Remapping Through Direct Interpolation and Optimization for Finite Element ALE Hydrodynamics
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GMI-IPS: Python Processing Software for Aircraft Campaigns
NASA's Atmospheric Tomography Mission (ATom) seeks to understand the impact of anthropogenic air pollution on gases in the Earth's atmosphere. Four flight campaigns are being deployed on a seasonal basis to establish a continuous global-scale data set intended to improve the representation of chemically reactive gases in global atmospheric chemistry models. The Global Modeling Initiative (GMI), is creating chemical transport simulations on a global scale for each of the ATom flight campaigns. To meet the computational demands required to translate the GMI simulation data to grids associated with the flights from the ATom campaigns, the GMI ICARTT Processing Software (GMI-IPS) has been developed and is providing key functionality for data processing and analysis in this ongoing effort. The GMI-IPS is written in Python and provides computational kernels for data interpolation and visualization tasks on GMI simulation data. A key feature of the GMI-IPS, is its ability to read ICARTT files, a text-based file format for airborne instrument data, and extract the required flight information that defines regional and temporal grid parameters associated with an ATom flight. Perhaps most importantly, the GMI-IPS creates ICARTT files containing GMI simulated data, which are used in collaboration with ATom instrument teams and other modeling groups. The initial main task of the GMI-IPS is to interpolate GMI model data to the finer temporal resolution (1-10 seconds) of a given flight. The model data includes basic fields such as temperature and pressure, but the main focus of this effort is to provide species concentrations of chemical gases for ATom flights. The software, which uses parallel computation techniques for data intensive tasks, linearly interpolates each of the model fields to the time resolution of the flight. The temporally interpolated data is then saved to disk, and is used to create additional derived quantities. In order to translate the GMI model data to the spatial grid of the flight path as defined by the pressure, latitude, and longitude points at each flight time record, a weighted average is then calculated from the nearest neighbors in two dimensions (latitude, longitude). Using SciPya's Regular Grid Interpolator, interpolation functions are generated for the GMI model grid and the calculated weighted averages. The flight path points are then extracted from the ATom ICARTT instrument file, and are sent to the multi-dimensional interpolating functions to generate GMI field quantities along the spatial path of the flight. The interpolated field quantities are then written to a ICARTT data file, which is stored for further manipulation. The GMI-IPS is aware of a generic ATom ICARTT header format, containing basic information for all flight campaigns. The GMI-IPS includes logic to edit metadata for the derived field quantities, as well as modify the generic header data such as processing dates and associated instrument files. The ICARTT interpolated data is then appended to the modified header data, and the ICARTT processing is complete for the given flight and ready for collaboration. The output ICARTT data adheres to the ICARTT file format standards V1.1. The visualization component of the GMI-IPS uses Matplotlib extensively and has several functions ranging in complexity. First, it creates a model background curtain for the flight (time versus model eta levels) with the interpolated flight data superimposed on the curtain. Secondly, it creates a time-series plot of the interpolated flight data. Lastly, the visualization component creates averaged 2D model slices (longitude versus latitude) with overlaid flight track circles at key pressure levels. The GMI-IPS consists of a handful of classes and supporting functionality that have been generalized to be compatible with any ICARTT file that adheres to the base class definition. The base class represents a generic ICARTT entry, only defining a single time entry and 3D spatial positioning parameters. Other classes inherit from this base class; several classes for input ICARTT instrument files, which contain the necessary flight positioning information as a basis for data processing, as well as other classes for output ICARTT files, which contain the interpolated model data. Utility classes provide functionality for routine procedures such as: comparing field names among ICARTT files, reading ICARTT entries from a data file and storing them in data structures, and returning a reduced spatial grid based on a collection of ICARTT entries. Although the GMI-IPS is compatible with GMI model data, it can be adapted with reasonable effort for any simulation that creates Hierarchical Data Format (HDF) files. The same can be said of its adaptability to ICARTT files outside of the context of the ATom mission. The GMI-IPS contains just under 30,000 lines of code, eight classes, and a dozen drivers and utility programs. It is maintained with GIT source code management and has been used to deliver processed GMI model data for the ATom campaigns that have taken place to date.
Damon, M. R.↗
High-throughput computation of electric polarization in solids via Berry flux diagonalization
Electric polarization in the absence of an externally applied electric field is a key property of polar materials, but the standard interpolation-based ab initio approach to compute polarization differences within the modern theory of polarization presents challenges for automated high-throughput calculations. Berry flux diagonalization [J. Bonini et al., Phys. Rev. B 102, 045141 (2020)] has been proposed as an efficient and reliable alternative, though it has yet to be widely deployed. Here, we assess Berry flux diagonalization using ab initio calculations of a large set of materials, introducing and validating heuristics that ensure branch alignment with a minimal number of intermediate interpolated structures. Our automated implementation of Berry flux diagonalization succeeds in cases where prior interpolation-based workflows fail due to band-gap closures or branch ambiguities. Benchmarking with ab initio calculations of 176 candidate ferroelectrics, we demonstrate the efficacy of the approach on a broad range of insulating materials and obtain accurate effective polarization values with fewer interpolated structures than prior automated interpolation-based workflows. Our real-space heuristics that can predict gauge stability a priori from ionic displacements enable a general automated framework for reliable polarization calculations and efficient high-throughput screening of chemically and structurally diverse polar insulators. These results establish Berry flux diagonalization as a robust and efficient method to compute the effective polarization of solids and to accelerate the data-driven discovery of functional polar materials.
Poteshman, Abigail N. [University of Chicago, IL (↗
Resolution enhancement of ERTS imagery
A method is described for combined interpolation and enhancement of ERTS multispectral scanner data sets. Previous research has shown that good enhancement is most easily achieved when there are a large number of data points contained within the radius of gyration of the system point spread function. This requirement can be met using ERTS data by interpolating the data before enhancement. By varying the interpolation scale factor the data set can be empirically matched to a precalculated optimum restoration filter. Once the proper match of data and filter has been found the enhancement can be carried out directly or the enhancement and interpolation operations can be combined into a single filter thereby greatly reducing the processing time. Experimental results of applying this technique are shown along with more conventional methods of image interpolation and enlargement.
Mcgillem, C. D.↗
GRID2D/3D: A computer program for generating grid systems in complex-shaped two- and three-dimensional spatial domains. Part 2: User's manual and program listing
An efficient computer program, called GRID2D/3D, was developed to generate single and composite grid systems within geometrically complex two- and three-dimensional (2- and 3-D) spatial domains that can deform with time. GRID2D/3D generates single grid systems by using algebraic grid generation methods based on transfinite interpolation in which the distribution of grid points within the spatial domain is controlled by stretching functions. All single grid systems generated by GRID2D/3D can have grid lines that are continuous and differentiable everywhere up to the second-order. Also, grid lines can intersect boundaries of the spatial domain orthogonally. GRID2D/3D generates composite grid systems by patching together two or more single grid systems. The patching can be discontinuous or continuous. For continuous composite grid systems, the grid lines are continuous and differentiable everywhere up to the second-order except at interfaces where different single grid systems meet. At interfaces where different single grid systems meet, the grid lines are only differentiable up to the first-order. For 2-D spatial domains, the boundary curves are described by using either cubic or tension spline interpolation. For 3-D spatial domains, the boundary surfaces are described by using either linear Coon's interpolation, bi-hyperbolic spline interpolation, or a new technique referred to as 3-D bi-directional Hermite interpolation. Since grid systems generated by algebraic methods can have grid lines that overlap one another, GRID2D/3D contains a graphics package for evaluating the grid systems generated. With the graphics package, the user can generate grid systems in an interactive manner with the grid generation part of GRID2D/3D. GRID2D/3D is written in FORTRAN 77 and can be run on any IBM PC, XT, or AT compatible computer. In order to use GRID2D/3D on workstations or mainframe computers, some minor modifications must be made in the graphics part of the program; no modifications are needed in the grid generation part of the program. The theory and method used in GRID2D/3D is described.
Bailey, R. T.↗
GRID2D/3D: A computer program for generating grid systems in complex-shaped two- and three-dimensional spatial domains. Part 1: Theory and method
An efficient computer program, called GRID2D/3D was developed to generate single and composite grid systems within geometrically complex two- and three-dimensional (2- and 3-D) spatial domains that can deform with time. GRID2D/3D generates single grid systems by using algebraic grid generation methods based on transfinite interpolation in which the distribution of grid points within the spatial domain is controlled by stretching functions. All single grid systems generated by GRID2D/3D can have grid lines that are continuous and differentiable everywhere up to the second-order. Also, grid lines can intersect boundaries of the spatial domain orthogonally. GRID2D/3D generates composite grid systems by patching together two or more single grid systems. The patching can be discontinuous or continuous. For continuous composite grid systems, the grid lines are continuous and differentiable everywhere up to the second-order except at interfaces where different single grid systems meet. At interfaces where different single grid systems meet, the grid lines are only differentiable up to the first-order. For 2-D spatial domains, the boundary curves are described by using either cubic or tension spline interpolation. For 3-D spatial domains, the boundary surfaces are described by using either linear Coon's interpolation, bi-hyperbolic spline interpolation, or a new technique referred to as 3-D bi-directional Hermite interpolation. Since grid systems generated by algebraic methods can have grid lines that overlap one another, GRID2D/3D contains a graphics package for evaluating the grid systems generated. With the graphics package, the user can generate grid systems in an interactive manner with the grid generation part of GRID2D/3D. GRID2D/3D is written in FORTRAN 77 and can be run on any IBM PC, XT, or AT compatible computer. In order to use GRID2D/3D on workstations or mainframe computers, some minor modifications must be made in the graphics part of the program; no modifications are needed in the grid generation part of the program. This technical memorandum describes the theory and method used in GRID2D/3D.
Shih, T. I.-P.↗
A Streamlined Approach to Spatial Mapping of Complex 3D Thermal Boundary Condition Data
Spatial mapping of 1D, 2D, and particularly 3D thermal boundary condition data is essential for accurate thermal simulation of spacecraft and launch vehicles. This information typically is available in simple ASCII file format but can be problematic to use for thermal simulations. Difficulties that can be encountered include the ability to directly use the available file format, transformation of the data into the desired reference coordinate system in 3D space, and accurate interpolation of the data onto the thermal calculation domain. This paper presents a streamlined approach to spatial mapping of complex unsymmetrical 3D cold wall heat flux data using the fields’ capability in Simcenter3D. A recent example of 3D thermal plume simulation at MSFC will be employed to illustrate the use of text, csv, and Excel files, specifying coordinate systems for transformation of data in 3D space, and use of the various interpolation schemes available for spatial mapping. Spatial boundary condition verification is also very important, and the spacecraft thermal analyst needs effective visualization tools to develop confidence in the boundary condition definitions. Visualization of the spacecraft plume raw field data, the calculated field data, and the interpolated field data onto the thermal calculation domain will be discussed, with a particular focus on real-time viewing of the interpolated data for available interpolation schemes. The objective of this paper is to outline the modeling techniques used with the integrated thermal analysis of a terrestrial lunar lander demonstrator. Specifically, the techniques outlined herein focus on spatial mapping of convective and radiative exhaust plume results from a computational fluid dynamics (CFD) analysis. Two cases were investigated, however, the modeling techniques that were utilized translate to both cases seamlessly. Those two cases were as follows: • Lunar lander demonstrator firing on-pad (worst case). • Lunar lander demonstrator hovering at an elevated position above the launch pad. For the purposes of information control, this paper will focus on the modeling techniques only, using altered or dimensionless data where necessary. BACKGROUND The thermal model examined in this paper is of the lunar lander demonstrator known as XL-1T (terrestrial), born from a collaborative effort between Masten Space Systems (MSS) and NASA, under NASA’s Lunar CATALYST (also known as Lunar Cargo Transportation and Landing by Soft Touchdown) initiative. The lander is a reusable vertical takeoff/vertical landing (VTVL) test bed which is controlled by four throttleable main engines utilizing green hypergolic propellants.
Hawkins, Robert F.↗
Derivation of Effective Properties Based on Porous Scale Simulations Using Filtering Techniques
This study presents a method for derivation of effective properties at the interface and in-depth of porous materials. The method defines a Representative Elementary Volume (REV) and applies filtering techniques to computer effective properties such as porosity and flow quantities, such as velocity and pressure. The script, developed to process the data was tested on the VTK type files that contain the mesh information and the flow solution. The method allows to choose between two types of filters, such as cellular and top-hat and define the size of the REV and number of samples along the domain. Extraction of the REV from the domain is performed to exact boundaries requested for the user. This is done using a triangulation technique and cutting through the cells to comply to the requested boundaries of the volume. The method can be applied to both structured and unstructured meshes. Filtering the material porosity and flow quantities involves integration of the numerical data. The algorithm provides three integration methods, such as Riemann sum, Monte Carlo and Quadrature rule to perform the integration. The Monte-Carlo technique permits the use of either uniform or linearly spaced distribution of points. The Quadrature rule is currently applicable to tetrahedral element types. The Monte Carlo and Quadrature rule methods require interpolation of the flow quantities at the sample points. For interpolation, two methods were tested and are readily available, Gaussian interpolation and re-sampling. It has been shown that re-sampling method has better consistency and acceptable accuracy in interpolation of the data. The algorithm was written in Python language and uses a number of modules. The major module besides numpy is PyVista. It is used to process the computational domain, clip the REV and interpolate the data. Quadrature rule integration was performed using a quadpy module. ParaView software was used externally to convert the flow solution to the VTK (or more specifically VTU) format. Integration of ParaView in the same environment with PyVista encountered problems and could not be implemented in this work. The developed algorithm is expected to be applicable to unstructured meshes and more complex porous structures as soon as the data can be passed in VTK type format. With the report is provided Python script for filtering the solution and a Matlab script for simple generation and processing of 2-D and 3-D porous channel geometries. The two scripts don't communicate.
Alexsander Zibitsker↗
Magnetic Mapping in the Inner Magnetosphere using Kamodo
Many models require specialized access and interpolation schemes to effectively extract and interpolate their outputs. In particular, the Block-Adaptive Tree Solarwind Roe Upwind Scheme (BATSRUS) component of the Space Weather Modeling Framework (SWMF) requires Kamodo to take advantage of its block-based adaptive grid structure, and the Lyon-Fedder Mobarry magnetosphere model (or its successor GAMERA) needs a scheme that appreciates the distorted spherical arrangement of grid vertices on a non-orthogonal grid. With the flythrough layer developed by Ringuette et al. (SH42E-2337), the underlying model readers have been adapted to use multiple time steps in a single Python session to perform 4- dimensional interpolations in time and space. Kamodo now utilizes lazy interpolation that loads data only when needed. We present the successful integration of SWMF/BATSRUS magnetosphere access and interpolation into the new 4D Kamodo framework utilizing an external library of C code. Through function composition, Kamodo facilitates the calculation of derived quantities and the transformation of positions and vectors into different coordinate systems. This work is a significant step towards performing field line tracing in Kamodo with SWMF magnetosphere outputs.
Lutz Rastaetter↗
Arc Jet Facility Test Condition Predictions Using the ADSI Code
The Aerothermal Design Space Interpolation (ADSI) tool is used to interpolate databases of previously computed computational fluid dynamic solutions for test articles in a NASA Ames arc jet facility. The arc jet databases are generated using an Navier-Stokes flow solver using previously determined best practices. The arc jet mass flow rates and arc currents used to discretize the database are chosen to span the operating conditions possible in the arc jet, and are based on previous arc jet experimental conditions where possible. The ADSI code is a database interpolation, manipulation, and examination tool that can be used to estimate the stagnation point pressure and heating rate for user-specified values of arc jet mass flow rate and arc current. The interpolation is performed in the other direction (predicting mass flow and current to achieve a desired stagnation point pressure and heating rate). ADSI is also used to generate 2-D response surfaces of stagnation point pressure and heating rate as a function of mass flow rate and arc current (or vice versa). Arc jet test data is used to assess the predictive capability of the ADSI code.
fluid dynamics↗
On the applicability of the Redlich-Kister framework for viscosity estimation of molten halide salt mixtures
For molten halide salt mixtures already being utilized or under consideration for carbon-free energy production systems, it is crucial that their viscosity is well understood so that system thermal hydraulics can be reliably assessed. Because of the difficulty in accurately measuring molten halide viscosity and the sheer size of the matrix of possible higher order salt mixtures that may be of interest to the energy industry, there are several gaps in the quantified understanding of molten halide viscosity across this matrix. As such, both first-principles and semi-empirical modeling techniques may be crucial for rapidly assessing this broad, complex compositional domain. Herein, the Redlich-Kister framework is applied to assess the feasibility of broadly interpolating and estimating the viscosity of several pseudobinary and pseudoternary molten halide salt systems that may be of key interest to the energy industry. The framework is based on the assumption that an ideal component and a nonideal component collectively describe the viscosity as a function of composition and temperature for a given molten halide system. Three different ideal models were considered for the ideal component, including Grunburg-Nissan, Katti-Chaudhri, and Gambill methods. Regarding the pseudobinary interpolations, the Redlich-Kister models with either the Grunburg-Nissan or Katti-Chaudhri models as the ideal component resulted in either highly (average error less than 5%) or reasonably (average error less than 15%) accurate interpolations of pseudobinary halide viscosity; BeF 2 - or UF 4 -bearing salts tended to result in reasonably accurate interpolations, whereas other pseudobinary mixtures tended to show high accuracy. Regarding the pseudoternary extrapolations, the Redlich-Kister framework shows reasonable success at estimating the extent to which a pseudoternary system may indicate deviations from ideal Grunburg-Nissan mixing, where discrepancies with comparative experimental data generally stay within 30%. Finally, the primary reasons identified for such discrepancies are (1) inaccuracy in the underlying experimental data, (2) different complexation behavior in the higher order systems compared to the pseudobinary subsystems, and (3) extrapolation into temperatures too far out of the domain, which is valid for the underlying experimental data feeding the Redlich-Kister model.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Collocation methods for nonlinear differential equations on low-rank manifolds
We introduce new methods for integrating nonlinear differential equations on low-rank manifolds. These methods rely on interpolatory projections onto the tangent space, enabling low-rank time integration of vector fields that can be evaluated entry-wise. A key advantage of our approach is that it does not require the vector field to exhibit low-rank structure, thereby overcoming significant limitations of traditional dynamical low-rank methods based on orthogonal projection. To construct the interpolatory projectors, we develop a sparse tensor sampling algorithm based on the discrete empirical interpolation method (DEIM) that parameterizes tensor train manifolds and their tangent spaces with cross interpolation. Using these projectors, we propose two time integration schemes on low-rank tensor train manifolds. The first scheme integrates the solution at selected interpolation indices and constructs the solution with cross interpolation. The second scheme generalizes the well-known orthogonal projector-splitting integrator to interpolatory projectors. We demonstrate the proposed methods with applications to several tensor differential equations arising from the discretization of partial differential equations.
97 MATHEMATICS AND COMPUTING↗
A kinetic-based regularization method for data science applications
We propose a physics-based regularization technique for function learning, inspired by statistical mechanics. By drawing an analogy between optimizing the parameters of an interpolator and minimizing the energy of a system, we introduce corrections that impose constraints on the lower-order moments of the data distribution. This minimizes the discrepancy between the discrete and continuum representations of the data, in turn allowing to access more favorable energy landscapes, thus improving the accuracy of the interpolator. Our approach improves performance in both interpolation and regression tasks, even in high-dimensional spaces. Unlike traditional methods, it does not require empirical parameter tuning, making it particularly effective for handling noisy data. We also show that thanks to its local nature, the method offers computational and memory efficiency advantages over Radial Basis Function interpolators, especially for large datasets.
97 MATHEMATICS AND COMPUTING↗
Exponentially Reduced Circuit Depths Using Trotter Error Mitigation
Product formulas are a popular class of digital quantum simulation algorithms due to their conceptual simplicity, low overhead, and performance, which often exceeds theoretical expectations. Recently, Richardson extrapolation and polynomial interpolation have been proposed to mitigate the Trotter error incurred by the use of these formulas. This work provides a rigorous, general analysis of these techniques for computing time-evolved observables, simplifying the interpolation algorithm in the process, and shows that extrapolation generically improves the performance of product formulas for this task. We demonstrate that, to achieve error 𝜖 in a simulation of time 𝑇 using a 𝑝 th-order product formula with extrapolation, circuit depths of 𝑂(𝑇 1+1/𝑝 polylog (1/𝜖)) are sufficient—an exponential improvement in the precision over product formulas alone. Furthermore, we prove that these algorithms achieve commutator scaling, and improve the 𝑇 complexity for the interpolation algorithm. By relaxing the requirement of performing exact Chebyshev interpolation, our simplified algorithm eliminates the need for fractional implementations of Trotter steps, reducing computational overhead. Finally, we show these techniques can be combined with the classical shadows method to estimate many time-evolved local observables. Taken together, our findings provide the strongest evidence yet for the utility of Trotter error-mitigation techniques in algorithmic applications.
quantum algorithms & computation↗
An objective isobaric/isentropic technique for upper air analysis
An objective meteorological analysis technique is presented whereby both horizontal and vertical upper air analyses are performed. The process used to interpolate grid-point values from the upper-air station data is the same as for grid points on both an isobaric surface and a vertical cross-sectional plane. The nearby data surrounding each grid point are used in the interpolation by means of an anisotropic weighting scheme, which is described. The interpolation for a grid-point potential temperature is performed isobarically; whereas wind, mixing-ratio, and pressure height values are interpolated from data that lie on the isentropic surface that passes through the grid point. Two versions (A and B) of the technique are evaluated by qualitatively comparing computer analyses with subjective handdrawn analyses. The objective products of version A generally have fair correspondence with the subjective analyses and with the station data, and depicted the structure of the upper fronts, tropopauses, and jet streams fairly well. The version B objective products correspond more closely to the subjective analyses, and show the same strong gradients across the upper front with only minor smoothing.
Mancuso, R. L.↗
Transformation of two and three-dimensional regions by elliptic systems
Finite difference methods for composite grids were analyzed. It was observed that linear interpolation between grids would suffice only where low order accuracy was required. In the context of fluid flow, this would be in regions where the flow was essentially free stream. Higher order interpolation schemes were also investigated. The well known quadratic and cubic interpolating polynomials would increase the formal accuracy of the overall numerical algorithm. However, it can also be shown that the stability of the algorithm may be adversely affected. Further numerical results are needed in order to assess the nature of this instability induced by the interpolation procedure. Finally, error analysis and the order of difference expressions on general curvilinear coordinates are discussed.
Thompson, J. F.↗
Topics in the two-dimensional sampling and reconstruction of images
Mathematical analysis of image sampling and interpolative reconstruction is summarized and extended to two dimensions for application to data acquired from satellite sensors such as the Thematic mapper and SPOT. It is shown that sample-scene phase influences the reconstruction of sampled images, adds a considerable blur to the average system point spread function, and decreases the average system modulation transfer function. It is also determined that the parametric bicubic interpolator with alpha = -0.5 is more radiometrically accurate than the conventional bicubic interpolator with alpha = -1, and this at no additional cost. Finally, the parametric bicubic interpolator is found to be suitable for adaptive implementation by relating the alpha parameter to the local frequency content of an image.
Schowengerdt, R.↗
A Natural Bias Approach to Cardinal Spline Curves
The cardinal spline approach to defining interpolatory curves is of interest in the application of computer graphics to modelling and animation problems. The formulation of this interpolation problem (C) a vector valued function V is obtained which forms a C1 map from 0,n into the plane in such a way that V(i) and V prime (i) attain prespecified (vector) values P sub i and T sub i for the integers i=0, 1,...n. The intent is that the planar curves V(s) pass through each point P sub i in the direction corresponding to T sub i. In actual practice it is common for only the interpolation points P sub i to be user specified. Suitable tangents T sub i are then provided by some heuristic to complete the specification of (C). A convex control polygon yields a convex interpolant. Examples exist where the interpolant fails to be convex if the tangents are left unbiased.
Fletcher, G. Y.↗