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Solving DWF dirac equation using multi-splitting preconditioned conjugate gradient with tensor cores on NVIDIA GPUs
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Parallel Memory-Efficient Computation of Symmetric Higher-Order Joint Moment Tensors.
Abstract not provided.
Tensor Methods A Unified and Interpretable Approach for Material Design
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G2Aero (Separable shape tensors for aerodynamic design) [SWR-22-44]
G2Aero is a flexible and practical tool for design and deformation of 2D airfoils and 3D blades using data-driven approaches. G2Aero utilizes the geometry of matrix manifolds—specifically the Grassmannian—to build a novel framework for representing physics-based separable deformations of shapes. G2Aero offers the flexibility to generate perturbations in a customizable way over any portion of the blade. The G2Aero framework utilizes data-driven methods based on a curated database of physically relevant airfoils. Specific tools include: - principal geodesic analysis over normal coordinate neighborhoods of matrix manifolds; - a variety of data-regularized deformations to nominal 2D airfoil shapes; - Riemannian interpolation connecting a sequence of airfoil cross-sections to build 3D blades from 2D data; - consistent perturbations over the span of interpolated 3D blades based on dominant modes from the data-driven analysis.
A General, Automated Method for Building Structural Tensors of Arbitrary Order for Anisotropic Function Representations
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PyZFS: A Python Package for First-Principles Calculations of Zero-Field Splitting Tensors.
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G2Aero: A Python package for separable shape tensors
G2Aero is a Python package for the design and deformation of discrete planar curves and tubular surfaces using a geometric data-driven approach. G2Aero utilizes a topology of product manifolds: the Grassmannian, $\mathcal{G}$($\mathcal{n}$, 2) - the set of 2-dimensional subspaces in $\mathbb{R}$ $\mathcal{n}$ - and the symmetric positive-definite (SPD) manifold, $\mathcal{S}^{2}_{++}$ - the set of 2x2 SPD matrices. The package provides a novel framework for representing separable deformations to shapes, which consist of stretching, scaling, rotating, and translating - also known as affine deformations - and a set of complementary deformations - which we refer to as undulation-type deformations. We focus on airfoil and blade design applications to emphasize the utility of the methods in an environment where the separation of affine and undulation-type deformations is critical. Notable functionalities of the framework for blade design include: 1) generating novel 2D (airfoil) shapes informed by a database of physically relevant airfoils, 2) building 3D blades by interpolating sequences of 2D airfoil cross-sections, and 3) generating blades with consistent perturbations along the blade span. We discuss the framework and provide examples in the context of wind energy applications, specifically wind turbine blade design. Figure 1 shows the wire frame obtained by interpolating airfoils defining the IEA 15-MW wind turbine blade and applying affine transformations corresponding to twist, chordal scaling, and bending. This, and all other figures in the paper, can be reproduced following examples and referencing supporting documentation provided in the G2Aero package.
Watertight Tensor-Product Spline Reconstruction (KCNSC PDRD Technical Report)
The standard for representing geometric models in Computer Aided Design (CAD) systems is boundary representation with trimmed surfaces. However, the approximate nature of surface-surface intersections in CAD systems leaves many small gaps between mating surfaces. These gaps lead to problems for downstream analysis and manufacturing applications, requiring time consuming repair operations and further approximation of the geometry as polygonal meshes, which do not support design iteration. In this study, nVariate, Inc. evaluated its watertight reconstruction technology on a test part. The resulting watertight model has the same absolute model accuracy of the original model zero gaps, providing a representation that requires no repair and supports further design iterations in the CAD system.
Automatic Leptonic Tensor Calculation for Beyond the Standard Model (BSM) Theories
Colossal data output from neutrino experiments (e.g. DUNE, T2HK) will require testing of several BSM theories.
Automatic Leptonic Tensor Generation for Beyond the Standard Model Theories
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Uncertainty Quantification of Moment Tensor Inversions due to Earth Model Uncertainty.
Abstract not provided.
Spectral Equivalence of Higher-Order Tensor Product Finite Elements and Applications to Preconditioning.
Abstract not provided.
Generalized Canonical Polyadic Tensor Decompositions for Streaming Data.
Abstract not provided.