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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

The distribution-based remapping of the nodal mass and momentum between arbitrary meshes for staggered arbitrary Lagrangian-Eulerian hydrodynamics

We present a new distribution-based remapping of the nodal mass and momentum between arbitrary source (Lagrangian) and arbitrary target (rezoned) meshes for indirect staggered arbitrary Lagrangian-Eulerian hydrodynamics. Here, the method is based on the following ideas: define cell-centered momentum and mass on the source mesh; conservatively remap those cell-centered quantities from source to target meshes; and use local constrained optimization for each cell of the target mesh to conservatively distribute cell mass and momentum to the nodes of the cell. This new method is efficient, conservative, accurate and bounds preserving.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

A cell-centered AMR-ALE framework for 3D multi-material hydrodynamics. Part I: Lagrangian and indirect Euler AMR algorithms

Many applications of physics and engineering involve wide ranges of time and spatial scales. The numerical simulation of localized small scales such as shock waves and material interfaces requires a large number of computational cells in these regions. For these applications, Lagrangian and Arbitrary-Lagrangian-Eulerian (ALE) related methods are engaging since the moving mesh feature naturally brings mesh cells on shock discontinuities and material interfaces are carefully captured. In addition, Adaptive-Mesh-Refinement (AMR) strategies aim to optimize computational resources by concentrating finer mesh cells only in areas of interest while using coarser cells elsewhere. A key but challenging AMR requirement consists in efficiently distributing the computational effort to achieve high accuracy without the prohibitive computational costs associated with uniformly fine grids. Here, in this document, the coupling of the p4est AMR library with a cell-centered Lagrangian scheme is presented with the goal to perform reliable 3D Lagrangian-AMR and indirect Euler-AMR multi-material simulations. In particular, it is shown that starting from a 3D indirect ALE code, the memory management and load balancing requirements can be delegated to an external library (here the p4est library) to unlock ALE-AMR capabilities. First, we present a strategy to transcribe the octant-based connectivity of the 3D AMR framework with that of an unstructured mesh of polygonal cells used in Lagrangian hydrodynamics. Then, we show how refinement and coarsening operations must be adapted to the particular Lagrangian framework to ensure the conservation of volume during those steps. Finally, several numerical test cases are presented that demonstrate the capabilities of the Lagrangian-AMR and indirect Euler-AMR algorithms.

3D cell-centered Lagrangian numerical scheme↗
DOE OSTI2020

Summer Proceedings 2019

The Computer Science Research Institute (CSRI) brings university faculty and students to Sandia for focused collaborative research on Department of Energy (DOE) computer and computational science problems. The institute provides an opportunity for university researchers to learn about problems in computer and computational science at DOE laboratories. Participants conduct leading-edge research, interact with scientists and engineers at the laboratories, and help transfer results of their research to programs at the labs. Some specific CSRI research interest areas are: scalable solvers, optimization, adaptivity and mesh refinement, graph-based, discrete, and combinatorial algorithms, uncertainty estimation, mesh generation, dynamic load-balancing, virus and other malicious-code defense, visualization, scalable cluster computers and heterogeneous computers, data-intensive computing, environments for scalable computing, parallel input/output, advanced architectures, and theoretical computer science. The CSRI Summer Program includes the organization of a weekly seminar series and the publication of this summer proceedings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

CSRI Summer Proceedings 2020

The Computer Science Research Institute (CSRI) brings university faculty and students to Sandia for focused collaborative research on Department of Energy (DOE) computer and computational science problems. The institute provides an opportunity for university researchers to learn about problems in computer and computational science at DOE laboratories. Participants conduct leading-edge research, interact with scientists and engineers at the laboratories, and help transfer results of their research to programs at the labs. Some specific CSRI research interest areas are: scalable solvers, optimization, adaptivity and mesh refinement, graph-based, discrete, and combinatorial algorithms, uncertainty estimation, mesh generation, dynamic load-balancing, virus and other malicious-code defense, visualization, scalable cluster computers, data-intensive computing, environments for scalable computing, parallel input/output, advanced architectures, and theoretical computer science. The CSRI Summer Program is organized by CSRI and typically includes the organization of a weekly seminar series and the publication of a summer proceedings. In 2020, the CSRI summer program was executed completely virtually; all student interns worked from home, due to the COVID-19 pandemic.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

The eXtended virtual element method for elliptic problems with weakly singular solutions

This paper introduces a novel eXtended virtual element method, an extension of the conforming virtual element method. The X-VEM is formulated by incorporating appropriate enrichment functions in the local spaces. The method is designed to handle highly generic enrichment functions, including singularities arising from fractured domains. By achieving consistency on the enrichment space, the method is proven to achieve arbitrary approximation orders even in the presence of singular solutions. The paper includes a complete convergence analysis under general assumptions on mesh regularity, and numerical experiments validating the method’s accuracy on various mesh families, demonstrating optimal convergence rates in the L 2 - and H 1 - norms on fractured or L-shaped domains.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

11-th order of accuracy for numerical solution of 3-D Poisson equation with irregular interfaces on unfitted Cartesian meshes

For the first time the optimal local truncation error method (OLTEM) with 125-point stencils and unfitted Cartesian meshes has been developed in the general 3-D case for the Poisson equation for heterogeneous materials with smooth irregular interfaces. The 125-point stencils equations that are similar to those for quadratic finite elements are used for OLTEM. The interface conditions for OLTEM are imposed as constraints at a small number of interface points and do not require the introduction of additional unknowns, i.e., the sparse structure of global discrete equations of OLTEM is the same for homogeneous and heterogeneous materials. The stencils coefficients of OLTEM are calculated by the minimization of the local truncation error of the stencil equations. These derivations include the use of the Poisson equation for the relationship between the different spatial derivatives. Such a procedure provides the maximum possible accuracy of the discrete equations of OLTEM. In contrast to known numerical techniques with quadratic elements and third order of accuracy on conforming and unfitted meshes, OLTEM with the 125-point stencils provides 11-th order of accuracy, i.e., an extremely large increase in accuracy by 8 orders for similar stencils. The numerical results show that OLTEM yields much more accurate results than high-order finite elements with much wider stencils. The increased numerical accuracy of OLTEM leads to an extremely large increase in computational efficiency. Additionally, a new post-processing procedure with the 125-point stencil has been developed for the calculation of the spatial derivatives of the primary function. The post-processing procedure includes the minimization of the local truncation error and the use of the Poisson equation. It is demonstrated that the use of the partial differential equation (PDE) for the 125-point stencils improves the accuracy of the spatial derivatives by 6 orders compared to post-processing without the use of PDE as in existing numerical techniques. At an accuracy of 0.1% for the spatial derivatives, OLTEM reduces the number of degrees of freedom by 900 - 4∙10 6 times compared to quadratic finite elements. The developed post-processing procedure can be easily extended to unstructured meshes and can be independently used with existing post-processing techniques (e.g., with finite elements).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

CrossLink: Advancements in Scalable Unstructured Mesh Generation [Slides]

Traditional mesh generation approaches are labor intensive and have limited robustness when applied to parametric design exploration and optimization of complex geometries. While automatic mesh generation approaches exist, they tend to generate tetrahedral or mixed-hybrid meshes which are generally unsuitable for physics applications with strong shock waves, thin boundary layers, and strong gradients. In addition, simulations sizes in the billions of cells are becoming more common with traditional mesh generation methods quickly reaching scalability limits. CrossLink offers a topology-based mesh generation approach with unstructured block-filling methods and a scalable mesh generation engine. In addition, CrossLink incorporates a python based API for seamless workflow integration and robust repeatability of the geometry handling and mesh generation process. This makes it ideal for parametric design study and optimization of complex geometries. Finally, future versions of CrossLink will offer a parametric mesh capability that optimizes a high-order mesh and enables reconstruction of the final mesh in memory by the physics solver.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Simultaneous shape and topology optimization of inflatable soft robots

Simultaneous shape and topology optimization is used to design pressure-activated inflatable soft robots. The pressure loaded boundary is meshed conformingly and shape optimized, while the morphology of the robot is topology optimized. The design objective is to exert maximum force on an object, i.e. to produce soft “grippers”. The robot’s motion is modeled using nearly incompressible finite deformation hyperelasticity. To ensure stability of the robot, the buckling load factors obtained via linearized buckling analyses are constrained. The finite element method is used to evaluate the optimization cost and constraint functions and the adjoint method is employed to compute their sensitivities. The numerical examples produce pressure-driven soft robots with varying complexity. We also compare our simultaneous optimization results to those obtained via sequential topology and then shape optimization.

42 ENGINEERING↗
DOE OSTI2020

Coupling laser physics to radiation-hydrodynamics

In order to accurately model implosion hydrodynamics in a radiation-hydrodynamics code, it is essential to include accurate accounting for energy deposition physics. In inertial confinement fusion (ICF), where capsules are driven by lasers or laser-driven x-rays, energy deposition profiles and energy transport have a strong impact on the development and evolution of capsule dynamics and hydrodynamic instabilities. Nevertheless, accurately modeling laser beam propagation in radiation-hydrodynamics codes presents unique challenges associated with disparate resolution requirements, the potential to seed spurious noise in highly unstable systems, and computational expense. We discuss a new method for coupling laser ray-tracing physics to a radiation hydrodynamics code, developed in the process of implementing the Mazinisin laser ray-trace into the xRAGE radiation hydrodynamics code. In contrast to previous approaches, in which laser ray-tracing is performed on the radiation-hydrodynamics mesh, our method involves a mesh generation and evolution strategy that addresses the unique requirements of the laser ray-trace in a separate mesh, enabling performance enhancements and strategies to reduce noise seeded by the discretization of beams into computational rays. In addition, we have employed several methods to ensure that spurious mesh imprinting is minimized. These involved optimizing the laser and radiation-hydrodynamics meshes as well as interpolation between them and requires the use of an exact initialization method for the radiation-hydrodynamics mesh. Furthermore, these techniques have enabled efficient computation of laser-driven implosions and other experiments with minimal introduction of spurious noise.

47 OTHER INSTRUMENTATION↗
DOE OSTI2026

High-Order Mesh r-Adaptivity with Tangential Relaxation and Guaranteed Mesh Validity

High-order meshes are crucial for achieving optimal convergence rates in curvilinear domains, preserving symmetry, and aligning with key flow features in moving mesh simulations [1], but their quality is challenging to control. In prior work, we have developed techniques based on Target-Matrix Optimization Paradigm (TMOP) to adapt a given high-order mesh to the geometry and solution of the partial differential equation (PDE) [2, 3]. Here, we extend this framework to address two key gaps in the literature for highorder mesh 𝑟-adaptivity. First, we introduce tangential relaxation on curved surfaces using solely the discrete mesh representation, eliminating the need for access to underlying geometry (e.g., CAD model). Second, we ensure a continuously positive Jacobian determinant throughout the domain. This determinant positivity is essential for using the high-order mesh resulting from 𝑟-adaptivity with arbitrary quadrature schemes in simulations. The proposed approach is demonstrated to be robust using a variety of numerical experiments.

Mathematics and Computing↗
DOE OSTI2023

High-Order Mesh hr-adaptivity for Surface Fitting to Implicit Geometries

We present an ℎ𝑟-adaptivity framework for morphing a given mesh to fit a target surface prescribed as the zero isocontour of a discrete function. In this framework, high-order meshing is posed as a variational minimization problem that depends on the mesh quality prescribed via the target matrix optimization paradigm (TMOP) and position of a subset of mesh nodes with respect to the target surface. The proposed formulation ensures that the variational problem is converged and mesh quality degradation near the surface is limited, even when the mesh topology is incompatible with the target surface. Additionally, a mesh subset-based approach and ℎ-refinement is introduced to efficiently increase fitting accuracy while reducing the computational cost of the mesh morphing problem. The ℎ𝑟-adaptivity technique extends to different element types in two- and three-dimensions, and can be used in existing finite element and spectral element frameworks to obtain high-order body-fitted meshes. Various numerical experiments demonstrate the robustness and accuracy of the fitting approach for problems of practical interest such as Lagrangian hydrodynamics and topology optimization.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Efficient shallow Ritz method for 1D diffusion problems

This paper studies the shallow Ritz method for solving the one-dimensional diffusion problem. It is shown that the shallow Ritz method improves the order of approximation dramatically for non-smooth problems. To realize this optimal or nearly optimal order of the shallow Ritz approximation, we develop a damped block Newton (dBN) method that alternates between updates of the linear and non-linear parameters. Per each iteration, the linear and the non-linear parameters are updated by exact inversion and one step of a modified, damped Newton method applied to a reduced non-linear system, respectively. The computational cost of each dBN iteration is $\mathcal{O}$(n). Starting with the non-linear parameters as a uniform partition of the interval, numerical experiments show that the dBN is capable of efficiently moving mesh points to nearly optimal locations. In conclusion, to improve the efficiency of the dBN further, we propose an adaptive damped block Newton (AdBN) method by combining the dBN with the adaptive neuron enhancement (ANE) method [28].

Diffusion problems↗
DOE OSTI2022

Sequential Decision Making (SDM) for Mesh Refinement and Model Selection in Multiscale, Multi-Physics Applications

Intelligent automation and decision support are needed to enhance computational efficiency and robustness in multiscale and multi-physics problems, including materials science, manufacturing, and climate and weather modeling. Current scientific computing approaches for enabling decisions by scientists fail to explore the role of learning, reasoning, and probabilistic planning. Often these decisions are not performed in real-time during the computation but are made prior to the start of the computation, which must be interrupted in order to make changes to the prior choices. Such interruptions at different stages of the computation increase the total computing time and the need for a human expert to frequently monitor the results. State of art scientific computing methods consist of rule-based algorithms that cannot automatically adapt to a dynamically changing computing environment. The development of a Sequential Decision Making (SDM) framework will automate scientific computing by optimizing the policies for mesh refinement, time-stepping, model and algorithm selection, resource allocation, and pre and post-processing. Our agent SDM framework for scientific computing will consist of data-driven learning (Classifier), automated reasoning (contextual knowledge), and probabilistic planning (Reinforcement Learning). In this project, we focused on three problems to demonstrate our SDM framework on a set of ordinary and partial differential equations. Classification of Lorenz system regions using Feed-Forward Neural Networks examined learning in the SDM framework. On the other hand, reasoning and planning in the SDM framework were used in two problems: adaptive time-stepping for nonlinear ODEs using on-policy RL algorithms, and adaptive mesh refinement for 2-D PDEs using off-policy RL algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Yet another parameter-free shape optimization method

The use of node coordinates as design variables in shape optimization offers a larger design space than computer-aided design (CAD)-based shape parameterizations. It also allows for the optimization of legacy designs, i.e., a finite element mesh from an existing design can be readily optimized to meet new performance requirements without involving a CAD model. However, it is well known that the node coordinate parameterization method is fraught with numerical difficulties, which makes it impractical to use. This has led to several of “parameter-free” shape optimization methods that seek the advantages and avoid the pitfalls of the naïve node coordinate parameterization method. These methods come in two main varieties: sensitivity filtering (or gradient smoothing) and consistent filtering. The latter is analogous to the density filter method used in topology optimization (TO). In this work, we use the PDE filter from TO and energy-based filters to implement consistent shape optimization filtering schemes easily and efficiently. Numerical experiments demonstrate that consistent methods are more robust than sensitivity filtering methods.

42 ENGINEERING↗
DOE OSTI2024

Proximal Galerkin: A Structure-Preserving Finite Element Method for Pointwise Bound Constraints

The proximal Galerkin finite element method is a high-order, low iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of pointwise bound constraints in infinite-dimensional function spaces. This paper introduces the proximal Galerkin method and applies it to solve free boundary problems, enforce discrete maximum principles, and develop a scalable, mesh-independent algorithm for optimal design with pointwise bound constraints. This paper also introduces the latent variable proximal point (LVPP) algorithm, from which the proximal Galerkin method derives. When analyzing the classical obstacle problem, we discover that the underlying variational inequality can be replaced by a sequence of second-order partial differential equations (PDEs) that are readily discretized and solved with, e.g., the proximal Galerkin method. Throughout this work, we arrive at several contributions that may be of independent interest. These include (1) a semilinear PDE we refer to as the entropic Poisson equation; (2) an algebraic/geometric connection between high-order positivity-preserving discretizations and certain infinite-dimensional Lie groups; and (3) a gradient-based, bound-preserving algorithm for two-field, density-based topology optimization. The complete proximal Galerkin methodology combines ideas from nonlinear programming, functional analysis, tropical algebra, and differential geometry and can potentially lead to new synergies among these areas as well as within variational and numerical analysis. Open-source implementations of our methods accompany this work to facilitate reproduction and broader adoption.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

DISTRI: Distributed Multi-Facility HPC Simulator (DISTRI) v2.1

DISTRI is an advanced network simulator designed for multi-facility computational infrastructures with agentic behavior. It simulates HPC facilities where computational resources act as autonomous agents, making intelligent decisions about job scheduling, load balancing, and resource allocation. The simulator focuses on developing and testing decentralized algorithms that promote resilience and efficiency in multi-facility environments. Key Features: - Agentic Resource Behavior: Processors and DTNs act as autonomous agents with decision-making capabilities - Pheromone-Based Load Balancing: Decentralized load balancing inspired by ant colony optimization - Dual Topology Support: Mesh (normal operations) and Dumbell (network testing) topologies - Comprehensive TCP Simulation: Realistic TCP implementations with multiple congestion control algorithms - Failure Resilience Testing: Processor failure simulation with automatic job reassignment - Extensive Visualization: Detailed performance analysis and metrics collection - Research-Ready: Designed for algorithm development and benchmarking

Bez, Jean Luca [Lawrence Berkeley National Laborat↗
DOE OSTI2022

Analysis of cell-based diffusion acceleration for the slice balance approach

In this work, we perform analysis on the use of cell-based diffusion acceleration methodologies to accelerate the convergence of transport solutions discretized with the slice balance approach (SBA) on unstructured polygonal grids.We investigated both linear diffusion synthetic acceleration (DSA) and non linear diffusion acceleration (NDA), including its partial-current variant (pNDA). DSA and NDA were both shown to diverge for intermediate ranges of mesh optical thicknesses. However, pNDA and Krylov methods like GMRES and Broyden stabilized the acceleration schemes, including problems with degenerate cells formed by mesh refinement. (author)

42 ENGINEERING↗
DOE OSTI2022

Parallel transport sweeps on two-dimensional cartesian and hexagonal grids

This paper aims to provide a proof of concept for parallel transport sweeps on two-dimensional hexagonal grids for the discrete ordinates transport equation. While the method is an extension of the popular and well-established Koch-Baker-Alcoulffe (KBA) algorithm, there are significant differences between the cartesian and hexagonal grid and thereafter sweep. The most important is the three-way connectivity of hexagons within the grid which creates greater dependencies between the elements. The KBA method in structured orthogonal grids was first implemented in the DRAGON5 code and the method is first described here. The differences in implementation for the hexagonal grid are also described. Benchmark results are also presented, showing roughly 10 times speedup in computational times with roughly 100 processors, in both cases. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗