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DOE OSTI2022

Skyrmions and hopfions in three-dimensional frustrated magnets

Here, a model of an inversion-symmetric frustrated spin system is introduced which hosts three-dimensional extensions of magnetic skyrmions. In the continuum approximation, this model reduces to a nonlinear sigma model on a squashed sphere that has a natural interpolating parameter. At one limit of the parameter, the model reduces to a frustrated magnetic system earlier considered by Sutcliffe as a host to hopfions, and in the other limit, it becomes very similar to the 3D Skyrme model. To better understand the relation between hopfions and 3D skyrmions, a model interpolating between the Faddeev-Niemi and the Skyrme models is reconsidered and it is shown that energies of the solitons obey a linear Bogomol'nyi-Prasad-Sommerfeld bound. The 3D skyrmions in the frustrated magnetic model are found and compared to the rational map ansatz.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRSDate not supplied

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↗

DOE OSTI2022

Time-series forecasting using manifold learning, radial basis function interpolation, and geometric harmonics

We address a three-tier numerical framework based on nonlinear manifold learning for the forecasting of high-dimensional time series, relaxing the “curse of dimensionality” related to the training phase of surrogate/machine learning models. At the first step, we embed the high-dimensional time series into a reduced low-dimensional space using nonlinear manifold learning (local linear embedding and parsimonious diffusion maps). Then, we construct reduced-order surrogate models on the manifold (here, for our illustrations, we used multivariate autoregressive and Gaussian process regression models) to forecast the embedded dynamics. Finally, we solve the pre-image problem, thus lifting the embedded time series back to the original high-dimensional space using radial basis function interpolation and geometric harmonics. The proposed numerical data-driven scheme can also be applied as a reduced-order model procedure for the numerical solution/propagation of the (transient) dynamics of partial differential equations (PDEs). In conclusion, we assess the performance of the proposed scheme via three different families of problems: (a) the forecasting of synthetic time series generated by three simplistic linear and weakly nonlinear stochastic models resembling electroencephalography signals, (b) the prediction/propagation of the solution profiles of a linear parabolic PDE and the Brusselator model (a set of two nonlinear parabolic PDEs), and (c) the forecasting of a real-world data set containing daily time series of ten key foreign exchange rates spanning the time period 3 September 2001–29 October 2020.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Collisional excitation of interstellar PN by H 2 : New interaction potential and scattering calculations

Here, rotational excitation of interstellar PN molecules induced by collisions with H 2 is investigated. We present the first ab initio four-dimensional potential energy surface (PES) for the PN–H 2 van der Waals system. The PES was obtained using an explicitly correlated coupled cluster approach with single, double, and perturbative triple excitations [CCSD(T)-F12b]. The method of interpolating moving least squares was used to construct an analytical PES from these data. The equilibrium structure of the complex was found to be linear, with H 2 aligned at the N end of the PN molecule, at an intermolecular separation of 4.2 Å. The corresponding well-depth is 224.3 cm -1 . The dissociation energies were found to be 40.19 cm -1 and 75.05 cm -1 for complexes of PN with ortho-H 2 and para-H 2 , respectively. Integral cross sections for rotational excitation in PN–H 2 collisions were calculated using the new PES and were found to be strongly dependent on the rotational level of the H 2 molecule. These new collisional data will be crucial to improve the estimation of PN abundance in the interstellar medium from observational spectra.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Geophysical and Environmental Monitoring Data, and Subsurface Flow Modelling Results for Chicken Bone Meadow, Mt. Snodgrass, Crested Butte, CO

This dataset includes geoelectrical monitoring data acquired between October 2021 and November 2022, soil moisture and temperature data, groundwater data obtained from borehole SNIB covering the period from June 2021 to September 2022, and hydrological modelling results. The data were acquired to investigate how variations in bedrock type and topography, and vegetation cover control subsurface flow dynamics. To provide insights into the subsurface flow dynamics and their controls, a monitoring transect was installed at the Chicken Bone Meadow, Mt. Snodgrass, Crested Butte, CO, measuring the spatio-temporal variations of soil moisture, soil and snow temperature, subsurface electrical resistivity variations, and groundwater dynamics. Field data are organized in a folder structure, with Electrical Resistivity Tomography (ERT) data being provided as one file per measurement, and data of the soil moisture and temperature sensors being provided as text files covering the entire monitoring period. The ‘Locations.csv’ file contains the location of all sensors, given in NAD83 – UTM Zone 13N. ERT monitoring data has been processed to filter data based on reciprocal errors (data with errors > 30% were removed), a linear error model was fitted to each survey, and to ensure a constant set of measurements for time-lapse inversion, filtered data were interpolated and assigned a 100% measurement error. Soil moisture and temperature data were acquired at 15 min intervals, and averaged to provide 1h data. Weather data and borehole data (groundwater depth, conductivity and temperature) were acquired at 30 min intervals, and are provided as daily measurements; all measurements are averaged, except of precipitation values, which are given as daily accumulation. The hydrological model was set up along the ERT monitoring transect, and net infiltration was used as surface boundary condition and derived from the weather data. Four different results are provided, (1) results for a parameterization using hydraulic permeability and porosity as derived from the ERT data through petrophysical relationships, and (2) three simplified model results, using 1 to 3 geological layers above the bedrock. Modelling was performed using PFLOTRAN, and for each model the PFLOTRAN input files are provided. The result files include weekly hydrological modelling results (e.g., saturation, velocities, pressures), as well as the model parameterization. The dataset additionally includes a file-level metadata (flmd.csv) file that lists each file contained in the dataset with associated metadata; and a data dictionary (dd.csv) file that contains column/row headers used throughout the files along with a definition, units, and data type.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1984

ADS: A FORTRAN program for automated design synthesis, version 1.00

A new general-purpose optimization program for engineering design is described. ADS-1 (Automated Design Synthesis - Version 1) is a FORTRAN program for solution of nonlinear constrained optimization problems. The program is segmented into three levels, being strategy, optimizer, and one-dimensional search. At each level, several options are available so that a total of over 100 possible combinations can be created. Examples of available strategies are sequential unconstrained minimization, the Augmented Lagrange Multiplier method, and Sequential Linear Programming. Available optimizers include variable metric methods and the Method of Feasible Directions as examples and one-dimensional search options include polynomial interpolation and the Golden Section method as examples. Emphasis is placed on ease of use of the program. All information is transferred via a single parameter list. Default values are provided for all internal program parameters such as convergence criteria, and the user is given a simple means to over-ride these, if desired. The program is demonstrated with a simple structural design example.

Vanderplaats, G. N.↗

NASA NTRS1985

ADS: A FORTRAN program for automated design synthesis: Version 1.10

A new general-purpose optimization program for engineering design is described. ADS (Automated Design Synthesis - Version 1.10) is a FORTRAN program for solution of nonlinear constrained optimization problems. The program is segmented into three levels: strategy, optimizer, and one-dimensional search. At each level, several options are available so that a total of over 100 possible combinations can be created. Examples of available strategies are sequential unconstrained minimization, the Augmented Lagrange Multiplier method, and Sequential Linear Programming. Available optimizers include variable metric methods and the Method of Feasible Directions as examples, and one-dimensional search options include polynomial interpolation and the Golden Section method as examples. Emphasis is placed on ease of use of the program. All information is transferred via a single parameter list. Default values are provided for all internal program parameters such as convergence criteria, and the user is given a simple means to over-ride these, if desired.

Vanderplaats, G. N.↗

DOE OSTI2026

Learning genetic perturbation effects with variational causal inference

Advances in sequencing technologies have enhanced the understanding of gene regulation in cells. In particular, Perturb-seq has enabled high-resolution profiling of the transcriptomic response to genetic perturbations at the single-cell level. This understanding has implications in functional genomics and potentially for identifying therapeutic targets. Various computational models have been developed to predict perturbational effects. While deep learning models excel at interpolating observed perturbational data, they tend to overfit in the lack of enough data and may not generalize well to unseen perturbations. In contrast, mechanistic models, such as linear causal models based on gene regulatory networks, hold greater potential for extrapolation, as they encapsulate regulatory information that can predict responses to unseen perturbations. However, their application has been limited to small studies due to overly simplistic assumptions, making them less effective in handling noisy, large-scale single-cell data. We propose a hybrid approach that combines a mechanistic causal model with variational deep learning, termed Single Cell Causal Variational Autoencoder (SCCVAE). The mechanistic model employs a learned regulatory network to represent perturbational changes as shift interventions that propagate through the learned network. SCCVAE integrates this mechanistic causal model into a variational autoencoder, generating rich, comprehensive transcriptomic responses. Our results indicate that SCCVAE exhibits superior performance over current state-of-the-art baselines for extrapolating to predict unseen perturbational responses. Additionally, for the observed perturbations, the latent space learned by SCCVAE allows for the identification of functional perturbation modules and simulation of single-gene knockdown experiments of varying penetrance, presenting a robust tool for interpreting and interpolating perturbational responses at the single-cell level.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2019

An isogeometric finite element formulation for phase transitions on deforming surfaces

This paper presents a general theory and isogeometric finite element implementation for studying mass conserving phase transitions on deforming surfaces. The mathematical problem is governed by two coupled fourth-order nonlinear partial differential equations (PDEs) that live on an evolving two-dimensional manifold. For the phase transitions, the PDE is the Cahn–Hilliard equation for curved surfaces, which can be derived from surface mass balance in the framework of irreversible thermodynamics. For the surface deformation, the PDE is the (vector-valued) Kirchhoff–Love thin shell equation. Both PDEs can be efficiently discretized using C 1 -continuous interpolations without derivative degrees-of-freedom (dofs). Structured NURBS and unstructured spline spaces with pointwise C 1 -continuity are utilized for these interpolations. The resulting finite element formulation is discretized in time by the generalized-α scheme with adaptive time-stepping, and it is fully linearized within a monolithic Newton–Raphson approach. A curvilinear surface parameterization is used throughout the formulation to admit general surface shapes and deformations. The behavior of the coupled system is illustrated by several numerical examples exhibiting phase transitions on deforming spheres, tori and double-tori.

42 ENGINEERING↗

DOE OSTI2016

A hybrid incremental projection method for thermal-hydraulics applications

In this paper, a new second-order accurate, hybrid, incremental projection method for time-dependent incompressible viscous flow is introduced in this paper. The hybrid finite-element/finite-volume discretization circumvents the well-known Ladyzhenskaya–Babuška–Brezzi conditions for stability, and does not require special treatment to filter pressure modes by either Rhie–Chow interpolation or by using a Petrov–Galerkin finite element formulation. The use of a co-velocity with a high-resolution advection method and a linearly consistent edge-based treatment of viscous/diffusive terms yields a robust algorithm for a broad spectrum of incompressible flows. The high-resolution advection method is shown to deliver second-order spatial convergence on mixed element topology meshes, and the implicit advective treatment significantly increases the stable time-step size. The algorithm is robust and extensible, permitting the incorporation of features such as porous media flow, RANS and LES turbulence models, and semi-/fully-implicit time stepping. A series of verification and validation problems are used to illustrate the convergence properties of the algorithm. The temporal stability properties are demonstrated on a range of problems with 2 ≤ CFL ≤ 100. The new flow solver is built using the Hydra multiphysics toolkit. The Hydra toolkit is written in C++ and provides a rich suite of extensible and fully-parallel components that permit rapid application development, supports multiple discretization techniques, provides I/O interfaces, dynamic run-time load balancing and data migration, and interfaces to scalable popular linear solvers, e.g., in open-source packages such as HYPRE, PETSc, and Trilinos.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2000

An Automated Approach to Very High Order Aeroacoustic Computations in Complex Geometries

Computational aeroacoustics requires efficient, high-resolution simulation tools. And for smooth problems, this is best accomplished with very high order in space and time methods on small stencils. But the complexity of highly accurate numerical methods can inhibit their practical application, especially in irregular geometries. This complexity is reduced by using a special form of Hermite divided-difference spatial interpolation on Cartesian grids, and a Cauchy-Kowalewslci recursion procedure for time advancement. In addition, a stencil constraint tree reduces the complexity of interpolating grid points that are located near wall boundaries. These procedures are used to automatically develop and implement very high order methods (>15) for solving the linearized Euler equations that can achieve less than one grid point per wavelength resolution away from boundaries by including spatial derivatives of the primitive variables at each grid point. The accuracy of stable surface treatments is currently limited to 11th order for grid aligned boundaries and to 2nd order for irregular boundaries.

Dyson, Rodger W.↗

NASA NTRS2017

Some Observations on Damage Tolerance Analyses in Pressure Vessels

AIAA standards S080 and S081 are applicable for certification of metallic pressure vessels (PV) and composite overwrap pressure vessels (COPV), respectively. These standards require damage tolerance analyses with a minimum reliable detectible flaw/crack and demonstration of safe life four times the service life with these cracks at the worst-case location in the PVs and oriented perpendicular to the maximum principal tensile stress. The standards require consideration of semi-elliptical surface cracks in the range of aspect ratios (crack depth a to half of the surface length c, i.e., (a/c) of 0.2 to 1). NASA-STD-5009 provides the minimum reliably detectible standard crack sizes (90/95 probability of detection (POD) for several non-destructive evaluation (NDE) methods (eddy current (ET), penetrant (PT), radiography (RT) and ultrasonic (UT)) for the two limits of the aspect ratio range required by the AIAA standards. This paper tries to answer the questions: can the safe life analysis consider only the life for the crack sizes at the two required limits, or endpoints, of the (a/c) range for the NDE method used or does the analysis need to consider values within that range? What would be an appropriate method to interpolate 90/95 POD crack sizes at intermediate (a/c) values? Several procedures to develop combinations of a and c within the specified range are explored. A simple linear relationship between a and c is chosen to compare the effects of seven different approaches to determine combinations of aj and cj that are between the (a/c) endpoints. Two of the seven are selected for evaluation: Approach I, the simple linear relationship, and a more conservative option, Approach III. For each of these two Approaches, the lives are computed for initial semi-elliptic crack configurations in a plate subjected to remote tensile fatigue loading with an R-ratio of 0.1, for an assumed material evaluated using NASGRO (registered 4) version 8.1. These calculations demonstrate that for this loading, using Approach I and the initial detectable crack sizes at the (a/c) endpoints in 5009 specified for the ET and UT NDE methods, the smallest life is not at the two required limits of the (a/c) range, but rather is at an intermediate configuration in the range (a/c) of 0.4 to 0.6. Similar analyses using both Approach I and III with the initial detectable crack size at the (a/c) endpoints in 5009 for PT NDE showed the smallest life may be at an (a/c) endpoint or an intermediate (a/c), depending upon which Approach is used. As such, analyses that interrogate only the two (a/c) values of 0.2 and 1 may result in unconservative life predictions. The standard practice may need to be revised based on these results.

Raju, Ivatury S.↗

DOE OSTI2022

Uncertainty Quantification of Calculated Temperatures for the AGR 5/6/7 Experiment

This report documents the quantification of uncertainty of the calculated temperature data for the Advanced Gas Reactor (AGR) 5/6/7 fuel irradiation experiment conducted in the Advanced Test Reactor at Idaho National Laboratory in support of the Advanced Reactor Technologies? research and development program. Recognizing uncertainties inherent in physics and thermal simulations of the AGR 5/6/7 capsules, the results of the numerical simulations are used in combination with statistical analysis methods to improve qualification of measured data. The calculated fuel temperatures for AGR tests are also used for validation of the fission product transport and fuel performance simulation models. These crucial roles of the calculated fuel temperatures in ensuring achievement of the AGR experimental program objectives require accurate determination of the model temperature uncertainties. This report covers temperature uncertainty results for each of the five AGR 5/6/7 capsules. To quantify the uncertainty of calculated temperatures determined using the ABAQUS finite element heat transfer code, this study identifies and analyzes model parameters of potential importance to the calculated temperatures of fuel compacts and thermocouples. The selection of input parameters for uncertainty quantification is based on the ranking of their influences upon temperature predictions. Thus, selected input parameters include those with high sensitivity and those with the largest uncertainty. Propagation of model parameter uncertainty and sensitivity is then used to quantify the overall uncertainty of calculated temperatures. Measurement uncertainty, analysis of modeling assumptions, and expert judgment are used as the basis to quantify the uncertainty range for selected input parameters. The input uncertainties are dynamic, accounting for the effect of unplanned events and changes in thermal properties of capsule components over extended exposure to high temperatures and fast neutron irradiation. The sensitivity analysis performed in this work went beyond the traditional local sensitivity. Using experimental design, analysis of pairwise interactions of model parameters was performed to establish sufficiency of the time dependent first order (linear) expansion terms in constructing the temperature response surface. To achieve completeness, uncertainty propagation made use of pairwise noise correlations of model parameters. Furthermore, using an interpolation scheme over the input parameter domain, the analysis obtains time dependent sensitivity over the test campaign duration. This allows computation of uncertainty for the calculated fuel temperatures and the calculated graphite temperatures at thermocouple locations during the entire irradiation period.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

A Statistical Interpolation Code for Ocean Analysis and Forecasting

Abstract We present a data assimilation package for use with ocean circulation models in analysis, forecasting, and system evaluation applications. The basic functionality of the package is centered on a multivariate linear statistical estimation for a given predicted/background ocean state, observations, and error statistics. Novel features of the package include support for multiple covariance models, and the solution of the least squares normal equations either using the covariance matrix or its inverse—the information matrix. The main focus of this paper, however, is on the solution of the analysis equations using the information matrix, which offers several advantages for solving large problems efficiently. Details of the parameterization of the inverse covariance using Markov random fields are provided and its relationship to finite-difference discretizations of diffusion equations are pointed out. The package can assimilate a variety of observation types from both remote sensing and in situ platforms. The performance of the data assimilation methodology implemented in the package is demonstrated with a yearlong global ocean hindcast with a 1/4° ocean model. The code is implemented in modern Fortran, supports distributed memory, shared memory, multicore architectures, and uses climate and forecasts compliant Network Common Data Form for input/output. The package is freely available with an open source license from www.tendral.com/tsis/ .

Srinivasan, Ashwanth↗

DOE OSTI2012

Pure and entangled N=4 linear supermultiplets and their one-dimensional sigma-models

'Pure' homogeneous linear supermultiplets (minimal and non-minimal) of the N=4-extended one-dimensional supersymmetry algebra are classified. 'Pure' means that they admit at least one graphical presentation (the corresponding graph/graphs are known as 'Adinkras'). We further prove the existence of 'entangled' linear supermultiplets which do not admit a graphical presentation, by constructing an explicit example of an entangled N=4 supermultiplet with field content (3, 8, 5). It interpolates between two inequivalent pure N=4 supermultiplets with the same field content. The one-dimensional N=4 sigma-model with a three-dimensional target based on the entangled supermultiplet is presented. The distinction between the notion of equivalence for pure supermultiplets and the notion of equivalence for their associated graphs (Adinkras) is discussed. Discrete properties such as 'chirality' and 'coloring' can discriminate different supermultiplets. The tools used in our classification include, among others, the notion of field content, connectivity symbol, commuting group, node choice group, and so on.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1987

Polynomial approximation of functions of matrices and its application to the solution of a general system of linear equations

During the process of solving a mathematical model numerically, there is often a need to operate on a vector v by an operator which can be expressed as f(A) while A is NxN matrix (ex: exp(A), sin(A), A sup -1). Except for very simple matrices, it is impractical to construct the matrix f(A) explicitly. Usually an approximation to it is used. In the present research, an algorithm is developed which uses a polynomial approximation to f(A). It is reduced to a problem of approximating f(z) by a polynomial in z while z belongs to the domain D in the complex plane which includes all the eigenvalues of A. This problem of approximation is approached by interpolating the function f(z) in a certain set of points which is known to have some maximal properties. The approximation thus achieved is almost best. Implementing the algorithm to some practical problem is described. Since a solution to a linear system Ax = b is x= A sup -1 b, an iterative solution to it can be regarded as a polynomial approximation to f(A) = A sup -1. Implementing the algorithm in this case is also described.

Tal-Ezer, Hillel↗

DOE OSTI2017

SHARP: A Spatially Higher-order, Relativistic Particle-in-cell Code

Numerical heating in particle-in-cell (PIC) codes currently precludes the accurate simulation of cold, relativistic plasma over long periods, severely limiting their applications in astrophysical environments. We present a spatially higher-order accurate relativistic PIC algorithm in one spatial dimension, which conserves charge and momentum exactly. We utilize the smoothness implied by the usage of higher-order interpolation functions to achieve a spatially higher-order accurate algorithm (up to the fifth order). We validate our algorithm against several test problems—thermal stability of stationary plasma, stability of linear plasma waves, and two-stream instability in the relativistic and non-relativistic regimes. Comparing our simulations to exact solutions of the dispersion relations, we demonstrate that SHARP can quantitatively reproduce important kinetic features of the linear regime. Our simulations have a superior ability to control energy non-conservation and avoid numerical heating in comparison to common second-order schemes. We provide a natural definition for convergence of a general PIC algorithm: the complement of physical modes captured by the simulation, i.e., those that lie above the Poisson noise, must grow commensurately with the resolution. This implies that it is necessary to simultaneously increase the number of particles per cell and decrease the cell size. We demonstrate that traditional ways for testing for convergence fail, leading to plateauing of the energy error. This new PIC code enables us to faithfully study the long-term evolution of plasma problems that require absolute control of the energy and momentum conservation.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2018

Algorithmic Patterns for $$\mathcal {H}$$-Matrices on Many-Core Processors

In this work, we consider the reformulation of hierarchical ( $\mathcal {H}$ ) matrix algorithms for many-core processors with a model implementation on graphics processing units (GPUs). $\mathcal {H}$ matrices approximate specific dense matrices, e.g., from discretized integral equations or kernel ridge regression, leading to log-linear time complexity in dense matrix–vector products. The parallelization of $\mathcal {H}$ matrix operations on many-core processors is difficult due to the complex nature of the underlying algorithms. While previous algorithmic advances for many-core hardware focused on accelerating existing $\mathcal {H}$ matrix CPU implementations by many-core processors, we here aim at totally relying on that processor type. As main contribution, we introduce the necessary parallel algorithmic patterns allowing to map the full $\mathcal {H}$ matrix construction and the fast matrix–vector product to many-core hardware. In this work, crucial ingredients are space filling curves, parallel tree traversal and batching of linear algebra operations. The resulting model GPU implementation hmglib is the, to the best of the authors knowledge, first entirely GPU-based Open Source $\mathcal {H}$ matrix library of this kind. We investigate application examples as present in kernel ridge regression, Gaussian Process Regression and kernel-based interpolation. In this context, an in-depth performance analysis and a comparative performance study against a standard multi-core CPU $\mathcal {H}$ matrix library highlights profound speedups of our many-core parallel approach.

97 MATHEMATICS AND COMPUTING↗