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DOE OSTI2020

An Overview of Gemma FY20 Verification Activities

Gemma verification activities for FY20 can be divided into three categories: the development of specialized quadrature rules, initial progress towards the development of manufactured solutions for code verification, and automated code-verification testing. In the method-of-moments implementation of the electric-field integral equation, the presence of a Green’s function in the four-dimensional integrals yields singularities in the integrand when two elements are nearby. To address these challenges, we have developed quadrature rules to integrate the functions through which the singularities can be characterized. Code verification is necessary to develop confidence in the implementation of the numerical methods in Gemma. Therefore, we have begun investigating the use of manufactured solutions to more thoroughly verify Gemma. Manufactured solutions provide greater flexibility for testing aspects of the code; however, the aforementioned singularities provide challenges, and existing work is limited in rigor and quantity. Finally, we have implemented automated code-verification testing using the VVTest framework to automate the mesh refinement and execution of a Gemma simulation to generate mesh convergence data. This infrastructure computes the observed order of accuracy from these data and compares it with the theoretical order of accuracy to either develop confidence in the implementation of the numerical methods or detect coding errors.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Using Pilot Jobs and CernVM File System for Simplified Use of Containers and Software Distribution

High Energy Physics (HEP) experiments entail an abundance of computing resources, i.e. sites, to run simulations and analyses by processing data. This requirement is fulfilled by local batch farms, grid sites, private/commercial clouds, and supercomputing centers via High Throughput Computing (HTC). The growing needs of such experiments and resources being prone to trends of heterogeneity make it difficult for physicists to handle these resources directly. Additionally, HEP collaborations heavily rely on data and software releases, typically in the order of tens of gigabytes, while conducting simulations and analyses. Hence, aspects of scalability, reliability, and maintenance become crucial with regards to the distribution of the necessary data and software stack. The GlideinWMS [4] framework helps with the resource management problem by using pilot jobs, aka Glideins, to provision reliable elastic virtual clusters. Glideins are submitted to unreliable heterogeneous resources which are validated and customized by the Glideins to make the worker nodes available for end-user job execution. On the other hand, the CernVM File System (CernVM-FS or CVMFS) [1] helps with data distribution. It is a write-once, read-everywhere filesystem used to deploy scientific software to thousands of nodes on a worldwide distributed computing infrastructure. CVMFS is based on the Hyper Text Transfer Protocol and has been widely used within the particle physics community for (1) distributing experiment software and data such as calibrations, and (2) facilitating containerization by efficiently hosting container images along with providing containerization software, especially Singularity [3] GlideinWMS relies on CVMFS installed locally on the computing resources to satisfy the experiments' software needs. This requires system administrators' effort to install and maintain CVMFS at the sites and limits the use of sites, especially HPC resources, that do not have CVMFS installed. This poster presents a solution, taking advantage of Glideins to provide CVMFS at most sites without the need for a local installation. Doing so expands the pool of resources available for HEP experiments and reduces the effort of system administrators for current resources. Additionally, the proposed solution allows GlideinWMS to also start Singularity [3], a containerization software that can run unprivileged, on sites where neither CVMFS nor Singularity are available, including HPC sites. The benefits provided by this solution are: (1) lower overhead for site administrators in that they have less software to install, (2) an expanded pool of resources that run user jobs with easy access to software and data provided by CVMFS, thus making life easier for the scientists, and (3) improved flexibility to use HPC resources by enabling GlideinWMS pilot jobs to support HPC sites.

Urs, Namratha↗

DOE OSTI2024

Black Box Equations of State: Creating Semi-analytic Solutions to the Noh Problem and Verifying Equation of State Interfaces

The objective of this report is threefold. First, it details a method for deriving a semi-analytic solution to the Noh Problem when using a “black-box” equation of state. Such capability allows us to perform verification on complicated, more realistic equations of state. Examples include Steinberg equations of state for materials and tabulated equations of state. The second objective is to apply the methodology to verify the singularity-eos equation of state library. We do so by solving the Rankine-Hugoinot jump conditions for the Noh Problem, ensuring singularity derives the correct solution and comparing the error to an exact implementation of the equation of state. The third objective is to perform verification of the xRAGE Eulerian hydrodynamics code when interfaced with singularity. We provide the theory, analysis, documentation for a python implementation of the proposed solver, and verification results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1972

A layered composite with a broken laminate

The problem of a laminate composite in the presence of a crack located normal to the bond lines is considered. Stress analysis of the limiting case when the crack extends to the bond lines is carried out. An integral transform technique is used to formulate the problem in terms of a singular integral equation. The power of stress singularity around the crack tip terminating at the interface is obtained using the above technique. The singular integral equation is solved numerically and the effect of material properties on the stress intensity factor is calculated.

Gupta, G. D.↗

NASA NTRS1972

An integral equation approach to the strip problem

A semi-infinite strip held rigidly on its short end is considered. Loads in the strip at infinity (far away from the fixed end) are prescribed. Integral transform technique is used to provide an exact formulation of the problem in terms of a singular integral equation. Stress singularity at the strip corner is obtained from the singular integral equation which is then solved numerically. Stresses along the rigid end are determined and the effect of the material properties on the stress intensity factor is presented. The method can also be applied to the problem of a laminate composite with a flat inclusion normal to the interfaces.

Gupta, G. D.↗

NASA NTRS1973

The problem of a finite strip compressed between two rough rigid stamps

A finite strip compressed between two rough rigid stamps is considered. The elastostatic problem is formulated in terms of a singular integral equation from which the proper stress singularities at the corners are determined. The singular integral equation is solved numerically to determine the stresses along the fixed ends of the strip. The effect of material properties and strip geometry on the stress intensity factor is presented graphically.

Gupta, G. D.↗

NASA NTRS1973

Interaction between a circular inclusion and an arbitrarily oriented crack

The plane interaction problem for a circular elastic inclusion imbedded into an elastic matrix which contains an arbitrarily oriented crack is considered. Using the existing solutions for the edge dislocations as Green's functions, first the general problem of a through crack in the form of an arbitrary smooth arc located in the matrix in the vicinity of the inclusion is formulated. The integral equations for the line crack are then obtained as a system of singular integral equation with simple Cauchy kernels. The singular behavior of the stresses around the crack tips is examined and the expressions for the stress intensity factors representing the strength of the stress singularities are obtained in terms of the asymptotic values of the density functions of the integral equations. The problem is solved for various typical crack orientations and the corresponding stress intensity factors are given.

Erdogan, F.↗

NASA NTRS1973

2-SPEED, a single-gimbal control moment gyro attitude control system.

In 2-SPEED (Two Scissored Pair Ensemble, Explicit Distribution) four single-gimbal control moment gyros (SGCMGs) configured into two scissored pairs are combined with an explicit distribution of angular momentum between pairs to produce a system relatively insensitive to the singularity problems which have plagued other SGCMG concepts. In this system, the singularity surfaces in momentum space degenerate to discrete curves. Further, the system permits a smooth passage through these remaining singularities with, at worst, a temporary delay while momentum redistribution takes place. Finally, CMG-out operation is possible within the full volume of the reduced momentum envelope.

Crenshaw, J. W.↗

NASA NTRS1973

An integral equation approach to the semi-infinite strip problem.

A semi-infinite strip held rigidly on its short end is considered. Loads in the strip at infinity (far away from the fixed end) are prescribed. The integral transform technique is used to provide an exact formulation of the problem in terms of a singular integral equation. The stress singularity at the strip corner is obtained from the singular integral equation, which is then solved numerically. Stresses along the rigid end are determined, and the effect of the material properties on the stress-intensity factor is presented. The method can also be applied to the problem of a laminate composite with a flat inclusion normal to the interfaces.

Gupta, G. D.↗

NASA NTRS1973

A layered composite with a broken laminate.

The problem of a laminate composite in presence of a crack located normal to the bond lines is considered. Stress analysis of the limiting case when the crack extends to the bond lines is carried out. Integral transform technique is used to formulate the problem in terms of a singular integral equation from which the power of stress singularity around the crack tip terminating at the interface is obtained. The singular integral equation is solved numerically and the effect of material properties on the stress intensity factor is calculated.

Gupta, G. D.↗

NASA NTRS1974

Limitations to the small scale yielding approximation for crack tip plasticity

Recent finite-element results by S. G. Larsson and A. J. Carlsson suggest a limited range of validity to the 'small scale yielding approximation,' whereby small crack tip plastic zones are correlated in terms of the elastic stress intensity factor. It is shown with the help of a model for plane strain yielding that their results may be explained by considering the non-singular stress, acting parallel to the crack at its tip, which accompanies the inverse square-root elastic singularity. Further implications of the non-singular stress term for crack tip deformations and fracturing are examined. It is suggested that its effect on crack tip parameters, such as the opening displacement and J-integral, is less pronounced than its effect on the yield zone size.

Rice, J. R.↗

NASA NTRS1973

Aircraft maneuver optimization of reduced-order approximation

Review of recent work in recasting the energy type of approximation to aircraft flight in terms of singular perturbation theory and in extending this theory to three-dimensional maneuvers. Singular perturbations for differential equations arising in optimal control are first examined for a system of fairly general form but low order. The attitude dynamics for optimal flight of a rocket in vacuum is then studied as an introductory, and fairly transparent, example. The question of the choice of variables is then discussed. Finally, optimal aircraft flight in various reduced-order approximations is investigated. In particular, the problem of three-dimensional aircraft flight is formulated for singular perturbation treatment, and possibilities for decoupling into several lower-order problems are illustrated. The use of reduced-order approximation facilitates numerical computations by reducing the number of multiplier initial values that must be determined simultaneously and by improving the conditioning of the differential equations.

Kelley, H. J.↗

NASA NTRS1975

A steering law for three double-gimbal control moment gyro systems

A steering law for three double-gimbal control moment gyro (CMG) systems is proposed. This steering law is applicable to systems with almost any configuration of CMGs and the CMG-out operation needs no special modification. Examples of three double gimbal CMG systems in an orthogonal configuration and in a parallel configuration are shown along with the results of digital simulations. Simulation results show that any command torque can always be met except when the system is in a singular state and that, whenever the system is in, or close to, a singularity, the steering law drives the system state out of the vicinity of the singularity.

Yoshikawa, T.↗

NASA NTRS1974

A note on a broken layer in an orthotropic laminate composite

An orthotropic laminate composite containing a completely broken layer is considered. The problem is formulated in terms of integral transforms and then reduced to a singular integral equation which is solved numerically. The strength of stress singularity at the crack tip is determined from a characteristic equation which is obtained by studying the dominant part of the singular integral equation near the end points. The stress intensity factors are given for various material properties.

Arin, K.↗

NASA NTRS1975

The scatter of obliquely incident plane waves from a corrugated conducting surface

A physical optics solution is presented for the scattering of place waves from a perfectly conducting corrugated surface in the case of waves incident from an arbitrary direction and for an observer far from the surface. This solution is used to compute the radar cross section of the surface in the case of backscatter from irregular (i. e. , stochastic) corrugations and is used to point out a correction to the literature on this problem. An interesting feature of the solution is the occurrence of singularities in the scattered fields. These singularities appear to be a manifestation of focussing by the surface at its "stationary" points. Whether or not the singularities occur in the solution depends on the manner in which one restricts the analysis to the far field.

David M Le Vine↗

NASA NTRS1974

Mixed mode stress field effect in adhesive fracture

Numerical or analytical analyses were performed on seven different test specimens including blister test, 90-degree peel test, torsion test, and various cone tests. These specimens are in general subjected to complex stress fields having various amounts of Mode I, Mode II, and Mode III loads. The specimens were then constructed using polymethyl methacrylate for the adherends and a transparent polyurethane elastomer (Solithane 113) for the adhesive. This combination permitted direct observation of the bondline as load was applied. Although initial debonds as well as bond end termination singularities were present in all specimens, in some cases the debond did not initiate at the singularity points as would normally have been expected. An explanation for this behavior is presented, as well as a comparison of loading mode effect on those specimens for which the debond did propagate from a bond terminus singular point.

Anderson, G. P.↗

NASA NTRS1975

Interaction between a circular inclusion and an arbitrarily oriented crack

The plane interaction problem for a circular elastic inclusion embedded in an elastic matrix which contains an arbitrarily oriented crack is considered. Using the existing solutions for the edge dislocations as Green's functions, first the general problem of a through crack in the form of an arbitrary smooth arc located in the matrix in the vicinity of the inclusion is formulated. The integral equations for the line crack are then obtained as a system of singular integral equations with simple Cauchy kernels. The singular behavior of the stresses around the crack tips is examined and the expressions for the stress-intensity factors representing the strength of the stress singularities are obtained in terms of the asymptotic values of the density functions of the integral equations. The problem is solved for various typical crack orientations and the corresponding stress-intensity factors are given.

Erdogan, F.↗

NASA NTRS1975

The problem of a finite strip compressed between two rough rigid stamps

Gupta, G. D.↗