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Results for “lagrange interpolation”

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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6 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

A high-order computational framework for particle-resolved simulations of disperse multiphase flows

This work presents a high-order numerical approach for particle-resolved simulations of disperse multiphase flows, where the Navier-Stokes equations for fluid flow are solved using a high-order spectral element method in the Eulerian framework, and the particle phase is directly simulated with a discrete element method. The coupling between particles and fluids is explicitly handled using an adapted direct-forcing immersed boundary method. Unlike the conventional schemes, a high-order barycentric Lagrange interpolation method and a Gaussian projection kernel are used to ensure accurate momentum exchange between local boundary points and surrounding fluid nodes in the framework of high-order fluid solver. Benchmark tests of increasing complexity are conducted to demonstrate the accuracy and efficiency of our method. Here, it is found that our approach exhibits an excellent convergence performance, as the fluid element/grid is refined and the number of boundary points increases. Compared to conventional low-order methods, the proposed high-order framework enables the use of substantially larger fluid elements while maintaining high accuracy in modeling fluid-particle interactions, owing to the enhanced resolution of high-order basis functions. Moreover, since the primary unknowns are stored at element or grid nodes, the high-order approach offers improved efficiency in both CPU memory usage and total computational cost.

42 ENGINEERING↗
DOE OSTI2024

Simple and General Unitarity Conserving Numerical Real-Time Propagators of the Time-Dependent Schrödinger Equation Based on Magnus Expansion

Magnus expansion (ME) provides a general way to expand the real-time propagator of a time-dependent Hamiltonian within the exponential such that the unitarity is satisfied at any order. Here, we use this property and explicit integration of Lagrange interpolation formulas for the time-dependent Hamiltonian within each time interval and derive approximations that preserve unitarity for the differential time evolution operators of general time-dependent Hamiltonians. The resulting second-order approximation is the same as using the average of Hamiltonians for two end points of time. We identify three fourth-order approximations involving commutators of Hamiltonians at different times and also derive a sixth-order expression. A test of these approximations along with other available expressions for a two-state time-dependent Hamiltonian with sinusoidal time dependences provides information on the relative performance of these approximations and suggests that the derived expressions can serve as useful numerical tools for time evolution in time-resolved spectroscopy, quantum control, quantum sensing, real-time ab initio quantum dynamics, and open system quantum dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Quantum error mitigation by layerwise Richardson extrapolation

A widely used method for mitigating errors in noisy quantum computers is Richardson extrapolation, a technique in which the overall effect of noise on the estimation of quantum expectation values is captured by a single parameter that, after being scaled to larger values, is eventually extrapolated to the zero-noise limit. We generalize this approach by introducing layerwise Richardson extrapolation (LRE), an error mitigation protocol in which the noise of different individual layers (or larger chunks of the circuit) is amplified and the associated expectation values are linearly combined to estimate the zero-noise limit. The coefficients of the linear combination are analytically obtained from the theory of multivariate Lagrange interpolation. LRE leverages the flexible configurational space of layerwise unitary folding, allowing for a more nuanced mitigation of errors by treating the noise level of each layer of the quantum circuit as an independent variable. Furthermore, we provide numerical simulations demonstrating scenarios where LRE achieves superior performance compared to traditional (single-variable) Richardson extrapolation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Explicit Form for the Most General Lorentz Transformation Revisited

Explicit formulae for the 4×4 Lorentz transformation matrices corresponding to a pure boost and a pure three-dimensional rotation are very well known. Significantly less well known is the explicit formula for a general Lorentz transformation with arbitrary non-zero boost and rotation parameters. We revisit this more general formula by presenting two different derivations. The first derivation (which is somewhat simpler than previous ones appearing in the literature) evaluates the exponential of a 4×4 real matrix A, where A is a product of the diagonal matrix diag(+1,−1,−1,−1) and an arbitrary 4×4 real antisymmetric matrix. The formula for expA depends only on the eigenvalues of A and makes use of the Lagrange interpolating polynomial. The second derivation exploits the observation that the spinor product η†σ¯μχ transforms as a Lorentz four-vector, where χ and η are two-component spinors. The advantage of the latter derivation is that the corresponding formula for a general Lorentz transformation Λ reduces to the computation of the trace of a product of 2×2 matrices. Both computations are shown to yield equivalent expressions for Λ.

Science & Technology - Other Topics↗
DOE OSTI2023

Securely Aggregated Coded Matrix Inversion

Coded computing is a method for mitigating straggling workers in a centralized computing network, by using erasure-coding techniques. Federated learning is a decentralized model for training data distributed across client devices. In this work we propose approximating the inverse of an aggregated data matrix, where the data is generated by clients; similar to the federated learning paradigm, while also being resilient to stragglers. To do so, we propose a coded computing method based on gradient coding. We modify this method so that the coordinator does not access the local data at any point; while the clients access the aggregated matrix in order to complete their tasks. Here, the network we consider is not centrally administrated, and the communications which take place are secure against potential eavesdroppers.

97 MATHEMATICS AND COMPUTING↗