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Results for “Preservation of linearity”

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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Noise in phase-preserving linear amplifiers

The purpose of a phase-preserving linear amplifier is to make a small signal larger, so that it can be perceived by instruments incapable of resolving the original signal, while sacrificing as little as possible in signal-to-noise. Quantum mechanics limits how well this can be done: the noise added by the amplifier, referred to the input, must be at least half a quantum at the operating frequency. This well-known quantum limit only constrains the second moments of the added noise. Here we provide the quantum constraints on the entire distribution of added noise: any phasepreserving linear amplifier is equivalent to a parametric amplifier with a physical state σ for the ancillary mode; σ determines the properties of the added noise.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

A linearity preserving nodal variation limiting algorithm for continuous Galerkin discretization of ideal MHD equations

A stabilized continuous Galerkin (CG) method for magnetohydrodynamics (MHD) is presented herein. Ideal, compressible inviscid MHD equations are discretized in space on unstructured meshes using piecewise linear or bilinear finite element bases to get a semi-discrete scheme. Stabilization is then introduced to the semi-discrete method in a strategy that follows the algebraic flux correction paradigm. This involves adding some artificial diffusion to the high order, semi-discrete method and mass lumping in the time derivative term. The result is a low order method that provides local extremum diminishing properties for hyperbolic systems. The difference between the low order method and the high order method is scaled element-wise using a limiter and added to the low order scheme. The limiter is solution dependent and computed via an iterative linearity preserving nodal variation limiting strategy. The stabilization also involves an optional consistent background high order dissipation that reduces phase errors. The resulting stabilized scheme is a semi-discrete method that can be applied to inviscid shock MHD problems and may be even extended to resistive and viscous MHD problems. To satisfy the divergence free constraint of the MHD equations, we add parabolic divergence cleaning to the system. Various time integration methods can be used to discretize the scheme in time. We demonstrate the robustness of the scheme by solving several shock MHD problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2004

Linearity-Preserving Limiters on Irregular Grids

This paper examines the behavior of flux and slope limiters on non-uniform grids in multiple dimensions. We note that on non-uniform grids the scalar formulation in standard use today sacrifices k-exactness, even for linear solutions, impacting both accuracy and convergence. We rewrite some well-known limiters in a n way to highlight their underlying symmetry, and use this to examine both traditional and novel limiter formulations. A consistent method of handling stretched meshes is developed, as is a new directional formulation in multiple dimensions for irregular grids. Results are presented demonstrating improved accuracy and convergence using a combination of model problems and complex three-dimensional examples.

Berger, Marsha↗
NASA NTRS2005

Analysis of Slope Limiters on Irregular Grids

This paper examines the behavior of flux and slope limiters on non-uniform grids in multiple dimensions. Many slope limiters in standard use do not preserve linear solutions on irregular grids impacting both accuracy and convergence. We rewrite some well-known limiters to highlight their underlying symmetry, and use this form to examine the proper - ties of both traditional and novel limiter formulations on non-uniform meshes. A consistent method of handling stretched meshes is developed which is both linearity preserving for arbitrary mesh stretchings and reduces to common limiters on uniform meshes. In multiple dimensions we analyze the monotonicity region of the gradient vector and show that the multidimensional limiting problem may be cast as the solution of a linear programming problem. For some special cases we present a new directional limiting formulation that preserves linear solutions in multiple dimensions on irregular grids. Computational results using model problems and complex three-dimensional examples are presented, demonstrating accuracy, monotonicity and robustness.

Berger, Marsha↗
DOE OSTI2022

A Note on the Effects of Linear Topology Preservation in Monte Carlo Simulations of Knotted Proteins

Monte Carlo simulations are a powerful technique and are widely used in different fields. When applied to complex molecular systems with long chains, such as those in synthetic polymers and proteins, they have the advantage of providing a fast and computationally efficient way to sample equilibrium ensembles and calculate thermodynamic and structural properties under desired conditions. Conformational Monte Carlo techniques employ a move set to perform the transitions in the simulation Markov chain. While accepted conformations must preserve the sequential bonding of the protein chain model and excluded volume among its units, the moves themselves may take the chain across itself. We call this a break in linear topology preservation. In this manuscript, we show, using simple protein models, that there is no difference in equilibrium properties calculated with a move set that preserves linear topology and one that does not. However, for complex structures, such as those of deeply knotted proteins, the preservation of linear topology provides correct equilibrium results but only after long relaxation. In any case, to analyze folding pathways, knotting mechanisms and folding kinetics, the preservation of linear topology may be an unavoidable requirement.

Especial, João N. C. (ORCID:0000000254765370)↗
DOE OSTI2012

Linear maps preserving maximal deviation and the Jordan structure of quantum systems

In the algebraic approach to quantum theory, a quantum observable is given by an element of a Jordan algebra and a state of the system is modelled by a normalized positive functional on the underlying algebra. Maximal deviation of a quantum observable is the largest statistical deviation one can obtain in a particular state of the system. The main result of the paper shows that each linear bijective transformation between JBW algebras preserving maximal deviations is formed by a Jordan isomorphism or a minus Jordan isomorphism perturbed by a linear functional multiple of an identity. It shows that only one numerical statistical characteristic has the power to determine the Jordan algebraic structure completely. As a consequence, we obtain that only very special maps can preserve the diameter of the spectra of elements. Nonlinear maps preserving the pseudometric given by maximal deviation are also described. The results generalize hitherto known theorems on preservers of maximal deviation in the case of self-adjoint parts of von Neumann algebras proved by Molnar.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Optimization-based, property-preserving algorithm for passive tracer transport

Here we present a new optimization-based property-preserving algorithm for passive tracer transport. The algorithm utilizes a semi-Lagrangian approach based on incremental remapping of the mass and the total tracer. However, unlike traditional semi-Lagrangian schemes, which remap the density and the tracer mixing ratio through monotone reconstruction or flux correction, we utilize an optimization-based remapping that enforces conservation and local bounds as optimization constraints. In so doing we separate accuracy considerations from preservation of physical properties to obtain a conservative, second-order accurate transport scheme that also has a notion of optimality. Moreover, we prove that the optimization-based algorithm preserves linear relationships between tracer mixing ratios. We illustrate the properties of the new algorithm using a series of standard tracer transport test problems in a plane and on a sphere.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Security and Cloud Outsourcing Framework for Economic Dispatch

The computational complexity and problem sizes of power grid applications have increased significantly with the advent of renewable resources and smart grid technologies. The current paradigm of solving these issues consist of inhouse high performance computing infrastructures, which have drawbacks of high capital expenditures, maintenance, and limited scalability. Cloud computing is an ideal alternative due to its powerful computational capacity, rapid scalability, and high cost-effectiveness. A major challenge, however, remains in that the highly confidential grid data is susceptible for potential cyberattacks when outsourced to the cloud. In this work, a security and cloud outsourcing framework is developed for the Economic Dispatch (ED) linear programming application. As a result, the security framework transforms the ED linear program into a confidentiality-preserving linear program, that masks both the data and problem structure, thus enabling secure outsourcing to the cloud. Results show that for large grid test cases the performance gain and costs outperforms the in-house infrastructure.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

A new approach to enforcing discrete maximum principles in continuous Galerkin methods for convection-dominated transport equations

This work introduces a set of design principles and new algorithmic tools for enforcing maximum principles and/or positivity preservation in continuous finite element approximations to convection-dominated transport problems. Enabling a linear first-order advection equation as a model problem, we address the design of first-order artificial diffusion operators and their higherorder counterparts at the element matrix level. The proposed methodology leads to a nonlinear high-resolution scheme capable of resolving moving fronts and internal/boundary layers as sharp localized nonoscillatory features. The amount of numerical dissipation depends on the difference between the solution value at a given node and a local maximum or minimum. The shockcapturing numerical diffusion coefficient is designed to vanish as the nodal values approach a mass-weighted or linearity-preserving average. The universal applicability and simplicity of the element-based limiting procedure makes it an attractive alternative to edge-based algebraic flux correction.

Kuzmin, D.↗
DOE OSTI2022

Conservative remapping of material-dependent fields between possibly misaligned material regions

In this work, we propose an interpolation or remapping algorithm of material-dependent fields on polyhedral meshes where any source or target cell contains only one material. It is conservative and it preserves sharp material boundaries on the target mesh, even if the source and target regions delineating the same material are slightly misaligned. If those material regions are aligned, then the algorithm is also linearity-preserving and bounds-preserving. For a given material, it consists of a conservative field reconstruction on a target mesh part from a source mesh part associated with that material, followed by a repair step in case of misaligned boundaries. No assumption is made regarding the topology of the input meshes

36 MATERIALS SCIENCE↗
DOE OSTI2015

The terminator "toy" chemistry test: A simple tool to assess errors in transport schemes

This test extends the evaluation of transport schemes from prescribed advection of inert scalars to reactive species. The test consists of transporting two interacting chemical species in the Nair and Lauritzen 2-D idealized flow field. The sources and sinks for these two species are given by a simple, but non-linear, "toy" chemistry that represents combination (X+X → X 2 ) and dissociation (X 2 → X+X). This chemistry mimics photolysis-driven conditions near the solar terminator, where strong gradients in the spatial distribution of the species develop near its edge. Despite the large spatial variations in each species, the weighted sum X T = X+2X 2 should always be preserved at spatial scales at which molecular diffusion is excluded. The terminator test demonstrates how well the advection–transport scheme preserves linear correlations. Chemistry–transport (physics–dynamics) coupling can also be studied with this test. Examples of the consequences of this test are shown for illustration.

58 GEOSCIENCES↗
DOE OSTI2019

A Positive Asymptotic-Preserving Scheme for Linear Kinetic Transport Equations

We present a positive- and asymptotic-preserving numerical scheme for solving linear kinetic transport equations that relax to a diffusive equation in the limit of infinite scattering. The proposed scheme is developed using a standard spectral angular discretization and a classical micro-macro decomposition. The three main ingredients are a semi-implicit temporal discretization, a dedicated finite difference spatial discretization, and realizability limiters in the angular discretization. Under mild assumptions, the scheme becomes a consistent numerical discretization for the limiting diffusion equation when the scattering cross-section tends to infinity. The scheme also preserves positivity of the particle concentration on the space-time mesh and therefore fixes a common defect of spectral angular discretizations. The scheme is tested on the well-known line source benchmark problem with the usual uniform material medium as well as a medium composed of different materials that are arranged in a checkerboard pattern. We also tested the scheme on a Riemann problem with a nonuniform material medium. The observed order of space-time accuracy of the proposed scheme is reported.

nite difference methods↗
DOE OSTI2018

Local bounds preserving stabilization for continuous Galerkin discretization of hyperbolic systems

The objective of this paper is to present a local bounds preserving stabilized finite element scheme for hyperbolic systems on unstructured meshes based on continuous Galerkin (CG) discretization in space. A CG semi-discrete scheme with low order artificial dissipation that satisfies the local extremum diminishing (LED) condition for systems is used to discretize a system of conservation equations in space. The low order artificial diffusion is based on approximate Riemann solvers for hyperbolic conservation laws. In this case we consider both Rusanov and Roe artificial diffusion operators. In the Rusanov case, two designs are considered, a nodal based diffusion operator and a local projection stabilization operator. The result is a discretization that is LED and has first order convergence behavior. To achieve high resolution, limited antidiffusion is added back to the semi-discrete form where the limiter is constructed from a linearity preserving local projection stabilization operator. The procedure follows the algebraic flux correction procedure usually used in flux corrected transport algorithms. To further deal with phase errors (or terracing) common in FCT type methods, high order background dissipation is added to the antidiffusive correction. The resulting stabilized semi-discrete scheme can be discretized in time using a wide variety of time integrators. Numerical examples involving nonlinear scalar Burgers equation, and several shock hydrodynamics simulations for the Euler system are considered to demonstrate the performance of the method. In conclusion, for time discretization, Crank–Nicolson scheme and backward Euler scheme are utilized.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

A mesh partitioning algorithm for preserving spatial locality in arbitrary geometries

Highlights: •An algorithm for partitioning computational meshes is proposed. •The Morton order space-filling curve is modified to achieve improved locality. •A spatial locality metric is defined to compare results with existing approaches. •Results indicate improved performance of the algorithm in complex geometries. -- Abstract: A space-filling curve (SFC) is a proximity preserving linear mapping of any multi-dimensional space and is widely used as a clustering tool. Equi-sized partitioning of an SFC ignores the loss in clustering quality that occurs due to inaccuracies in the mapping. Often, this results in poor locality within partitions, especially for the conceptually simple, Morton order curves. We present a heuristic that improves partition locality in arbitrary geometries by slicing a Morton order curve at points where spatial locality is sacrificed. In addition, we develop algorithms that evenly distribute points to the extent possible while maintaining spatial locality. A metric is defined to estimate relative inter-partition contact as an indicator of communication in parallel computing architectures. Domain partitioning tests have been conducted on geometries relevant to turbulent reactive flow simulations. The results obtained highlight the performance of our method as an unsupervised and computationally inexpensive domain partitioning tool.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗