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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Randomized Adiabatic Quantum Linear Solver Algorithm with Optimal Complexity Scaling and Detailed Running Costs

Solving linear systems of equations is a fundamental problem with a wide variety of applications across many fields of science, and there is increasing effort to develop quantum linear solver algorithms. Subaşı et al. [Phys. Rev. Lett. 122, 060504 (2019)] proposed a randomized algorithm inspired by adiabatic quantum computing, based on a sequence of random Hamiltonian simulation steps, with suboptimal scaling in the condition number 𝜅 of the linear system and the target error 𝜖. Here we go beyond these results in several ways. Firstly, using filtering [Lin and Tong, Quantum 4, 361 (2020)] and Poissonization techniques [Cunningham and Roland, ArXiv:2406.03972 (2024)], the algorithm complexity is improved to the optimal scaling 𝑂⁡(𝜅⁢log (1/𝜖))—an exponential improvement in 𝜖, and a shaving of a log 𝜅 scaling factor in 𝜅. Secondly, the algorithm is further modified to achieve constant factor improvements, which are vital as we progress towards hardware implementations on fault-tolerant devices. We introduce a cheaper randomized walk operator method replacing Hamiltonian simulation—which also removes the need for potentially challenging classical precomputations; randomized routines are sampled over optimized random variables; circuit constructions are improved. We obtain a closed formula rigorously upper bounding the expected number of times one needs to apply a block-encoding of the linear system matrix to output a quantum state encoding the solution to the linear system. The upper bound is 837⁢𝜅 at 𝜖 = 10 −10 for Hermitian matrices.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1965

Linear feedback guidance

Determination of closed loop guidance function with linear, time-variable feedback studied by behavior of motion equations

FEEDBACK↗
NASA NTRS1996

Multigrid Methods for Fully Implicit Oil Reservoir Simulation

In this paper we consider the simultaneous flow of oil and water in reservoir rock. This displacement process is modeled by two basic equations: the material balance or continuity equations and the equation of motion (Darcy's law). For the numerical solution of this system of nonlinear partial differential equations there are two approaches: the fully implicit or simultaneous solution method and the sequential solution method. In the sequential solution method the system of partial differential equations is manipulated to give an elliptic pressure equation and a hyperbolic (or parabolic) saturation equation. In the IMPES approach the pressure equation is first solved, using values for the saturation from the previous time level. Next the saturations are updated by some explicit time stepping method; this implies that the method is only conditionally stable. For the numerical solution of the linear, elliptic pressure equation multigrid methods have become an accepted technique. On the other hand, the fully implicit method is unconditionally stable, but it has the disadvantage that in every time step a large system of nonlinear algebraic equations has to be solved. The most time-consuming part of any fully implicit reservoir simulator is the solution of this large system of equations. Usually this is done by Newton's method. The resulting systems of linear equations are then either solved by a direct method or by some conjugate gradient type method. In this paper we consider the possibility of applying multigrid methods for the iterative solution of the systems of nonlinear equations. There are two ways of using multigrid for this job: either we use a nonlinear multigrid method or we use a linear multigrid method to deal with the linear systems that arise in Newton's method. So far only a few authors have reported on the use of multigrid methods for fully implicit simulations. Two-level FAS algorithm is presented for the black-oil equations, and linear multigrid for two-phase flow problems with strong heterogeneities and anisotropies is studied. Here we consider both possibilities. Moreover we present a novel way for constructing the coarse grid correction operator in linear multigrid algorithms. This approach has the advantage in that it preserves the sparsity pattern of the fine grid matrix and it can be extended to systems of equations in a straightforward manner. We compare the linear and nonlinear multigrid algorithms by means of a numerical experiment.

Molenaar, J.↗
NASA NTRS2001

The Detection of Radiated Modes from Ducted Fan Engines

The bypass duct of an aircraft engine is a low-pass filter allowing some spinning modes to radiate outside the duct. The knowledge of the radiated modes can help in noise reduction, as well as the diagnosis of noise generation mechanisms inside the duct. We propose a nonintrusive technique using a circular microphone array outside the engine measuring the complex noise spectrum on an arc of a circle. The array is placed at various axial distances from the inlet or the exhaust of the engine. Using a model of noise radiation from the duct, an overdetermined system of linear equations is constructed for the complex amplitudes of the radial modes for a fixed circumferential mode. This system of linear equations is generally singular, indicating that the problem is illposed. Tikhonov regularization is employed to solve this system of equations for the unknown amplitudes of the radiated modes. An application of our mode detection technique using measured acoustic data from a circular microphone array is presented. We show that this technique can reliably detect radiated modes with the possible exception of modes very close to cut-off.

Farassat, F.↗
DOE OSTI2023

Sensitivity analysis of a layered piezoelectric system using ZFEM

The complex variable finite element method (ZFEM) is a numerical technique which aims to find the partial derivatives of the independent variables with respect to variation in dependent parameters declared in the physics. This is done by combining the complex Taylor series expansion within the weak formulation of the governing equation in a coupled system of linear equations forming a complex valued block matrix given by the Cauchy–Riemann matrix representation. In this work, two-dimensional linear first-order elements have been implemented in ZFEM to predict the design derivatives of the mechanical displacement field and the voltage potential field for a layered piezoelectric system in a steady-state study with Dirichlet boundary condition applied at the top and bottom edges of the geometry. This approach allows the standard FEM solution to quantify the sensitivity of the mechanical displacement and voltage potential fields with respect to small variations in the material properties through the information obtained from the computation of the derivatives. The domain is formed by a layered body with PZT-4 and PZT-5 stacked together. For result verification, the numerical solution obtained with ZFEM was compared to results from a commercial FEM package and the solution from the imaginary part was compared to the exact solution of a well-known benchmark problem. In conclusion, comparison of the results showed good agreement for both the real and imaginary parts of the solution and the largest sensitivities were found in PZT-5 specifically in C 13 , C 33 , and ε 33 .

42 ENGINEERING↗
NASA NTRS1996

Scalable Solutions to Integral Equation and Finite Element Simulations

The application of advanced computer architecture and software to a broad range of electromagnetic problems had allowed more accurate simulations of electrically larger and more complex components and systems...This paper overviews solutions to Maxwell's equations implicitly defined through systems of linear equations.

parallel↗
NASA NTRS1982

Burgers approximation for two-dimensional flow past an ellipse

A linearization of the Navier-Stokes equation due to Burgers in which vorticity is transported by the velocity field corresponding to continuous potential flow is examined. The governing equations are solved exactly for the two dimensional steady flow past an ellipse of arbitrary aspect ratio. The requirement of no slip along the surface of the ellipse results in an infinite algebraic system of linear equations for coefficients appearing in the solution. The system is truncated at a point which gives reliable results for Reynolds numbers R in the range 0 R 5. Predictions of the Burgers approximation regarding separation, drag and boundary layer behavior are investigated. In particular, Burgers linearization gives drag coefficients which are closer to observed experimental values than those obtained from Oseen's approximation. In the special case of flow past a circular cylinder, Burgers approximation predicts a boundary layer whose thickness is roughly proportional to R-1/2.

Dorrepaal, J. M.↗
NASA NTRS1977

Dynamic model for an instrument pointing system

The instrument pointing system concept discussed in the present paper was developed for Spacelab missions. The system is mounted on soft shockmounts to minimize Shuttle disturbances (such as man motion, thruster firings, etc.) and to reduce the effect of large center of mass offsets between the instrument and the pointing system gimbal axes. The instrument pointing system is soft mounted to the Spacelab pallet located in the Orbiter payload bay. The nonlinear model, incorporating the dynamic equations of motion, the controller equations and the definition of sensor dynamics and gimbal bearing friction, is given, along with a system of linearized equations of motion of the Space Shuttle Orbiter and instrument pointing system (linearized model).

Howell, J. T.↗
NASA NTRS1984

Parallel triangularization of substructured finite element problems

Much of the computational effort of the finite element process involves the solution of a system of linear equations. The coefficient matrix of this system, known as the global stiffness matrix, is symmetric, positive definite, and generally sparse. An important technique for reducing the time required to solve this system is substructuring or matrix partitioning. Substructuring is based on the idea of dividing a structure into pieces, each of which can then be analyzed relatively indepenently. As a result of this division, each point in the finite element discretization is either interior to a substructure or on a boundary between substructures. Contributions to the global stiffness matrix from connections between boundary points from the K(bb) matrix are reported. The triangularization of a general K(bb) matrix on a parallel machine is specifically discussed.

Leuze, M. R.↗
NASA NTRS1996

Multigrid and Krylov Subspace Methods for the Discrete Stokes Equations

Discretization of the Stokes equations produces a symmetric indefinite system of linear equations. For stable discretizations, a variety of numerical methods have been proposed that have rates of convergence independent of the mesh size used in the discretization. In this paper, we compare the performance of four such methods: variants of the Uzawa, preconditioned conjugate gradient, preconditioned conjugate residual, and multigrid methods, for solving several two-dimensional model problems. The results indicate that where it is applicable, multigrid with smoothing based on incomplete factorization is more efficient than the other methods, but typically by no more than a factor of two. The conjugate residual method has the advantage of being both independent of iteration parameters and widely applicable.

Elman, Howard C.↗
DOE OSTI2022

On the Convergence of Inexact Predictor-Corrector Methods for Linear Programming

Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear system of equations at each iteration. In common applications of linear programming, particularly in machine learning and scientific computing, the size of this linear system can become prohibitively large, requiring the use of iterative solvers, which provide an approximate solution to the linear system. However, approximately solving the linear system at each iteration of an IPM invalidates the theoretical guarantees of common IPM analyses. To remedy this, we theoretically and empirically analyze (slightly modified) predictor-corrector IPMs when using approximate linear solvers: our approach guarantees that, when certain conditions are satisfied, the number of IPM iterations does not increase and that the final solution remains feasible. We also provide practical instantiations of approximate linear solvers that satisfy these conditions for special classes of constraint matrices using randomized linear algebra.

Dexter, Gregory↗
NASA NTRS1993

Planar Cubics Through a Point in a Direction

It is shown that the planar cubics through three points and the associated tangent directions can be found by solving a cubic equation and a 2 x 2 system of linear equations. The result is combined with a previous published scheme to produce a better curve-fitting method.

Chou, J. J.↗
NASA NTRS1985

Burgers flow past an arbitrary ellipse

The two-dimensional steady flow past an ellipse of arbitrary aspect ratio is investigated analytically, applying a linearized version of the Navier-Stokes equation based on the approximation of Burgers (1928). The resulting infinite system of linear equations is truncated to give reliable results for Reynolds numbers between zero and five, and separation, drag, and boundary-layer phenomena are characterized and illustrated with graphs. The Burgers approximation is found to provide good qualitative results near the ellipse, with reasonable quantitative accuracy for the special case of a circular cylinder.

Dorrepaal, J. M.↗
DOE OSTI2020

Optimizing the hypre solver for manycore and GPU architectures

The solution of large-scale combustion problems with codes such as Uintah on modern computer architectures requires the use of multithreading and GPUs to achieve performance. Uintah uses a low-Mach number approximation that requires iteratively solving a large system of linear equations. The Hypre iterative solver has solved such systems in a scalable way for Uintah, but the use of OpenMP with Hypre leads to at least slowdown due to OpenMP overheads. The proposed solution uses the MPI Endpoints within Hypre, where each team of threads acts as a different MPI rank. This approach minimizes OpenMP synchronization overhead and performs as fast or (up to 1.44) faster than Hypre's MPI-only version, and allows the rest of Uintah to be optimized using OpenMP. The profiling of the GPU version of Hypre shows the bottleneck to be the launch overhead of thousands of micro-kernels. The GPU performance was improved by fusing these micro-kernels and was further optimized by using Cuda-aware MPI, resulting in an overall speedup of 1.16—1.44 compared to the baseline GPU implementation. The above optimization strategies were published in the International Conference on Computational Science 2020 [1]. This work extends the previously published research by carrying out the second phase of communication-centered optimizations in Hypre to improve its scalability on large-scale supercomputers. Additionally, this includes an efficient non-blocking inter-thread communication scheme, communication-reducing patch assignment, and expression of logical communication parallelism to a new version of the MPICH library that utilizes the underlying network parallelism [2]. The above optimizations avoid communication bottlenecks previously observed during strong scaling and improve performance by up to 2 on 256 nodes of Intel Knight's Landing processor.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Simulation of an inductively coupled plasma with a two-dimensional Darwin particle-in-cell code

A two-dimensional particle-in-cell code for the simulation of low-frequency electromagnetic processes in laboratory plasmas has been developed. The code uses the Darwin method omitting the electromagnetic wave propagation. The Darwin method separates the electric field into solenoidal and irrotational parts. The solenoidal electric field is calculated with a new algorithm based on the equation for the electric field vorticity. The system of linear equations in the new algorithm is readily solved using a standard iterative method. The irrotational electric field is the electrostatic field calculated with the direct implicit algorithm. The code is verified by reproducing the two-stream instability, electron electromagnetic waves, and shear Alfvén waves. The code is applied to simulate an inductively coupled plasma with the driving current flowing around the plasma region. In this simulation, a ring of dense plasma forms at the initial stage but then the density becomes maximal in the center and decays monotonically toward the walls. The skin effect is in the transitional mode between local and non-local, and the electron velocity distribution function is non-Maxwellian.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗