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Mitchell, Scott A.

Publications and source records attributed to Mitchell, Scott A..

5 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Towards a More Effective Hybrid Workforce Culture in a Computationally Focused Research Center

It is essential to Sandia National Laboratory’s continued success in scientific and technological advances and mission delivery to embrace a hybrid workforce culture under which current and future employees can thrive. This report focuses on the findings of the Hybrid Work Team for the Center for Computing Research, which met weekly from March to June 2023 and conducted a survey across the Center at Sandia. Conclusions in this report are drawn from the 9 authors of this report, which comprises the Hybrid Work Team, and 15 responses to a center-wide survey, as well as numerous conversations with colleagues. A major finding was widespread dissatisfaction with the quantity, execution, and tooling surrounding formal meetings with remote participants. While there was consensus that remote work enables people to produce high quality individual and technical work, there was also consensus that there was widespread social disconnect, with particular concern about hires that were made after the onset of the Covid-19 pandemic. There were many concerns about tooling and policy to facilitate remote collaboration both within Sandia and with its external collaborators. This report includes recommendations for mitigating these problems. For problems for which obvious recommendations cannot be made, ideas of what a successful solution might look like are presented.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2023

Incremental Interval Assignment by Integer Linear Algebra with Improvements

Interval Assignment (IA) is the problem of selecting the number of mesh edges (intervals) for each curve for conforming quad and hex meshing. The intervals x is fundamentally integer-valued. Many other approaches perform numerical optimization then convert a floating-point solution into an integer solution, which is slow and error prone. We avoid such steps: we start integer, and stay integer. Incremental Interval Assignment (IIA) uses integer linear algebra (Hermite normal form) to find an initial solution to the meshing constraints, satisfying the integer matrix equation Solving for reduced row echelon form provides integer vectors spanning the nullspace of A. Here we add vectors from the nullspace to improve the initial solution, maintaining Ax = b Heuristics find good integer linear combinations of nullspace vectors that provide strict improvement towards variable bounds or goals. IIA always produces an integer solution if one exists. In practice we usually achieve solutions close to the user goals, but there is no guarantee that the solution is optimal, nor even satisfies variable bounds, e.g. has positive intervals. We describe several algorithmic changes since first publication that tend to improve the final solution. The software is freely available.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Not so HOT Triangulations

Here, we propose primal–dual mesh optimization algorithms that overcome shortcomings of the standard algorithm while retaining some of its desirable features. “Hodge-Optimized Triangulations” defines the “HOT energy” as a bound on the discretization error of the diagonalized Delaunay Hodge star operator. HOT energy is a natural choice for an objective function, but unstable for both mathematical and algorithmic reasons: it has minima for collapsed edges, and its extrapolation to non-regular triangulations is inaccurate and has unbounded minima. We propose a different extrapolation with a stronger theoretical foundation, and avoid extrapolation by recalculating the objective just beyond the flip threshold. We propose new objectives, based on normalizations of the HOT energy, with barriers to edge collapses and other undesirable configurations. We propose mesh improvement algorithms coupling these. When HOT optimization nearly collapses an edge, we actually collapse the edge. Otherwise, we use the barrier objective to update positions and weights and remove vertices. By combining discrete connectivity changes with continuous optimization, we more fully explore the space of possible meshes and obtain higher quality solutions.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1995

An aspect ration bound for triangulating a d-grid cut by a hyperplane

We consider the problem of triangulating a d-dimensional uniform grid of d-cubes that is cut by a k-dimensional affine subspace. The goal is to obtain a triangulation with bounded aspect ratio. To achieve this goal, we allow some of the box faces near the affine subspace to be displaced. This problem has applications to finite element mesh generation. For general d and k, the bound on aspect ratio that we attain is double-exponential in d. For the important special case of d = 3, the aspect ratio bound is small enough that the technique is useful in practice.

Mitchell, Scott A.↗