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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 145 records · Page 8

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NASA NTRS1991

Eigenvalue calculation procedure for an Euler/Navier-Stokes solver with application to flows over airfoils

A Lanczos procedure is presently applied to a Navier-Stokes (N-S) solver for eigenvalues and eigenvectors associated with the small-perturbation analysis of the N-S equations' finite-difference representation for airfoil flows; the matrix used is very large, sparse, real, and nonsymmetric. The Lanczos procedure is shown to furnish complete spectral information for the eigenvalues, as required for transient-stability analysis of N-S solvers.

Mahajan, Aparajit J.↗

DOE OSTI2021

Parallel Solver Framework for Mixed-Integer PDE-Constrained Optimization

ROL-PEBBL is a C++, MPI-based parallel code for mixed-integer PDE-constrained optimization (MIPDECO). In these problems we wish to optimize (control, design, etc.) physical systems, which must obey the laws of physics, when some of the decision variables must take integer values. ROL-PEBBL combines a code to efficiently search over integer choices (PEBBL = Parallel Enumeration Branch-and-Bound Library) and a code for efficient nonlinear optimization, including PDE-constrained optimization (ROL = Rapid Optimization Library). In this report, we summarize the design of ROL-PEBBL and initial applications/results. For an artificial source-inversion problem, finding sources of pollution on a grid from sparse samples, ROL-PEBBLs solution for the nest grid gave the best optimization guarantee for any general solver that gives both a solution and a quality guarantee.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1990

Optimal parallel solution of sparse triangular systems

A method for the parallel solution of triangular sets of equations is described that is appropriate when there are many right-handed sides. By preprocessing, the method can reduce the number of parallel steps required to solve Lx = b compared to parallel forward or backsolve. Applications are to iterative solvers with triangular preconditioners, to structural analysis, or to power systems applications, where there may be many right-handed sides (not all available a priori). The inverse of L is represented as a product of sparse triangular factors. The problem is to find a factored representation of this inverse of L with the smallest number of factors (or partitions), subject to the requirement that no new nonzero elements be created in the formation of these inverse factors. A method from an earlier reference is shown to solve this problem. This method is improved upon by constructing a permutation of the rows and columns of L that preserves triangularity and allow for the best possible such partition. A number of practical examples and algorithmic details are presented. The parallelism attainable is illustrated by means of elimination trees and clique trees.

Alvarado, Fernando L.↗

NASA NTRS1991

Iterative solution techniques in boundary element analysis

Iterative techniques for the solution of the algebraic equations associated with the direct boundary element analysis (BEA) method are discussed. Continuum structural response analysis problems are considered, employing single- and multizone boundary element models with and without zone condensation. The impact on convergence rate and computer resource requirements associated with the sparse and blocked matrices, resulting in multizone BEA, is studied. Both conjugate gradient and generalized minimum residual preconditioned iterative solvers are applied for these problems and the performance of these algorithms is reported. Included is a quantification of the impact of the preconditioning utilized to render the boundary element matrices solvable by the respective iterative methods in a time competitive with direct methods.

Kane, J. H.↗

NASA NTRS2025

Tutorial: MATLAB Implementation of a Successive Convexification Algorithm for 3 DoF Rocket Landings

The primary objective of this work is to fill in gaps and explore an alternate way of solving the 3 DoF rocket-powered landing problem presented in the 2016 AIAA paper by Szmuk, Ackimese, and Berning using successive convexification (SCvx). In the original paper, CVX, an automatic parsing package, was used to transcribe the high-level trajectory optimization problem into a format that could be read by a conic solver. The parsing step, generally computationally intensive, is hidden from the user. The use of CVX is sufficient for the generation of trajectories off-line due to the lack of runtime and flight software implementation constraints. For on-line applications, it is necessary to parse the problem for flight software implementation. References on hand-parsing powered descent guidance (PDG) problems are sparse. In this Tech Memo, the process of transcribing the 3 DoF PDG problem into the format required by MATLAB’s built-in second-order cone solver, coneprog.m, is presented in detail. Due to the abridged 3 DoF dynamics and the relatively simple nonlinearities, this reference is the natural starting point for anyone interested in grasping the concepts behind SCvx pertaining to PDG and the parsing step. Simulation results shown in this report were independently created by solving the problem using coneprog.m. The intent of this memo is to serve as a supplemental material to the original paper by breaking down the concept behind successive convexification and shed light into the parsing process. Readers are encouraged to first familiarize themselves with the material laid out in the original reference.

Alex Hayes↗

NASA NTRS1998

Parallel Implicit Algorithms for CFD

The main goal of this project was efficient distributed parallel and workstation cluster implementations of Newton-Krylov-Schwarz (NKS) solvers for implicit Computational Fluid Dynamics (CFD.) "Newton" refers to a quadratically convergent nonlinear iteration using gradient information based on the true residual, "Krylov" to an inner linear iteration that accesses the Jacobian matrix only through highly parallelizable sparse matrix-vector products, and "Schwarz" to a domain decomposition form of preconditioning the inner Krylov iterations with primarily neighbor-only exchange of data between the processors. Prior experience has established that Newton-Krylov methods are competitive solvers in the CFD context and that Krylov-Schwarz methods port well to distributed memory computers. The combination of the techniques into Newton-Krylov-Schwarz was implemented on 2D and 3D unstructured Euler codes on the parallel testbeds that used to be at LaRC and on several other parallel computers operated by other agencies or made available by the vendors. Early implementations were made directly in Massively Parallel Integration (MPI) with parallel solvers we adapted from legacy NASA codes and enhanced for full NKS functionality. Later implementations were made in the framework of the PETSC library from Argonne National Laboratory, which now includes pseudo-transient continuation Newton-Krylov-Schwarz solver capability (as a result of demands we made upon PETSC during our early porting experiences). A secondary project pursued with funding from this contract was parallel implicit solvers in acoustics, specifically in the Helmholtz formulation. A 2D acoustic inverse problem has been solved in parallel within the PETSC framework.

Keyes, David E.↗

DOE OSTI2025

Predicting Flow in Fracture Networks With Quantum Algorithms

Uncertainty quantification plays a crucial role in the modeling of subsurface flow. For instance, uncertainties in the properties of geologic fracture networks significantly impact flow, requiring numerous simulations to accurately estimate quantities of interest. However, each simulation is computationally expensive because it requires solving a large linear system to capture features that involve both small and large fractures. An example is in percolation, where the interaction of many small fractures (which cumulatively can have a large surface area) with the rock matrix must be modeled precisely. Quantum computing is an emerging tool with the potential to address this issue. Quantum algorithms offer a significant speedup in solving linear systems, achieving efficiencies that are challenging to match with classical approaches. These classical approaches include direct solvers, such as LU decomposition, and iterative methods, notably preconditioned conjugate gradient, commonly used in subsurface modeling to solve large sparse systems. However, applying quantum algorithms to geologic fracture flow requires careful attention to algorithmic and problem-specific constraints to fully realize this quantum advantage. In this work we describe a quantum algorithm for generalized Monte Carlo applications with a quadratic speedup over the classical approaches which can be combined with the quantum speedup, currently under investigation, for solving quantum linear systems for subsurface flow. We show that for quantum algorithms the computational cost of estimating a quantity of interest for a statistical ensemble of networks is roughly the same as that of a single realization, essentially implying that one can get uncertainty quantification for free.

58 GEOSCIENCES↗

NASA NTRS1989

Krylov methods preconditioned with incompletely factored matrices on the CM-2

The performance is measured of the components of the key interative kernel of a preconditioned Krylov space interative linear system solver. In some sense, these numbers can be regarded as best case timings for these kernels. Sweeps were timed over meshes, sparse triangular solves, and inner products on a large 3-D model problem over a cube shaped domain discretized with a seven point template. The performance of the CM-2 is highly dependent on the use of very specialized programs. These programs mapped a regular problem domain onto the processor topology in a careful manner and used the optimized local NEWS communications network. The rather dramatic deterioration in performance was documented when these ideal conditions no longer apply. A synthetic workload generator was developed to produce and solve a parameterized family of increasingly irregular problems.

Berryman, Harry↗

NASA NTRS1993

Determination of solid/porous wall boundary conditions from wind tunnel data for computational fluid dynamics codes

A computational and experimental study has been undertaken to investigate methods of modeling solid and porous wall boundary conditions in CFD codes. The procedure utilizes experimental measurements at the walls to develop a flow field solution based on the method of singularities. This flow field solution is then imposed as a boundary condition in a CFD simulation of the internal flow field. The effectiveness of this method in describing the boundary conditions at the wind tunnel walls using only sparse experimental measurements has been investigated. Verification of the approach using computational studies has been carried out using an incompressible flow solver. The current work demonstrates this technique for low speed flows and compares the result with experimental data obtained from a heavily instrumented variable porosity test section. Position and refinement of experimental measurements required to describe porous wall boundary conditions has also been considered for application to other porous wall wind tunnels.

Beutner, Thomas J.↗

NASA NTRS1994

Determination of solid/porous wall boundary conditions from wind tunnel data for computational fluid dynamics codes

A computational and experimental study has been undertaken to investigate methods of modelling solid and porous wall boundary conditions in computational fluid dynamics (CFD) codes. The procedure utilizes experimental measurements at the walls to develop a flow field solution based on the method of singularities. This flow field solution is then imposed as a pressure boundary condition in a CFD simulation of the internal flow field. The effectiveness of this method in describing the boundary conditions at the wind tunnel walls using only sparse experimental measurements has been investigated. Verification of the approach using computational studies has been carried out using an incompressible flow solver. The current work demonstrates this technique for low speed flows and compares the result with experimental data obtained from a heavily instrumented variable porosity test section. Position and refinement of experimental measurements required to describe porous wall boundary conditions have also been considered for application to other porous wall wind tunnels. The approach developed is simple, computationally inexpensive, and does not require extensive or intrusive measurements. It may be applied to both solid and porous wall wind tunnel tests. Some consideration is given to the extension of this method to three dimensions.

Beutner, Thomas J.↗

NASA NTRSDate not supplied

Component-Based Development of CFD Software FUN3D

FUN3D, a suite of Computational Fluid Dynamics simulation and design tools developed at the NASA Langley Research Center, has undergone continuous development since the late1980s. It contains a large portion of legacy code. Extending it with new capabilities becomes increasingly difficult. To improve the extensibility and reusability, FUN3D is moving toward component-based development. New features, such as Stabilized Finite Elements, Yoga, and Sparse Linear Algebra Toolkit, are integrated into the system as components. Some existing features such as the Node-Centered Finite Volume Solver, are also being refactored to components. The integration of these components poses new requirements on the development workflow. In this paper, we describe the Continuous Integration of FUN3D to support component-based development, and discuss the tools used, the practices followed, and lessons learned during the transition from the traditional approach.

computational fluid dynamics software↗

NASA NTRS1988

Domain decomposition methods for the parallel computation of reacting flows

Domain decomposition is a natural route to parallel computing for partial differential equation solvers. Subdomains of which the original domain of definition is comprised are assigned to independent processors at the price of periodic coordination between processors to compute global parameters and maintain the requisite degree of continuity of the solution at the subdomain interfaces. In the domain-decomposed solution of steady multidimensional systems of PDEs by finite difference methods using a pseudo-transient version of Newton iteration, the only portion of the computation which generally stands in the way of efficient parallelization is the solution of the large, sparse linear systems arising at each Newton step. For some Jacobian matrices drawn from an actual two-dimensional reacting flow problem, comparisons are made between relaxation-based linear solvers and also preconditioned iterative methods of Conjugate Gradient and Chebyshev type, focusing attention on both iteration count and global inner product count. The generalized minimum residual method with block-ILU preconditioning is judged the best serial method among those considered, and parallel numerical experiments on the Encore Multimax demonstrate for it approximately 10-fold speedup on 16 processors.

Keyes, David E.↗

DOE OSTI2020

GentenMPI: Distributed Memory Sparse Tensor Decomposition

GentenMPl is a toolkit of sparse canonical polyadic (CP) tensor decomposition algorithms that is designed to run effectively on distributed-memory high-performance computers. Its use of distributed-memory parallelism enables it to efficiently decompose tensors that are too large for a single compute node's memory. GentenMPl leverages Sandia's decades-long investment in the Trilinos solver framework for much of its parallel-computation capability. Trilinos contains numerical algorithms and linear algebra classes that have been optimized for parallel simulation of complex physical phenomena. This work applies these tools to the data science problem of sparse tensor decomposition. In this report, we describe the use of Trilinos in GentenMPl, extensions needed for sparse tensor decomposition, and implementations of the CP-ALS (CP via alternating least squares) and GCP-SGD (generalized CP via stochastic gradient descent) sparse tensor decomposition algorithms. We show that GentenMPl can decompose sparse tensors of extreme size, e.g., a 12.6-terabyte tensor on 8192 computer cores. We demonstrate that the Trilinos backbone provides good strong and weak scaling of the tensor decomposition algorithms.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Iterative methods in GPU-resident linear solvers for nonlinear constrained optimization

Linear solvers are major computational bottlenecks in a wide range of decision support and optimization computations. The challenges become even more pronounced on heterogeneous hardware, where traditional sparse numerical linear algebra methods are often inefficient. For example, methods for solving ill-conditioned linear systems have relied on conditional branching, which degrades performance on hardware accelerators such as graphical processing units (GPUs). To improve the efficiency of solving ill-conditioned systems, our computational strategy separates computations that are efficient on GPUs from those that need to run on traditional central processing units (CPUs). Our strategy maximizes the reuse of expensive CPU computations. Iterative methods, which thus far have not been broadly used for ill-conditioned linear systems, play an important role in our approach. In particular, we extend ideas from Arioli et al., (2007) to implement iterative refinement using inexact LU factors and flexible generalized minimal residual (FGMRES), with the aim of efficient performance on GPUs. In conclusion, we focus on solutions that are effective within broader application contexts, and discuss how early performance tests could be improved to be more predictive of the performance in a realistic environment.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

A nonhydrostatic formulation for MPAS-Ocean

The Model for Prediction Across Scales-Ocean (MPAS-Ocean) is an open-source, global ocean model and is one component of a family of climate models within the MPAS framework, including atmosphere, sea-ice, and land-ice models. Here, in this work, a new formulation for the ocean model is presented that solves the nonhydrostatic, incompressible Boussinesq equations on an unstructured, staggered, z-level grid. The introduction of this nonhydrostatic capability is necessary for the resolution of internal wave dynamics and large eddy simulations. Compared to the standard, hydrostatic formulation, a nonhydrostatic pressure solver and a vertical momentum equation are added, where the PETSc (Portable Extensible Toolkit for Scientific Computation) library is used for the inversion of a large sparse system for the nonhydrostatic pressure. Numerical results on a stratified seiche, internal solitary wave, overflow and lock-exchange test cases are presented, and the parallel efficiency of the code is evaluated using up to 1024 processors.

3D Poisson equation↗

DOE OSTI2025

A nonhydrostatic formulation for MPAS-Ocean

3D Poisson equation↗

DOE OSTI2020

Bayesian differential programming for robust systems identification under uncertainty

This paper presents a machine learning framework for Bayesian systems identification from noisy, sparse and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of recent developments in differentiable programming to propagate gradient information through ordinary differential equation solvers and perform Bayesian inference with respect to unknown model parameters using Hamiltonian Monte Carlo sampling. This allows an efficient inference of the posterior distributions over plausible models with quantified uncertainty, while the use of sparsity-promoting priors enables the discovery of interpretable and parsimonious representations for the underlying latent dynamics. A series of numerical studies is presented to demonstrate the effectiveness of the proposed methods, including nonlinear oscillators, predator–prey systems and examples from systems biology. Taken together, our findings put forth a flexible and robust workflow for data-driven model discovery under uncertainty. All codes and data accompanying this article are available at https://bit.ly/34FOJMj .

Science & Technology - Other Topics↗

DOE OSTI2020

Parameter Sensitivity Analysis of the SparTen High Performance Sparse Tensor Decomposition Software (Extended Analysis)

Tensor decomposition models play an increasingly important role in modern data science applications. One problem of particular interest is fitting a low-rank Canonical Polyadic (CP) tensor decomposition model when the tensor has sparse structure and the tensor elements are nonnegative count data. SparTen is a high-performance C++ library which computes a low-rank decomposition using different solvers: a first-order quasi-Newton or a second-order damped Newton method, along with the appropriate choice of runtime parameters. Since default parameters in SparTen are tuned to experimental results in prior published work on a single real-world dataset conducted using MATLAB implementations of these methods, it remains unclear if the parameter defaults in SparTen are appropriate for general tensor data. Furthermore, it is unknown how sensitive algorithm convergence is to changes in the input parameter values. This report addresses these unresolved issues with large-scale experimentation on three benchmark tensor data sets. Experiments were conducted on several different CPU architectures and replicated with many initial states to establish generalized profiles of algorithm convergence behavior.

97 MATHEMATICS AND COMPUTING↗