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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.

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DOE OSTI2021

Analysis of a New Implicit Solver for a Semiconductor Model

Here, we present and analyze a new iterative solver for implicit discretizations of a simplified Boltzmann--Poisson system. The algorithm builds on recent work that incorporated a sweeping algorithm for the Vlasov--Poisson equations as part of nested inner-outer iterative solvers for the Boltzmann--Poisson equations. The new method eliminates the need for nesting and requires only one transport sweep per iteration. It arises as a new fixed-point formulation of the discretized system which we prove to be contractive for a given electric potential. We also derive an accelerator to improve the convergence rate for systems in the drift-diffusion regime. We numerically compare the efficiency of the new solver, with and without acceleration, against a recently developed nested iterative solver.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Scalable Implicit Solvers with Dynamic Mesh Adaptation for a Relativistic Drift-Kinetic Fokker–Planck–Boltzmann Model

In this work we consider a relativistic drift-kinetic model for runaway electrons along with a Fokker–Planck operator for small-angle Coulomb collisions, a radiation damping operator, and a secondary knock-on (Boltzmann) collision source. Here, we develop a new scalable fully implicit solver utilizing finite volume and conservative finite difference schemes and dynamic mesh adaptivity. A new data management framework in the PETSc library based on the p4est library is developed to enable simulations with dynamic adaptive mesh refinement (AMR), distributed memory parallelization, and dynamic load balancing of computational work. This framework and the runaway electron solver building on the framework are able to dynamically capture both bulk Maxwellian at the low-energy region and a runaway tail at the high-energy region. To effectively capture features via the AMR algorithm, a new AMR indicator prediction strategy is proposed that is performed alongside the implicit time evolution of the solution. This strategy is complemented by the introduction of computationally cheap feature-based AMR indicators that are analyzed theoretically. Numerical results quantify the advantages of the prediction strategy in better capturing features compared with nonpredictive strategies; and we demonstrate trade-offs regarding computational costs. The robustness with respect to model parameters, algorithmic scalability, and parallel scalability are demonstrated through several benchmark problems including manufactured solutions and solutions of different physics models. We focus on demonstrating the advantages of using implicit time stepping and AMR for runaway electron simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

An efficient, conservative, time-implicit solver for the fully kinetic arbitrary-species 1D-2V Vlasov-Ampère system

In this paper, we consider the solution of the fully kinetic (including electrons) Vlasov-Ampère system in a one-dimensional physical space and two-dimensional velocity space (1D-2V) for an arbitrary number of species with a time-implicit Eulerian algorithm. The problem of velocity-space meshing for disparate thermal and bulk velocities is dealt with by an adaptive coordinate transformation of the Vlasov equation for each species, which is then discretized, including the resulting inertial terms. Mass, momentum, and energy are conserved, and Gauss's law is enforced to within the nonlinear convergence tolerance of the iterative solver through a set of nonlinear constraint functions while permitting significant flexibility in choosing discretizations in time, configuration, and velocity space. We mitigate the temporal stiffness introduced by, e.g., the plasma frequency through the use of high-order/low-order (HOLO) acceleration of the iterative implicit solver. We present several numerical results for canonical problems of varying degrees of complexity, including the multiscale ion-acoustic shock wave problem, which demonstrate the efficacy, accuracy, and efficiency of the scheme.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

A scalable multidimensional fully implicit solver for Hall magnetohydrodynamics

We propose an optimally performant fully implicit algorithm for the Hall magnetohydrodynamics (HMHD) equations based on multigrid-preconditioned Jacobian-free Newton-Krylov methods. HMHD is a challenging system to solve numerically because it supports stiff fast dispersive waves. The preconditioner is formulated using an operator-split approximate block factorization (Schur complement), informed by physics insight. We use a vector-potential formulation (instead of a magnetic field one) to allow a clean segregation of the problematic $\nabla$ x $\nabla$ x operator in the electron Ohm's law subsystem. This segregation allows the formulation of an effective damped block-Jacobi smoother for multigrid. We demonstrate by analysis that our proposed block-Jacobi iteration is convergent and has the smoothing property. The resulting HMHD solver is verified linearly with wave propagation examples, and nonlinearly with the GEM challenge reconnection problem by comparison against another HMHD code. We demonstrate the excellent algorithmic and parallel performance of the algorithm up to 16384 MPI tasks in two dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

A fast implicit solver for semiconductor models in one space dimension

Several different approaches are proposed for solving fully implicit discretizations of a simplified Boltzmann-Poisson system with a linear relaxation-type collision kernel. This system models the evolution of free electrons in semiconductor devices under a low-density assumption. At each implicit time step, the discretized system is formulated as a fixed-point problem, which can then be solved with a variety of methods. A key algorithmic component in all the approaches considered here is a recently developed sweeping algorithm for Vlasov-Poisson systems. A synthetic acceleration scheme has been implemented to accelerate the convergence of iterative solvers by using the solution to a drift-diffusion equation as a preconditioner. The performance of four iterative solvers and their accelerated variants has been compared on problems modeling semiconductor devices with various electron mean-free-path.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Electromagnetic Transient Simulation of Photovoltaic Inverter Using Implicit-Explicit Solver

This paper introduces the implementation of electromagnetic transient (EMT) simulations of a photovoltaic (PV) inverter module using the Implicit-Explicit (ImEx) solver in the Suite of Nonlinear and Differential/Algebraic Equation Solvers (SUNDIALS). This study demonstrates the effectiveness of the ImEx solver in overcoming the challenges inherent in simulating the complex dynamics of PV inverter modules. Furthermore, using SUNDIALS’ ImEx solver module ARKODE for EMT simulation automates key aspects of the process, such as numerical integration, providing substantial benefits including enhanced consistency, faster implementation, reduced human error, and the capability to handle the complexities of advanced numerical integration. By conducting comparative simulations with an implicit method used in commercial software, the research showcases the ImEx solver’s capability in achieving high accuracy and reliability. Results indicate that leveraging the ImEx approach significantly enhances modeling fidelity and reduces simulation setup times, offering a promising tool for the EMT analysis of PV inverter systems in power electronics-dominated power grids.

Choi, Jongchan [ORNL] (ORCID:000000025952455X)↗
DOE OSTI2021

A Scalable Semi-Implicit Barotropic Mode Solver for the MPAS-Ocean

A scalable semi-implicit barotropic mode solver for the ocean component of the model for prediction across scales has been implemented as a competitor to an existing explicit-subcycling scheme to allow faster and more stable simulations while not sacrificing accuracy. The semi-implicit solver adopts the pipelined preconditioned bi-conjugate gradient stabilization algorithm as an iterative solver in conjunction with the restricted additive Schwarz preconditioner that accelerates the convergence rate of the iterative solver. The preconditioner is constructed from a linearized barotropic system that also reorders the system for optimal performance, while the semi-implicit solver deals with the fully nonlinear barotropic system that requires reassembly of the coefficient matrix for every time step. Several numerical experiments, from simple one-dimensional tests to three-dimensional real-world tests, demonstrate that the semi-implicit solver has almost the same accuracy and better parallel scalability compared with the existing scheme while allowing faster and more stable simulations. Furthermore, the semi-implicit solver accelerates the barotropic mode up to 2.9 times faster than the existing scheme on 16,320 processors, leading to an overall runtime speedup of 1.9.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Mathematical solutions in internal dose assessment: A comparison of Python-based differential equation solvers in biokinetic modeling

Abstract In biokinetic modeling systems employed for radiation protection, biological retention and excretion have been modeled as a series of discretized compartments representing the organs and tissues of the human body. Fractional retention and excretion in these organ and tissue systems have been mathematically governed by a series of coupled first-order ordinary differential equations (ODEs). The coupled ODE systems comprising the biokinetic models are usually stiff due to the severe difference between rapid and slow transfers between compartments. In this study, the capabilities of solving a complex coupled system of ODEs for biokinetic modeling were evaluated by comparing different Python programming language solvers and solving methods with the motivation of establishing a framework that enables multi-level analysis. The stability of the solvers was analyzed to select the best performers for solving the biokinetic problems. A Python-based linear algebraic method was also explored to examine how the numerical methods deviated from an analytical or semi-analytical method. Results demonstrated that customized implicit methods resulted in an enhanced stable solution for the inhaled 60 Co (Type M) and 131 I (Type F) exposure scenarios for the inhalation pathway of the International Commission on Radiological Protection (ICRP) Publication 130 Human Respiratory Tract Model (HRTM). The customized implementation of the Python-based implicit solvers resulted in approximately consistent solutions with the Python-based matrix exponential method ( expm ). The differences generally observed between the implicit solvers and expm are attributable to numerical precision and the order of numerical approximation of the numerical solvers. This study provides the first analysis of a list of Python ODE solvers and methods by comparing their usage for solving biokinetic models using the ICRP Publication 130 HRTM and provides a framework for the selection of the most appropriate ODE solvers and methods in Python language to implement for modeling the distribution of internal radioactivity.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2020

Exact and locally implicit source term solvers for multifluid-Maxwell systems

Recently, a family of models that couple multifluid systems to the full Maxwell equations have been used in laboratory, space, and astrophysical plasma modeling. These models are more complete descriptions of the plasma than reduced models like magnetohydrodynamic (MHD) since they are derived more closely from the full kinetic Vlasov-Maxwell system, without assumptions like quasi-neutrality, negligible electron mass, etc. Thus these models naturally retain non-ideal MHD effects like electron inertia, Hall term, pressure anisotropy/nongyrotropy, displacement current, among others. One obstacle to broader application of these model is that an explicit treatment of their source terms leads to the need to resolve rapid processes like plasma oscillation and electron cyclotron motion, even when these are not important. In this paper, we suggest two ways to address this issue. First, we derive the analytic solutions to the source update equations, which can be implemented as a practical, but less generic solver. We then develop a time-centered, locally implicit algorithm to update the source terms, allowing stepping over the fast kinetic time-scales. For a plasma with S species, the locally implicit algorithm involves inverting a local (3 S + 3) × (3 S + 3) matrix only, thus is very efficient. The performance can be further increased by using the direct update formulas to skip null calculations. In this paper, we present benchmarks illustrating the exact energy-conservation of the locally implicit solver, as well as its efficiency and robustness for both small-scale, idealized problems and largescale, complex systems. The locally implicit algorithm can be also easily extended to include other local sources, like collisions and ionization, which are difficult to solve analytically.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Domain Aware Deep-learning Algorithms Integrated with Scientific-computing Technologies (DADAIST)

This technical report summarized the contribution of the DADAIST project funded by the Data Model Convergence Initiative via the Laboratory Directed Research and Development (LDRD) investments at Pacific Northwest National Laboratory (PNNL). Specifically, we report the development of the NeuroMANCER (Neural Modules with Adaptive Nonlinear Constraints and Efficient Regularizations), a new open-source Scientific Machine Learning library for formulating and solving parametric constrained optimization problems, physics-informed system identification, and parametric optimal control problems. NeuroMANCER is using differentiable programming to combine modern data-driven models and optimization modeling language into a coherent algorithmic and software framework. NeuroMANCER is a Pytorch-based framework and adopts much of its philosophy focused on research and development, rapid prototyping, and streamlined deployment. Strong emphasis is given to extensibility, interoperability with the PyTorch ecosystem, and quick adaptability to custom domain problems. Neuromancer repository contains a comprehensive library of differentiable modules, including custom activation functions, matrix factorizations, deep learning architectures, neural differential equations, differential equation solvers, implicit layers such as iterative solvers, high-level API for symbolic expressions, API for modeling and control of dynamical systems, and extensive set of tutorial code examples in the form of python scripts and jupyter notebooks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

An implicit barotropic mode solver for MPAS-ocean using a modern Fortran solver interface

Here, we demonstrate use of a modern Fortran solver interface to manage solver algorithms for an implicit barotropic mode solver in the Model for Predictions Across Scales-Ocean (MPAS-O). ForTrilinos, a Fortran interface to Trilinos that contains a large collection of solver capabilities written in C++, has been implemented in MPAS-O to provide access to a suite of linear solver options. By virtue of the simplified wrapper and interface generator (SWIG) automation tool that generates modern Fortran interfaces to C++ code, we were able to implement the Fortran solver interface in MPAS-O using a familiar Fortran coding style while minimizing performance degradation. The ForTrilinos solver interface is written within MPAS-O’s time stepping modules as a subroutine in conjunction with MPAS-O code. Applied to an idealized ocean and a high-resolution realistic ocean test case, parallel performance of ForTrilinos solvers is examined. It is found that parallel scalability of the ForTrilinos solvers is highly dependent on the number of global synchronization points per solver iteration in each iterative solver algorithm. ForTrilinos solvers perform best compared to the Fortran hand-crafted (FHC) solver when the amount of work per processor is large enough. However, parallel scalability is better with the FHC solver and so when the work per core is modest FHC outperforms ForTrilinos. The intercomparison between the ForTrilinos and FHC solvers reveals that this performance hit in the ForTrilinos solver mostly comes from the global synchronization process, while suggesting that the matrix-vector multiplication process in the FHC solver needs to be optimized for better performance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Implicit fast sweeping method for hyperbolic systems of conservation laws

Implicit time-accurate methods are often used to integrate stiff problems where explicit schemes impose severe time step restrictions. This paper presents an efficient numerical framework based on the Fast Sweeping Method (FSM) for solving linear and nonlinear hyperbolic systems of conservation laws. The solution at each discrete location is computed by sweeping the numerical domain in several predetermined directions that follow the causality of the characteristic families. The use of a fractional step strategy eliminates the need for a solution selection criterion while one-sided stencils limit the number of sweeps to at most 2 d for d space dimensions. This work focuses on the first-order implicit upwind method since it constitutes the building block for high-order conservative schemes. For problems where the degree of stiffness evolves over time, implicit-explicit hybridization can be accomplished with the same algorithm by simply switching the stencil at each time level. As opposed to traditional implicit solvers, the sweeping method does not require a local time linearization of the fluxes thereby preserving the nonlinear stability properties of the original implicit scheme. It also avoids the large computational and memory requirements associated with solving large block-diagonal systems of equations. Here, a series of one- and two-dimensional test cases are presented for the inviscid Burgers' equation and the reactive Euler equations. The results indicate that the implicit FSM can allow a major reduction in the number of time steps even in the presence of discontinuous solution profiles.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

A physics-constrained neural ordinary differential equations approach for robust learning of stiff chemical kinetics

The high computational cost associated with solving for detailed chemistry poses a significant challenge for predictive computational fluid dynamics (CFD) simulations of turbulent reacting flows. While deep learning techniques have been explored to develop faster surrogate models, they often fail to integrate reliably with CFD solvers. This instability arises because traditional deep learning approaches optimize for training error without ensuring compatibility with ordinary differential equation (ODE) solvers, resulting in accumulation of errors over time. Recently, neuralODE (NODE) based approaches have been shown to be a promising technique to emulate and accelerate detailed chemistry computations. Here, in the present work, we extend this NODE framework for stiff chemical kinetics by incorporating mass conservation constraints directly into the loss function during training. This ensures that the total mass as well as the individual elemental species masses are conserved in an a-posteriori manner. Proof-of-concept studies are performed with the novel physics-constrained NODE (PC-NODE) approach for homogeneous autoignition of hydrogen-air mixture over a range of composition and thermodynamic conditions. It is demonstrated that the PC-NODE framework not only improves the physical consistency of the resulting data-driven model with respect to mass conservation criteria, but also improves training efficiency. PC-NODE is shown to achieve 2–100× speedup relative to the hydrogen-air detailed chemical mechanism depending on the type of the ODE solver (implicit or explicit) used during autoregressive inference tests. Lastly, a-posteriori studies are performed wherein the trained PC-NODE model is coupled with a CFD solver. It is shown that higher accuracy is achieved with PC-NODE relative to the purely data-driven NODE approach. Moreover, PC-NODE also exhibits robustness and generalizability to unseen initial conditions from within (interpolative capability) as well as outside (extrapolative capability) the training regime.

computational combustion↗
DOE OSTI2023

An implicit, conservative and asymptotic-preserving electrostatic particle-in-cell algorithm for arbitrarily magnetized plasmas in uniform magnetic fields

Here, we introduce a new electrostatic particle-in-cell algorithm capable of using large timesteps compared to particle gyro-period under a uniform external magnetic field. The algorithm extends earlier electrostatic fully implicit PIC implementations with a new asymptotic-preserving particle-push scheme that allows timesteps much larger than particle gyroperiods. In the large-timestep limit, the integrator preserves all particle drifts, while recovering the full orbit for small timesteps. The scheme allows for a seamless, efficient treatment of particles with coexisting magnetized and unmagnetized species, and conserves energy and charge exactly without spoiling implicit solver performance. We demonstrate by numerical experiment with several problems of variable species magnetization (diocotron instability, modified two-stream instability, and drift instability) that orders of magnitude wall-clock-time speedups vs. the standard fully implicit electrostatic PIC algorithm are possible without sacrificing solution accuracy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Vacuum Neutral Transport Model in UEDGE for Tokamak Far Scrape‐Off Layer

A model for neutral transport in the far scrape-off layer (SOL) vacuum region (vacuum neutral model) has been developed and implemented in UEDGE. Free-streaming neutral trajectories between the outermost UEDGE boundary and the vessel wall are preprocessed using DEGAS2 to construct a tele-transport matrix that captures non-local neutral relocation through the vacuum. Here, this matrix is then used in UEDGE as a non-local boundary condition for the neutral equations, preserving the robustness and convergence of the implicit solver without introducing statistical noise. Simulations of a DIII-D lower single-null configuration show that the vacuum neutral model relocates neutrals from the divertor to the upstream region, increasing the outer midplane separatrix density required for detachment onset by about 30%. However, the characteristic target temperature at detachment (T e, osp ~ 3 - 4eV) and the radiation front behavior remain unchanged.

DEGAS2↗
DOE OSTI2021

Sierra/SolidMechanics 5.0 Goodyear Specific

Sierra/SolidMechanics (Sierra/SM) is a Lagrangian, three-dimensional finite element analysis code for solids and structures subjected to extensive contact and large deformations, encompassing explicit and implicit dynamic as well as quasistatic loading regimes. This document supplements the primary Sierra/SM 5.0 User’s Guide, describing capabilities specific to Goodyear analysis use cases, including additional implicit solver options, material models, finite element formulations, and contact settings.

97 MATHEMATICS AND COMPUTING↗