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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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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Combining Sparse Approximate Factorizations with Mixed-precision Iterative Refinement

The standard LU factorization-based solution process for linear systems can be enhanced in speed or accuracy by employing mixed-precision iterative refinement. Most recent work has focused on dense systems. We investigate the potential of mixed-precision iterative refinement to enhance methods for sparse systems based on approximate sparse factorizations. In doing so, we first develop a new error analysis for LU- and GMRES-based iterative refinement under a general model of LU factorization that accounts for the approximation methods typically used by modern sparse solvers, such as low-rank approximations or relaxed pivoting strategies. We then provide a detailed performance analysis of both the execution time and memory consumption of different algorithms, based on a selected set of iterative refinement variants and approximate sparse factorizations. Our performance study uses the multifrontal solver MUMPS, which can exploit block low-rank factorization and static pivoting. We evaluate the performance of the algorithms on large, sparse problems coming from a variety of real-life and industrial applications showing that mixed-precision iterative refinement combined with approximate sparse factorization can lead to considerable reductions of both the time and memory consumption.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A Robust Numerical Treatment of Solid-Phase Diffusion in Pseudo Two-Dimensional Lithium-Ion Battery Models

Solid-phase diffusion in active materials of lithium-ion batteries significantly affects charging and safety-related behavior of lithium-ion batteries. Therefore, it is essential to develop an efficient and robust numerical algorithm for solving solid-phase diffusion equations in physics-based battery models. In this work, we discuss the origins of numerical instabilities that can occur when solving the solid-phase diffusion equations using iterative methods. Then, in order to resolve such issues, we propose a simple numerical treatment to the surface flux term of discretized solid-phase diffusion equations. To demonstrate its numerical robustness, the proposed method is implemented into a pseudo two-dimensional (P2D) physics-based battery model and simulations are conducted at wide ranges of operating conditions. Even with extremely poor initial guesses for the Li+ concentrations of the active materials, computations using the proposed method do not diverge and the their computational speeds are comparable to those with conventional initial guesses. Comprehensive tests of the proposed method are also performed with a dynamic current profile based on US06 driving profile and a multi-stage charging profile with very high initial C-rate (12C).

battery modeling↗
DOE OSTI2025

Reconstruction of 2D line-integrated electron density using angular filter refractometry and a fast marching Eikonal solver

Refraction of an optical probe beam by a plasma can be measured with angular filter refractometry (AFR), which produces an image of the beam’s 2D spatial profile that contains intensity contours corresponding to curves of constant refraction angle. Further analysis is required to reconstruct the underlying line-integrated electron density. Most prior efforts to calculate density from AFR data have been limited to 1D analysis or forward-fitting techniques. Here, in this paper, we detail the use of a fast-marching Eikonal solver to directly invert AFR data and obtain the full 2D line-integrated electron density. The analysis method is first verified with synthetic data and then applied to experimental measurements of single and colliding plasma plumes collected at the OMEGA EP Laser Facility. The calculated densities agree with 1D results and are shown to be consistent with the original AFR measurements via forward modeling. We also discuss ways to improve the precision of this technique.

McCluskey, B. [Princeton Univ., NJ (United States)↗
NASA NTRS1978

A split-recoupled-semidirect computational technique applied to transonic flow over lifting airfoils

A new version of the semidirect iterative method eliminates significant restrictions of previous versions of the method. A semidirect method solves finite-difference equations by a rapid globally implicit iterative process driven by a fast direct elliptic solver. The new approach can treat complex systems of equations in an efficient 'correction form', and allows the use of general, nonorthogonal, boundary-fitted coordinate transformations. These features are expected to lead to significant practical applications with conservation-equation systems in either two or three dimensions. The present application to the full potential equations for steady transonic flow over an airfoil at angle of attack illustrates the utility of the technique.

Martin, E. D.↗
NASA NTRS1989

Numerical algorithms for steady and unsteady incompressible Navier-Stokes equations

The numerical analysis of the incompressible Navier-Stokes equations are becoming important tools in the understanding of some fluid flow problems which are encountered in research as well as in industry. With the advent of the supercomputers, more realistic problems can be studied with a wider choice of numerical algorithms. An alternative formulation is presented for viscous incompressible flows. The incompressible Navier-Stokes equations are cast in a velocity/vorticity formulation. This formulation consists of solving the Poisson equations for the velocity components and the vorticity transport equation. Two numerical algorithms for the steady two-dimensional laminar flows are presented. The first method is based on the actual partial differential equations. This uses a finite-difference approximation of the governing equations on a staggered grid. The second method uses a finite element discretization with the vorticity transport equation approximated using a Galerkin approximation and the Poisson equations are obtained using a least squares method. The equations are solved efficiently using Newton's method and a banded direct matrix solver (LINPACK). The method is extended to steady three-dimensional laminar flows and applied to a cubic driven cavity using finite difference schemes and a staggered grid arrangement on a Cartesian mesh. The equations are solved iteratively using a plane zebra relaxation scheme. Currently, a two-dimensional, unsteady algorithm is being developed using a generalized coordinate system. The equations are discretized using a finite-volume approach. This work will then be extended to three-dimensional flows.

Hafez, Mohammed↗
NASA NTRS1990

Computation of the unsteady facilitated transport of oxygen in hemoglobin

The transport of a reacting permeant diffusing through a thin membrane is extended to more realistic dissociation models. A new nonlinear analysis of the reaction-diffusion equations, using implicit finite-difference methods and direct block solvers, is used to study the limits of linearized and equilibrium theories. Computed curves of molecular oxygen permeating through hemoglobin solution are used to illustrate higher-order reaction models, the effect of concentration boundary layers at the membrane interfaces, and the transient buildup of oxygen flux.

Davis, Sanford↗
NASA NTRS1990

On the far-field stream function condition for two-dimensional incompressible flows

The present demonstration of the usefulness of the integral series expansion of the stream function as a far-field computational boundary condition shows the method to require only a 10-percent/time-step increase in computational effort over alternative boundary conditions, in the case of implementation of unsteady problems using a direct elliptic solver. So long as the vorticity was encompassed within the computational domain, the method proved sufficiently accurate to yield virtually identical results for two widely different domains. While the integral-series condition yielded the best results for periodic flow, the Neumann condition gave comparable accuracy with less computation time for the steady-flow case despite its inability to treat periodic flow with vortex shedding.

Sa, Jong-Youb↗
NASA NTRS1991

Shedding patterns of the near-wake vortices behind a circular cylinder

The unsteady incompressible Navier-Stokes equations have been accurately solved for the laminar flow past a circular cylinder in the Reynolds number range 50-200. A direct elliptic solver called the SEVP is used to rapidly advance the streamfunction in time, facilitating the overall convergence to the fully periodic or quasi-steady state. A new integral-series method is developed for the far-field streamfunction condition on a finite two-dimensional computational domain. The use of fourth-order Hermitain relations for the convection terms in the conservation-form vorticity transport equation has also contributed to the good comparison of the present results with the earlier experimental data. The vortex-shedding patterns visualized by the experimentalist are numerically reproduced here in the given Reynolds number range. Discussions that may be helpful in interpreting the behavior of the shedding frequency are presented in the main text.

Sa, Jong-Youb↗
NASA NTRS1992

Parallel computation in a three-dimensional elastic-plastic finite-element analysis

A CRAY parallel processing technique called autotasking was implemented in a three-dimensional elasto-plastic finite-element code. The technique was evaluated on two CRAY supercomputers, a CRAY 2 and a CRAY Y-MP. Autotasking was implemented in all major portions of the code, except the matrix equations solver. Compiler directives alone were not able to properly multitask the code; user-inserted directives were required to achieve better performance. It was noted that the connect time, rather than wall-clock time, was more appropriate to determine speedup in multiuser environments. For a typical example problem, a speedup of 2.1 (1.8 when the solution time was included) was achieved in a dedicated environment and 1.7 (1.6 with solution time) in a multiuser environment on a four-processor CRAY 2 supercomputer. The speedup on a three-processor CRAY Y-MP was about 2.4 (2.0 with solution time) in a multiuser environment.

Shivakumar, K. N.↗
NASA NTRS1999

The Thin Oil Film Equation

A thin film of oil on a surface responds primarily to the wall shear stress generated on that surface by a three-dimensional flow. The oil film is also subject to wall pressure gradients, surface tension effects and gravity. The partial differential equation governing the oil film flow is shown to be related to Burgers' equation. Analytical and numerical methods for solving the thin oil film equation are presented. A direct numerical solver is developed where the wall shear stress variation on the surface is known and which solves for the oil film thickness spatial and time variation on the surface. An inverse numerical solver is also developed where the oil film thickness spatial variation over the surface at two discrete times is known and which solves for the wall shear stress variation over the test surface. A One-Time-Level inverse solver is also demonstrated. The inverse numerical solver provides a mathematically rigorous basis for an improved form of a wall shear stress instrument suitable for application to complex three-dimensional flows. To demonstrate the complexity of flows for which these oil film methods are now suitable, extensive examination is accomplished for these analytical and numerical methods as applied to a thin oil film in the vicinity of a three-dimensional saddle of separation.

Brown, James L.↗
NASA NTRS2015

Comprehensive Thematic T-Matrix Reference Database: A 2014-2015 Update

The T-matrix method is one of the most versatile and efficient direct computer solvers of the macroscopic Maxwell equations and is widely used for the computation of electromagnetic scattering by single and composite particles, discrete random media, and particles in the vicinity of an interface separating two half-spaces with different refractive indices. This paper is the seventh update to the comprehensive thematic database of peer-reviewed T-matrix publications initiated by us in 2004 and includes relevant publications that have appeared since 2013. It also lists a number of earlier publications overlooked previously.

electromagnetic scattering↗
NASA NTRS2017

Modeling of Electromagnetic Scattering by Discrete and Discretely Heterogeneous Random Media by Using Numerically Exact Solutions of the Maxwell Equations

In this paper, we discuss some aspects of numerical modeling of electromagnetic scattering by discrete random medium by using numerically exact solutions of the macroscopic Maxwell equations. Typical examples of such media are clouds of interstellar dust, clouds of interplanetary dust in the Solar system, dusty atmospheres of comets, particulate planetary rings, clouds in planetary atmospheres, aerosol particles with numerous inclusions and so on. Our study is based on the results of extensive computations of different characteristics of electromagnetic scattering obtained by using the superposition T-matrix method which represents a direct computer solver of the macroscopic Maxwell equations for an arbitrary multisphere configuration. As a result, in particular, we clarify the range of applicability of the low-density theories of radiative transfer and coherent backscattering as well as of widely used effective-medium approximations.

Dlugach, Janna M.↗
NASA NTRS1993

Application of fast Fourier transforms to the direct solution of a class of two-dimensional separable elliptic equations on the sphere

An efficient, direct, second-order solver for the discrete solution of a class of two-dimensional separable elliptic equations on the sphere (which generally arise in implicit and semi-implicit atmospheric models) is presented. The method involves a Fourier transformation in longitude and a direct solution of the resulting coupled second-order finite-difference equations in latitude. The solver is made efficient by vectorizing over longitudinal wave-number and by using a vectorized fast Fourier transform routine. It is evaluated using a prescribed solution method and compared with a multigrid solver and the standard direct solver from FISHPAK.

Moorthi, Shrinivas↗
NASA NTRS2016

Overview of the CHarring Ablator Response (CHAR) Code

An overview of the capabilities of the CHarring Ablator Response (CHAR) code is presented. CHAR is a one-, two-, and three-dimensional unstructured continuous Galerkin finite-element heat conduction and ablation solver with both direct and inverse modes. Additionally, CHAR includes a coupled linear thermoelastic solver for determination of internal stresses induced from the temperature field and surface loading. Background on the development process, governing equations, material models, discretization techniques, and numerical methods is provided. Special focus is put on the available boundary conditions including thermochemical ablation, surface-to-surface radiation exchange, and flowfield coupling. Finally, a discussion of ongoing development efforts is presented.

Amar, Adam J.↗
NASA NTRS2016

Overview of the CHarring Ablator Response (CHAR) Code

An overview of the capabilities of the CHarring Ablator Response (CHAR) code is presented. CHAR is a one-, two-, and three-dimensional unstructured continuous Galerkin finite-element heat conduction and ablation solver with both direct and inverse modes. Additionally, CHAR includes a coupled linear thermoelastic solver for determination of internal stresses induced from the temperature field and surface loading. Background on the development process, governing equations, material models, discretization techniques, and numerical methods is provided. Special focus is put on the available boundary conditions including thermochemical ablation and contact interfaces, and example simulations are included. Finally, a discussion of ongoing development efforts is presented.

Amar, Adam J.↗
DOE OSTI2025

Ipopt Interface to Re::Solve Linear Solver

The software provides Ipopt optimization package an interface to the Re::Solve linear solver library. Re::Solve features GPU-resident direct and iterative linear solvers that could be used to accelerate optimization computations.

Alam, Maksudul [Oak Ridge National Laboratory (ORN↗
DOE OSTI2026

Scientific Core Library Stack (SCLS) v2026

SCLS (Scientific Core Library Stack) is an opinionated build and packaging system for scientific computing libraries developed at Lawrence Berkeley National Laboratory. It produces a coherent, reproducible stack of numerical libraries — including BLAS/LAPACK, MPI, sparse direct and iterative solvers, graph partitioners, and parallel I/O libraries (e.g., PETSc, SLEPc, HDF5, NetCDF, MUMPS, OpenBLAS) — that work together without manual repair by downstream scientific software. From a single recipe-and-flavor model, SCLS produces native RPM packages for RHEL-family Linux, DEB packages for Debian/Ubuntu, direct Unix-style prefix installs for HPC and locked-down environments, and native macOS builds. Multiple build "flavors" (e.g., GCC+OpenBLAS, GCC+MKL, Intel+MKL, debug) coexist in distinct prefixes on the same host. Compared to general-purpose meta-build frameworks, SCLS is deliberately curated rather than infinitely configurable. It enforces deterministic, audit-friendly behavior: explicit build dependencies, no silent feature autodetection, a clear open-source license policy, and rpath-based runtime linkage so installs integrate cleanly with standard package-manager workflows.

Messe, Christian [Lawrence Berkeley National Labor↗