describe an open source application, ENRICO, that enables coupled neutronic and thermal-hydraulic simulations between multiple codes that can be chosen at runtime (as opposed to a coupling between two specific codes). The application has been designed such that the control flow logic, domain mapping, nonlinear fixed-point iteration, solution transfers, and convergence checks are all agnostic to the underlying physics solvers used. Special emphasis has also been placed on enabling efficient execution on distributed-memory computing environments. The transfer of solution fields between solvers is performed in memory rather than through filesystem I/O. Additionally, solvers can be configured to run on overlapping or disjoint sets of processes. To date, coupling with the OpenMC and Shift Monte Carlo codes, the Nek5000 CFD code, and a simplified heat diffusion and subchannel solver has been implemented in ENRICO. We present results for coupled simulations of a single light-water reactor fuel assembly based on the NuScale reactor using various combinations of the physics solvers. For this problem, the coupled simulations are shown to converge in about four Picard iterations. A comparison of the heat source and temperature distributions computed by ENRICO using OpenMC coupled with Nek5000 and Shift coupled with Nek5000 illustrates remarkable agreement between the codes.

42 ENGINEERING↗
DOE OSTI2024

Multi deep learning-based stochastic microstructure reconstruction and high-fidelity micromechanics simulation of time-dependent ceramic matrix composite response

A multi deep learning-based framework is developed for efficient, automated microstructure reconstruction and generation of stochastic representative volume elements (SRVEs) with periodic boundary conditions (PBCs) for accurate modeling of ceramic matrix composite (CMC) response. The methodology comprises a convolutional neural network coupled with regression layers to act as a vanilla regression network for semantic segmentation of the microstructure, allowing accurate characterization of the phases and their distributions at the microscale. Scanning electron microscope and confocal microscope are used to obtain C/SiNC and SiC/SiNC CMCs micrographs for vanilla regression testing. Microstructure variability in terms of fiber volume fraction and porosity are quantified through the output regression layer, ensuring accurate representation of material variability in SRVE construction. Generative adversarial network (GAN) and its variants are designed to produce high-fidelity SRVE, spanning CMCs microstructure variability space. A circular padding algorithm is developed to generate SRVEs with PBCs during training of GANs. The accuracy of the generated SRVEs is established through micromechanics simulations, where an efficient formulation of the high-fidelity generalized methods of cells (HFGMC) approach is used to compute the effective mechanical properties. Furthermore, an iterative algorithm is implemented in the HFGMC solver to simulate time-dependent deformation of SiC/SiNC subjected to creep loading conditions.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Surrogates for Valve-Controlled Pipe Flow: Accelerating Nuclear Reactor Design

Neural surrogate models are developed to replace expensive steady-state RANS CFD simulations for valve-controlled pipe flow in nuclear reactor design. Using parametric CFD data generated with MOOSE Pronghorn across a range of valve geometry and flow conditions, three approaches are compared: a POD-based reduced-order model, a structured UNet on a cylindrical grid, and unstructured models (DeepONet and BiStride MeshGraphNet) on nondimensionalized point clouds. POD achieves the highest accuracy (99%) with fast inference but requires storing all solution snapshots, while the DeepONet and BSMS-GNN both achieve ~89% accuracy at sub-second inference, with the BSMS-GNN offering superior geometric generalizability. These surrogates enable rapid ranking of candidate valve designs and can warm-start CFD solvers to accelerate convergence, supporting agentic design iteration on the Prometheus platform.

42 - ENGINEERING↗
DOE OSTI2020

Nonlinear Elimination Applied to Radiation Diffusion

We apply a nonlinearly preconditioned, quasi-Newton framework to accelerate the numerical solution of the thermal radiative transfer (TRT) equations. This framework was inspired by the unpublished method that has existed for years in Teton, Lawrence Livermore National Laboratory’s deterministic TRT code. In this paper, we cast this iteration scheme within a formal nonlinear preconditioning framework and compare its performance against other iteration schemes in the framework. With proper choices of iteration controls for the various levels of the solver, we can recover the standard linearized one-step method, a full nonlinear Newton scheme, as well as the method in Teton. In brief, the nonlinear preconditioning TRT scheme formally eliminates the material temperature equation from the nonlinear system in a nonlinear analog of a Schur complement. This nonlinear elimination step involves solving a decoupled nonlinear equation for each spatial degree of freedom and is therefore inexpensive. By applying a quasi-Newton iteration scheme on the new system, we obtain a three-level iteration scheme that is at least as efficient as commonly used TRT schemes. The new method allows full convergence to the nonlinear backward Euler time-discretized system, increasing accuracy and robustness, while using a similar number of linear iterations as the more common linearized one-step methods Eq. (4).

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2025

Alternative mixed integer linear programming optimization for joint job scheduling and data allocation in grid computing

This paper presents a novel approach to the joint optimization of job scheduling and data allocation in grid computing environments. We formulate this joint optimization problem as a mixed integer quadratically constrained program. To tackle the nonlinearity in the constraint, we alternatively fix a subset of decision variables and optimize the remaining ones via Mixed Integer Linear Programming (MILP). We solve the MILP problem at each iteration via an off-the-shelf MILP solver. Our experimental results show that our method significantly outperforms existing heuristic methods, employing either independent optimization or joint optimization strategies. We have also verified the generalization ability of our method over grid environments with various sizes and its high robustness to the algorithm setting.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Mixed-precision iterative refinement using tensor cores on GPUs to accelerate solution of linear systems

Double-precision floating-point arithmetic (FP64) has been the de facto standard for engineering and scientific simulations for several decades. Problem complexity and the sheer volume of data coming from various instruments and sensors motivate researchers to mix and match various approaches to optimize compute resources, including different levels of floating-point precision. In recent years, machine learning has motivated hardware support for half-precision floating-point arithmetic. A primary challenge in high-performance computing is to leverage reduced-precision and mixed-precision hardware. We show how the FP16/FP32 Tensor Cores on NVIDIA GPUs can be exploited to accelerate the solution of linear systems of equations Ax = b without sacrificing numerical stability. The techniques we employ include multiprecision LU factorization, the preconditioned generalized minimal residual algorithm (GMRES), and scaling and auto-adaptive rounding to avoid overflow. We also show how to efficiently handle systems with multiple right-hand sides. On the NVIDIA Quadro GV100 (Volta) GPU, we achieve a 4×-5× performance increase and 5× better energy efficiency versus the standard FP64 implementation while maintaining an FP64 level of numerical stability.

GMRES↗
DOE OSTI2021

Implementation of a 9-point stencil in SOLPS-ITER and implications for Alcator C-Mod divertor plasma simulations

The SOLPS-ITER code suite is used worldwide for plasma edge modeling, the interpretation of experiments, as well as for the design of the ITER divertor. The numerical scheme of the plasma solver of the code, B2.5, is based on the assumption of perfectly field-aligned grids, while in practice grids are often strongly distorted to match divertor target shapes. Neglecting these grid distortion leads to qualitatively and quantitatively incorrect results for fluid neutral simulations, and may affect results in cold (detached) divertors even when using kinetic neutral simulations. In this contribution, we present the first results of a newly implemented 9-point stencil in B2.5 to properly handle misaligned grids. The new scheme is then applied to fluid neutral simulations of a well-diagnosed and previously modeled Alcator C-Mod discharge. Results are compared with the original 5-point scheme neglecting grid distortion effects, as well as with simulations including a full kinetic neutral model. We conclude that the 9-point stencil is essential to correctly model the transport of fluid neutrals on distorted grids, and to capture the effects of divertor closure on the fluid neutral behavior.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

An Adaptive Newton-Based Free-Boundary Grad–Shafranov Solver

Equilibria in magnetic confinement devices result from force balancing between the Lorentz force and the plasma pressure gradient. In an axisymmetric configuration like a tokamak, such an equilibrium is described by an elliptic equation for the poloidal magnetic flux, commonly known as the Grad–Shafranov equation. It is challenging to develop a scalable and accurate free-boundary Grad–Shafranov solver, since it is a fully nonlinear optimization problem that simultaneously solves for the magnetic field coil current outside the plasma to control the plasma shape. In this work, we develop a Newton-based free-boundary Grad–Shafranov solver using adaptive finite elements and preconditioning strategies. The free-boundary interaction leads to the evaluation of a domain-dependent nonlinear form of which its contribution to the Jacobian matrix is achieved through shape calculus. The optimization problem aims to minimize the distance between the plasma boundary and specified control points while satisfying two nontrivial constraints, which correspond to the nonlinear finite element discretization of the Grad–Shafranov equation and a constraint on the total plasma current involving a nonlocal coupling term. The linear system is solved by a block factorization, and AMG is called for subblock elliptic operators. The unique contributions of this work include the treatment of a global constraint, preconditioning strategies, nonlocal reformulation, and the implementation of adaptive finite elements. Furthermore, it is found that the resulting Newton solver is robust, successfully reducing the nonlinear residual to 1e-6 and lower in a small handful of iterations while addressing the challenging case to find a Taylor state equilibrium where conventional Picard-based solvers fail to converge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Performance Improvements of the Griffin Solvers in FY24

The Griffin code is a MOOSE-based reactor physics application jointly developed by Idaho National Laboratory and Argonne National Laboratory under the Department of Energy Office of Nuclear Energy Nuclear Energy Advanced Modeling and Simulation Program. This fiscal year, we have made significant efforts to improve the performance of transport solver options and cross-section generation for the efficient use of Griffin in advanced reactor applications. For the HFEM-PN solver, the residual evaluations of HFEM kernels were optimized by utilizing the pre- computed averaged cross sections for individual elements. Numerical integration involving the evaluation of basis functions at quadrature points was bypassed by facilitating precomputed element mass matrices for response matrices. Red-black iterations were improved by introducing a new generalized minimum residual based solver. The memory usage of response matrix storage was significantly reduced by applying basis function rotations on interfaces and calculating volumetric odd-parity moments on the fly. Additionally, the adjoint flux and transient calculation capabilities of the HFEM-PN solver were successfully implemented and verified using the TWIGL benchmark problem. For the DFEM-SN solver, memory footprint and computation time were significantly reduced by not treating angular flux vectors as the MOOSE nonlinear system vectors. Specifically for IQS, scalar adjoint weighting was introduced to further eliminate angular adjoint flux storage in the MOOSE auxiliary system. It was demonstrated through the three-dimensional Advanced Burner Test Reactor core problem that the memory usage for transient calculations with the IQS method was reduced by over 7.5× compared to before the optimizations. For the self-shielding application programming interface, a new double-heterogeneity treatment method, named the Bell Function-Based Analytic Two-Region Slowing Down Method, was developed to efficiently flux-volume homogenize TRISO particles with the matrix. Additionally, optimizations were made to hyper- fine group (HFG) slowing down calculations by pretabulating collision probability coefficients and grouping isotopes, significantly reducing the computational time for calculating scattering sources per HFG. Lastly, the pin power reconstruction module was extended to account for temporal behavior in a microreactor analysis problem, specifically for a control drum transient. Verification tests for each of these improvements demonstrated significant performance enhancements and memory reduction.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

jaxhps: An elliptic PDE solver built with machine learning in mind

Elliptic partial differential equations (PDEs) can model many physical phenomena, such as electrostatics, acoustics, wave propagation, and diffusion. In scientific machine learning settings, a high-throughput PDE solver may be required to generate a training dataset, run in the inner loop of an iterative algorithm, or interface directly with a deep neural network. To provide value to machine learning users, such a PDE solver must be compatible with standard automatic differentiation frameworks, scale efficiently when run on graphics processing units (GPUs), and maintain high accuracy for a large range of input parameters. We have designed the jaxhps package with these use-cases in mind by implementing a highly efficient and accurate solver for elliptic problems with native hardware acceleration and automatic differentiation support.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Parallel-in-Time Solution of Allen-Cahn Equations by Integrating Operator Learning into the Parareal Method

While recent advances in deep learning have shown promising efficiency gains in solving time-dependent partial differential equations (PDEs), matching the accuracy of conventional numerical solvers still remains a challenge. One strategy to improve the accuracy of deep learning-based solutions for time-dependent PDEs is to use the learned model as the coarse propagator in the Parareal method and a traditional numerical method as the fine solver. However, successful integration of deep learning into the Parareal method requires consistency between the coarse and fine solvers, particularly for PDEs exhibiting rapid changes such as sharp transitions. Here, to ensure this consistency, we propose using convolutional neural networks (CNNs) to learn the fully discrete time-stepping operator defined by the same numerical scheme employed as the fine solver. We demonstrate the effectiveness of the proposed method in solving the classical and mass-conservative Allen–Cahn (AC) equations. Through iterative updates in the Parareal algorithm, our approach achieves a significant computational speedup compared to traditional fine solvers while converging to high-accuracy solutions. Our results highlight that the proposed hybrid Parareal algorithm effectively accelerates simulations, particularly when implemented on multiple GPUs, and converges to the desired accuracy in only a few iterations. Another advantage of our method is that the CNN model is trained on trajectory-based data generated from random initial conditions, such that the trained model can be used to solve the AC equations with various initial conditions without retraining. This work demonstrates the potential of integrating neural network methods into parallel-in-time frameworks for efficient and accurate simulations of time-dependent PDEs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Mixed-precision numerics in scientific applications: survey and perspectives

The explosive demand for artificial intelligence (AI) workloads has led to a significant increase in silicon area dedicated to lower-precision computations on recent high-performance computing hardware designs. However, mixed-precision capabilities, which can achieve performance improvements of up to 8x compared to double-precision in extreme compute-intensive workloads, remain largely untapped in most scientific applications. A growing number of efforts have shown that mixed-precision algorithmic innovations can deliver superior performance without sacrificing accuracy. These developments should prompt computational scientists to seriously consider whether their scientific modeling and simulation applications could benefit from the acceleration offered by new hardware and mixed-precision algorithms. In this survey, we (1) review progress across diverse scientific domains—fluid dynamics, weather and climate, quantum chemistry, and computational genomics—that have begun adopting mixed-precision strategies; (2) examine state-of-the-art algorithmic techniques such as iterative refinement, splitting and emulation schemes, and adaptive precision solvers; (3) assess their implications for accuracy, performance, and resource utilization; and (4) survey the emerging software ecosystem that enables mixed-precision methods at scale. We conclude with perspectives and recommendations on cross-cutting opportunities, domain-specific challenges, and the role of co-design between application scientists, numerical analysts, and computer scientists. Collectively, this survey underscores that mixed-precision numerics can reshape computational science by aligning algorithms with the evolving landscape of hardware capabilities.

Graphics processing units↗
DOE OSTI2023

Carbon Organisms Rhizosphere and Protection in Soil Environment model script and input data for soil moisture-respiration responses in tropical forests

Objectives: Climatic drying is predicted for many tropical forests, yet models remain poorly parameterized for tropical forests, hampering predictions of forest-climate feedbacks. We applied an integrated model–experiment approach, parameterizing an ecosystem model Carbon Organisms Rhizosphere and Protection in the Soil Environment (CORPSE) with tropical forest observational data, and comparing model predictions with a field drying manipulation. We hypothesized that drying would suppress soil CO2 fluxes (i.e., respiration) in already-drier tropical forests, but increases CO2 fluxes in wetter tropical forests by alleviating anaerobiosis. We measured soil CO2 fluxes, soil moisture, soil temperature, and forest floor biomass during wet-dry cycles (2015 – 2022) in four Panamanian forests that vary in rainfall and soil fertility. We used the field data to parameterize and run tests in the model.Results: Measured CO2 fluxes declined in the dry season and peaked in the early wet season ahead of peak soil moisture, resulting in a lower soil moisture optimum for respiration than previously modeled. We used this data to parameterize the model, which then predicted increased soil CO2 fluxes in wetter and fertile forests with drying, and decreased fluxes in drier, infertile forests. In contrast to model predictions, a chronic throughfall exclusion experiment in the forests initially suppressed soil CO2 fluxes across forests, with sustained suppression after four years in the wettest forest only (-28 ± 4% during the dry season), but elevated soil CO2 fluxes in a fertile forest after four years (+75 ± 28% during the late wet season), as predicted by the model. The unexpected negative drying effect in the wettest, most infertile forest could have resulted from reduced vertical flushing of nutrients into soils. Including hydro-nutrient interactions in ecosystem models could improve predictions of tropical forest-climate feedbacks (results presented in Cusack et al. 2023). Datasets included: Code files:CORPSE_array.py: Defines the equations of the CORPSE modelCORPSE_solvers: Functions for running the CORPSE model using either iterative or ordinary differential equation (ODE) solversrun_Panama_sims.py: Read in datasets and run the model simulations for this studyInput data:PanamaGradientEcosystemChem_BT_CPools_20152016CO2_DC_20190615.xlsx: Plot characteristics used in running model simulationsLiCor compiled surface flux only to 2020_03 DC_20200825.xlsx: Surface gas exchange fluxes used in model-data comparisonsPARCHED litterfall data for Ben Sulman LD 20200902.xlsx: Litterfall data used to drive model simulationsInitialization data:state_500y_20190823.csv: Initial state of model pools based on previous spinup runsOutput data:Outputs/prev_moisture_response.csv: Simulations of multiple sites using original model moisture response function.Outputs/updated_moisture_response.csv: Simulations of multiple sites using updated model moisture response function.Outputs/dry15_prev_moisture_response.csv: Simulations with soil moisture reduced by 15%, using original moisture response function.Outputs/dry15_updated_moisture_response.csv: Simulations with soil moisture reduced by 15%, using updated moisture response function.Outputs/dry30_prev_moisture_response.csv: Simulations with soil moisture reduced by 30%, using original moisture response function.Outputs/dry30_updated_moisture_response.csv: Simulations with soil moisture reduced by 30%, using updated moisture response function.Outputs/latestart_prev_moisture_response.csv: Simulations with extended dry season, using original moisture response function.Outputs/latestart_updated_moisture_response.csv: Simulations with extended dry season, using updated moisture response function.Outputs/[site name]_oneyear.csv: One-year simulation for each site in expanded site list using original moisture response function.Outputs/[site name]_oneyear_dried.csv: One-year simulation for each site in expanded site list using original moisture response function, with soil moisture reduced by 25%.Outputs/[site name]_oneyear_updated_moisture_response.csv: One-year simulation for each site in expanded site list using updated moisture response function.Outputs/[site name]_oneyear_updated_moisture_response_dried.csv: One-year simulation for each site in expanded site list using updated moisture response function, with soil moisture reduced by 25%.Field plot location data:There is also a .kml file that includes coordinates for all 32 plots included in the study of four forests (n = 4 throughfall reduction and n = 4 control plots per site).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Diffusion Synthetic Acceleration for Heterogeneous Domains, Compatible with Voids

A standard approach to solving the S N transport equations is to use source iteration with diffusion synthetic acceleration (DSA). Although this approach is widely used and effective on many problems, there remain some practical issues with DSA preconditioning, particularly on highly heterogeneous domains. For large-scale parallel simulation, it is critical that both (a) preconditioned source iteration converges rapidly and (b) the action of the DSA preconditioner can be applied using fast, scalable solvers, such as algebraic multigrid (AMG). For heterogeneous domains, these two interests can be at odds. In particular, there exist DSA diffusion discretizations that can be solved rapidly using AMG, but they do not always yield robust/fast convergence of the larger source iteration. Conversely, there exist robust DSA discretizations where source iteration converges rapidly on difficult heterogeneous problems, but fast parallel solvers like AMG tend to struggle applying the action of such operators. Moreover, very few current methods for the solution of deterministic transport are compatible with voids. This paper develops a new heterogeneous DSA preconditioner based on only preconditioning the optically thick subdomains. The resulting method proves robust on a variety of heterogeneous transport problems, including a linearized hohlraum mesh related to inertial confinement fusion. Moreover, the action of the preconditioner is easily computed using O(1) AMG iterations, convergence of the transport iteration typically requires 2 to 5× fewer iterations than current state-of-the-art “full” DSA, and the proposed method is trivially compatible with voids. On the hohlraum problem, rapid convergence is obtained by preconditioning less than 3% of the mesh elements with five to ten AMG iterations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗