Learning Algebraic Multigrid Prolongation with Residual Graph Neural Networks.
Abstract not provided.
Moore, Nicholas↗
SEARCH · Engineering Papers
Results for “abstract algebra”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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An Algebraic Monolithic Method for Volume-coupled Multiphysics Problems.
Abstract not provided.
Ohm, Peter Brian↗
An Algebraic Monolithic Method for Volume-coupled Multiphysics Problems.
Abstract not provided.
Ohm, Peter Brian↗
Smoothed aggregation for difficult stretched mesh and coefficient variation problems
Abstract Four adaptations of the smoothed aggregation algebraic multigrid (SA‐AMG) method are proposed with an eye toward improving the convergence and robustness of the solver in situations when the discretization matrix contains many weak connections. These weak connections can cause higher than expected levels of fill‐in within the coarse discretization matrices and can also give rise to suboptimal smoothing within the prolongator smoothing phase. These smoothing drawbacks are due to the relatively small size of some diagonal entries within the filtered matrix that one obtains after dropping the weak connections. The new algorithms consider modifications to the Jacobi‐like step that defines the prolongator smoother, modifications to the filtered matrix, and also direct modifications to the resulting grid transfer operators. Numerical results are given illustrating the potential benefits of the proposed adaptations.
Hu, Jonathan J.↗
A Monolithic Algebraic Multigrid Approach for Coupled Multiphysics Problems using the MueLu Framework.
Abstract not provided.
Ohm, Peter Brian↗
Algebraic Multigrid for mixed finite element discretizations of the Stokes Equations.
Abstract not provided.
Tuminaro, Raymond↗
Vertex algebra of extended operators in 4d N=2 superconformal field theories. Part I
Abstract We construct a class of extended operators in the cohomology of a pair of twisted Schur supercharges of 4d$$ \mathcal{N} $$ N =2 SCFTs. The extended operators are constructed from the local operators in this cohomology — the Schur operators — by a version of topological descent. They are line, surface, and domain wall world volume integrals of certain super descendants of Schur operators. Their world volumes extend in directions transverse to a spatial plane in Minkowski space-time. As operators in the cohomology of these twisted Schur supercharges, their correlators are (locally) meromorphic functions only of the positions where they intersect this plane. This implies the extended operators enlarge the vertex operator algebra of the Schur operators. We illustrate this enlarged vertex algebra by computing some extended-operator product expansions within a subalgebra of it for the free hypermultiplet SCFT.
Physics↗
Variational approach to relative entropies with an application to QFT
Abstract We define a new divergence of von Neumann algebras using a variational expression similar in nature to Kosaki’s formula for Umegaki’s relative entropy. Our divergence satisfies several of the usual desirable properties, upper bounds the sandwiched Renyi entropy and reduces to the fidelity in a limit. As an illustration, we use the formula in quantum field theory to compute our divergence between the vacuum in a bipartite system and an “orbifolded”—in the sense of a conditional expectation—system in terms of the Jones index. We take the opportunity to point out an entropic certainty relation associated with an inclusion of von Neumann factors related to the relative entropy. This certainty relation has an equivalent formulation in terms of error correcting codes.
Hollands, Stefan↗
Scalar fields in 3D asymptotically flat higher-spin gravity
Abstract In this work we construct a novel associative algebra and use it to define a theory of higher-spin gravity in (2 + 1)-dimensional asymptotically flat spacetimes. Our construction is based on a quotient of the universal enveloping algebra of i s l ( 2 , R ) with respect to the ideal generated by its Casimir elements, the mass squared M 2 and the three-dimensional analogue of the square of the Pauli–Lubanski vector S and propose to call the resulting associative algebra i h s ( M 2 , S ) . We provide a definition of its generators and even though we are not yet able to provide the complete set of multiplication rules of this algebra our analysis allows us to study many interesting and relevant sub-structures of i h s ( M 2 , S ) . We then show how to consistently couple a scalar field to an i h s ( M 2 , S ) higher-spin gauge theory.
Physics↗
Surface science insight note: A linear algebraic approach to elucidate native films on Fe 3 O 4 surface
Standard materials are often used to obtain spectra that can be compared to those from unknown samples. Spectra measured from these known substances are also used as a means of computing sensitivity factors to allow quantification by X-ray photoelectron spectroscopy (XPS) of less well-defined materials. Spectra from known materials also provide line shapes suitable for inclusion in spectral models which, when fitted to spectra, permit the chemical state for a sample to be assessed. Both types of information depend on isolating photoemission signals from the inelastically scattered signal. In this Insight note, technical issues associated with the use of XPS of as received Fe 3 O 4 powder sample surface are discussed. The Insight note is designed to show how linear algebraic techniques applied to data collected from a sample marketed as pure Fe 3 O 4 powder are used to verify that XPS has been performed on chemistry representative of the sample. The methods described in this Insight note can further be utilized in elucidating complex XPS data obtained from thin films formed or evolved during cyclic/non-steady use of complex (electro)catalyst surfaces, especially in the presence of contaminants.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
A symbolic framework to obtain mid-fidelity models of flexible multibody systems with application to horizontal-axis wind turbines
Abstract. The article presents a symbolic framework (also called computer algebra program) that is used to obtain, in symbolic mathematical form, the linear and nonlinear equations of motion of a mid-fidelity multibody system including rigid and flexible bodies. Our approach is based on Kane's method and a nonlinear shape function representation for flexible bodies. The shape function approach does not represent the state of the art for flexible multibody dynamics but is an effective trade-off to obtain mid-fidelity models with few degrees of freedom, taking advantage of the separation of space and time. The method yields compact symbolic equations of motion with implicit account of the constraints. The general and automatic framework facilitates the creation and manipulation of models with various levels of complexity by adding or removing degrees of freedom. The symbolic treatment allows for analytical gradients and linearized equations of motion. The linear and nonlinear equations can be exported to Python code or dedicated software. There are multiple applications, such as time domain simulation, stability analyses, frequency domain analyses, advanced controller design, state observers, and digital twins. In this article, we describe the method we used to systematically generate the equations of motion of multibody systems and present the implementation of the framework using the Python package SymPy. We apply the framework to generate illustrative land-based and offshore wind turbine models. We compare our results with OpenFAST simulations and discuss the advantages and limitations of the method. The Python implementation is provided as an open-source project.
Branlard, Emmanuel (ORCID:0000000277506128)↗
Preparing an Incompressible-Flow Fluid Dynamics Code for Exascale-Class Wind Energy Simulations
The U.S. Department of Energy has identified exascale-class wind farm simulation as critical to wind energy scientific discovery. A primary objective of the ExaWind project is to build high-performance, predictive computational fluid dynamics (CFD) tools that satisfy these modeling needs. GPU accelerators will serve as the computational thoroughbreds of next-generation, exascale-class supercomputers. Here, we report on our efforts in preparing the ExaWind unstructured mesh solver, Nalu-Wind, for exascale-class machines. For computing at this scale, a simple port of the incompressible-flow algorithms to GPUs is insufficient. To achieve high performance, one needs novel algorithms that are application aware, memory efficient, and optimized for the latest-generation GPU devices. The result of our efforts are unstructured-mesh simulations of wind turbines that can effectively leverage thousands of GPUs. In particular, we demonstrate a first-of-its-kind, incompressible-flow simulation using Algebraic Multigrid solvers that strong scales to more than 4000 GPUs on the Summit supercomputer.
algebraic multigrid↗
Porting hypre to heterogeneous computer architectures: Strategies and experiences
We report that linear systems are occurring in many applications, and solving them can take a large amount of the total simulation time. The high performance library hypre provides a variety of interfaces and linear solvers, including various multigrid methods, that have achieved good scalability on a variety of homogeneous parallel computer architectures. Heterogeneous architectures with nodes that have both CPUs and accelerators provide new challenges, since they require more fine-grained parallelism and reduced data movement between different memories on a single node as well as across nodes. We will discuss our experiences and strategies to port hypre to heterogeneous computers with accelerators, including the design of a new memory model, the use of abstractions, the BoxLoop macros in the structured and semi-structured interfaces, and the restructuring of algebraic multigrid (AMG) into modular components. We present numerical experiments comparing CPU and GPU performance for several test problems.
97 MATHEMATICS AND COMPUTING↗
Co-design for Particle Applications at Exascale
Co-design across the Exascale Computing Project (ECP) has been critical for both enabling science applications and bringing disparate communities together. Developing and porting applications to the various high-performance computing (HPC) architectures on pre-exascale and exascale computers has been quite challenging due to the diversity of hardware features and software stacks. The Co-design Center for Particle Applications (CoPA) has developed and enhanced the Cabana and PROGRESS/BML libraries to facilitate the creation of new particle applications, make existing particle applications exascale capable, and allow teams to explore new capabilities. Particle methods from atomistic, mesoscale, continuum, through cosmological scales have been built with Cabana, along with new possibilities for application coupling. Similarly, the PROGRESS/BML library has enabled quantum particle applications with linear algebra solvers to use advanced hardware. Across these CoPA-developed libraries, the co-design abstraction layer combines performance portability with math library support to facilitate separation of concerns and directly support science runs.
97 MATHEMATICS AND COMPUTING↗
LaRIS: Targeting Portability and Productivity for LAPACK Codes on Extreme Heterogeneous Systems by Using IRIS
In keeping with the trend of heterogeneity in high-performance computing, hardware manufacturers and vendors are developing new architectures and associated software stacks (e.g., libraries) to harness the best possible performance from commonly used kernels (e.g., linear algebra kernels). However, kernels tuned for one architecture are not portable to others. Moreover, the coexistence of different architectures in a single node makes orchestration difficult. To address these challenges, we introduce LaRIS, a portable framework for LAPACK functionalities. LaRIS ensures a separation between linear algebra algorithms and vendor-library kernels by using the IRIS run time and IRIS-BLAS library. Such abstraction at the algorithm level makes the implementation completely agnostic to the vendor library and architecture. LaRIS uses the IRIS run time to dynamically select the vendor-library kernel and suitable processor architecture at run time. Through LU factorization, we demonstrate that LaRIS can fully utilize different heterogeneous systems by launching and orchestrating different vendor-library kernels without any change in the source code.
Monil, M. A. H.↗
Effective rationality for local unitary invariants of mixed states of two qubits
Abstract We calculate the field of rational local unitary invariants for mixed states of two qubits, by employing methods from algebraic geometry. We prove that this field is rational (i.e. purely transcendental), and that it is generated by nine algebraically independent polynomial invariants. We do so by constructing a relative section, in the sense of invariant theory, whose Weyl group is a finite abelian group. From this construction, we are able to give explicit expressions for the generating invariants in terms of the Bloch matrix representation of mixed states of two qubits. We also prove similar rationality results for the local unitary invariants of symmetrically mixed states of two qubits. We also provide a sketch of how to generalize our results to the case of an arbitrary number of qubits. Our results apply to both complex-valued and real-valued invariants.
Physics↗
3-Manifolds and VOA Characters
Abstract By studying the properties ofq-series$$\widehat{Z}$$ Z ^ -invariants, we develop a dictionary between 3-manifolds and vertex algebras. In particular, we generalize previously known entries in this dictionary to Lie groups of higher rank, to 3-manifolds with toral boundaries, and to BPS partition functions with line operators. This provides a new physical realization of logarithmic vertex algebras in the framework of the 3d-3d correspondence and opens new avenues for their future study. For example, we illustrate how invoking a knot-quiver correspondence for$$\widehat{Z}$$ Z ^ -invariants leads to many infinite families of new fermionic formulae for VOA characters.
Physics↗
Deep Learning for Subgrid‐Scale Turbulence Modeling in Large‐Eddy Simulations of the Convective Atmospheric Boundary Layer
Abstract In large‐eddy simulations, subgrid‐scale (SGS) processes are parameterized as a function of filtered grid‐scale variables. First‐order, algebraic SGS models are based on the eddy‐viscosity assumption, which does not always hold for turbulence. Here we apply supervised deep neural networks (DNNs) to learn SGS stresses from a set of neighboring coarse‐grained velocity from direct numerical simulations of the convective boundary layer at friction Reynolds numbers Re τ up to 1243 without invoking the eddy‐viscosity assumption. The DNN model was found to produce higher correlation between SGS stresses compared to the Smagorinsky model and the Smagorinsky‐Bardina mixed model in the surface and mixed layers and can be applied to different grid resolutions and various stability conditions ranging from near neutral to very unstable. The DNN model can capture key statistics of turbulence in a posteriori (online) tests when applied to large‐eddy simulations of the atmospheric boundary layer.
54 ENVIRONMENTAL SCIENCES↗