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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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16 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

3D mesh regularization within an ALE code using a weighted line sweeping method

The Lagrangian formalism is widely used to simulate hydrodynamic responses in complex engineering applications, particularly those involving strong shock waves. However, as the mesh moves with the fluid, it can become highly distorted, requiring a regularization step. This involves constructing a new grid and remapping conservative quantities onto it to restore mesh quality. This work introduces a regularization method for block-structured meshes within a 3D ALE (Arbitrary Lagrangian-Eulerian) code. The proposed approach prevents mesh tangling while preserving the anisotropic features of the initial Lagrangian mesh. This regularization technique incorporates aspect ratio-based weights to control mesh smoothing. Unlike uniform rezoning techniques, this weighted approach maintains proximity to the Lagrangian mesh while improving mesh quality. Here, the method effectively handles concave geometries by mitigating the grid attraction phenomenon, which typically leads to mesh concentration along concave edges. Numerical experiments demonstrate its efficiency in regularizing severely deformed meshes, and its integration within the ALE framework is validated on challenging hydrodynamic test cases, including the triple point problem.

42 ENGINEERING↗
DOE OSTI2024

A graphics processing unit accelerated sparse direct solver and preconditioner with block low rank compression

We present the GPU implementation efforts and challenges of the sparse solver package STRUMPACK. The code is made publicly available on github with a permissive BSD license. STRUMPACK implements an approximate multifrontal solver, a sparse LU factorization which makes use of compression methods to accelerate time to solution and reduce memory usage. Multiple compression schemes based on rank-structured and hierarchical matrix approximations are supported, including hierarchically semi-separable, hierarchically off-diagonal butterfly, and block low rank. Here, in this paper, we present the GPU implementation of the block low rank (BLR) compression method within a multifrontal solver. Our GPU implementation relies on highly optimized vendor libraries such as cuBLAS and cuSOLVER for NVIDIA GPUs, rocBLAS and rocSOLVER for AMD GPUs and the Intel oneAPI Math Kernel Library (oneMKL) for Intel GPUs. Additionally, we rely on external open source libraries such as SLATE (Software for Linear Algebra Targeting Exascale), MAGMA (Matrix Algebra on GPU and Multi-core Architectures), and KBLAS (KAUST BLAS). SLATE is used as a GPU-capable ScaLAPACK replacement. From MAGMA we use variable sized batched dense linear algebra operations such as GEMM, TRSM and LU with partial pivoting. KBLAS provides efficient (batched) low rank matrix compression for NVIDIA GPUs using an adaptive randomized sampling scheme. The resulting sparse solver and preconditioner runs on NVIDIA, AMD and Intel GPUs. Interfaces are available from PETSc, Trilinos and MFEM, or the solver can be used directly in user code. We report results for a range of benchmark applications, using the Perlmutter system from NERSC, Frontier from ORNL, and Aurora from ALCF. For a high frequency wave equation on a regular mesh, using 32 Perlmutter compute nodes, the factorization phase of the exact GPU solver is about 6.5× faster compared to the CPU-only solver. The BLR-enabled GPU solver is about 13.8× faster than the CPU exact solver. For a collection of SuiteSparse matrices, the STRUMPACK exact factorization on a single GPU is on average 1.9× faster than NVIDIA’s cuDSS solver.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

A cell-centered AMR-ALE framework for 3D multi-material hydrodynamics. Part II: linesweep ALE rezoning for nonconformal block-structured AMR meshes

The simulation of flows presenting contact discontinuities, vorticity, and large variations in spatial scales can be performed in a framework coupling Arbitrary Lagrangian Eulerian (ALE) algorithms and Adaptive Mesh Refinement (AMR). This coupling requires adaptation of ALE rezoning techniques to meshes containing nonconformal nodes arising from both the AMR topology and the junction of mesh blocks. Here, in this paper, we present an ALE rezoning strategy that is compatible with such meshes, and that can also act as a disentangling algorithm. Emphasis is put on an algorithm that respects intrinsic Lagrangian mesh properties in order to preserve accuracy around discontinuities. To that end, we adapt the weighted linesweep algorithm to nonconformal block-structured AMR meshes. Then, we present control parameters introduced in the method for it to be applicable in practical situations. Notably, the method is coupled to a specific metric optimization in order to palliate some shortcomings of the linesweep method. Finally, numerical test cases are presented that feature the capabilities of the ALE-AMR algorithm for flows that present discontinuities, vorticity, and a variety of scales. Notably, we show that our ALE-AMR algorithm gives results at least similar to Euler-AMR, but provides better accuracy in cases where discontinuities are involved, thanks to a method that respects the Lagrangian features of the mesh. Additionally, it enables Euler-AMR-like computations on domains with temporally varying domain boundaries.

Adaptive mesh refinement↗
DOE OSTI2025

An FFT-based micromechanical model for gradient enhanced brittle fracture

Damage models incorporated within FFT-based micromechanical methods have received much attention recently because of the need to better understand and predict brittle and ductile fracture. An important aspect of a damage model is non-local regularization, which removes the mesh dependence of the predictions that otherwise become physically unacceptable upon grid refinement. In this work, the Helmholtz-type equation for non-local gradient regularization of a damage model on a distorted grid is solved using an FFT-based approach. Further, the resulting system of equations is solved using the Jacobi iterative method. The model is applied to simulate brittle fracture of an intermetallic. The influence of the time and space discretization, the length-scale parameter, and intermetallic crystallographic orientation on crack evolution is studied.

36 MATERIALS SCIENCE↗
DOE OSTI2026

PyHydroGeophysX: An extensible open-source platform for integrating hydrological models with geophysical measurements

Hydrological models and geophysical measurements are widely used tools for understanding subsurface hydrological processes relevant to water resource management, yet they typically remain disconnected due to technical barriers. We present PyHydroGeophysX, an open-source Python platform bridging this gap by providing standardized interfaces between hydrological modeling software (MODFLOW, ParFlow) and geophysical simulation tools (PyGIMLi, SimPEG). The platform implements bidirectional workflows: translating hydrological outputs into simulated geophysical responses through petrophysical models, and extracting hydrological information from geophysical inversions. Key features include bidirectional workflow modules, configurable petrophysical models, time-lapse inversion with temporal regularization, parallel computing, and mesh utilities for property transfer between geophysical and hydrological grids. The modular architecture of PyHydroGeophysX enables researchers to incorporate additional models and methods, fostering broader adoption of integrated hydrogeophysical approaches. The software is freely available on GitHub and is intended for researchers and practitioners working at the intersection of hydrology and geophysics.

Hydrogeophysics↗
DOE OSTI2026

PDE-constrained high-order mesh optimization

Here, we present a novel framework for PDE-constrained r-adaptivity of high-order meshes. The proposed method formulates mesh movement as an optimization problem, with an objective function defined as a convex combination of a mesh quality metric and a measure of the accuracy of the PDE solution obtained via finite element discretization. The proposed formulation achieves optimized, well-defined high-order meshes by integrating mesh quality control, PDE solution accuracy, and robust gradient regularization. We adopt the Target-Matrix Optimization Paradigm to control geometric properties across the mesh, independent of the PDE of interest. To incorporate the accuracy of the PDE solution, we introduce error measures that control the finite element discretization error. The implicit dependence of these error measures on the mesh nodal positions is accurately captured by adjoint sensitivity analysis. Additionally, a convolution-based gradient regularization strategy is used to ensure stable and effective adaptation of high-order meshes. We demonstrate that the proposed framework can improve mesh quality and reduce the error by up to 10 times for the solution of Poisson and linear elasto-static problems. The approach is general with respect to the dimensionality, the order of the mesh, the types of mesh elements, and can be applied to any PDE that admits well-defined adjoint operators.

Computer science↗
DOE OSTI2025

A Block-Structured Adaptive Mesh Framework to Solve Radiation Transfer Equation in Irregular Embedded Geometries

Radiation transport arises in various scientific, industrial, and medical fields, and understanding its effect in applications is needed to make accurate predictions, safety assessments and performance optimizations. Solving the Radiation Transport Equation (RTE) is challenging due to its integro-differential nature, which involves both differential and integral terms. The differential term describes the change in radiation intensity due to absorption and emission, while the integral term accounts for scattering. The accurate modeling of radiation is further complicated in many applications due to the complex, irregular geometries. Various methods exist for solving the RTE, including the zonal, Monte Carlo, spherical harmonics, discrete ordinates, and finite volume methods. Traditional mesh-based approaches, which rely on structured or unstructured meshes, struggle with irregular geometries due to: a) the difficulty of conforming structured grids to irregular domains, b) challenges in enforcing boundary conditions correctly, and c) the additional computational cost of unstructured mesh methods. This work presents a second-order accurate method for solving the RTE in irregular geometries. The radiation intensity is discretized using the finite-volume method in both spatial and angular directions on regular Cartesian grid blocks. Leveraging the block-structured adaptive mesh refinement (AMR) framework provided by AMReX, our method refines the grid locally to reduce spatial discretization error, ensuring a converged numerical solution while minimizing computational costs elsewhere. A two-stage deferred correction approach is employed: First, a first-order discretization on grid blocks is solved using an algebraic multigrid method in HYPRE. Second, a correction term is applied explicitly to achieve second-order accuracy. The correction term is calculated by approximating the radiation flux on cell faces using a Total Variation Diminishing (TVD) scheme. This approach ensures quick convergence of the multigrid method while preserving higher-order accuracy of the numerical solution. Irregular geometries are resolved as embedded boundaries (EB), resulting in both cut cells and regular cells. In cut cells, we modify the fluxes using face fractions and incorporate additional contributions from EB boundary conditions. To ensure higher-order convergence near the EB interface, the correction term is modified by interpolating the radiation intensity to fictitious ghost points. The implementation takes advantage of modern supercomputers by leveraging AMReX’sMPI/X parallelization strategy where X can be MPI or a GPU accelerator including CUDA, HIP and DPC++. We validate our solver using classical test cases, both with and without EB, demonstrating accuracy and efficiency. Additionally, we analyze the impact of adaptive mesh refinement on solution accuracy and computational cost, highlighting the advantages of our approach for high-resolution radiation transport simulations.

computational fluid dynamics (CFD)↗
DOE OSTI2024

One-shot omnidirectional pressure integration through matrix inversion

In this work, we present a method to perform 2D and 3D omnidirectional pressure integration from velocity measurements with a single-iteration matrix inversion approach. This work builds upon our previous work, where the rotating parallel ray approach was extended to the limit of infinite rays by taking continuous projection integrals of the ray paths and recasting the problem as an iterative matrix inversion problem. This iterative matrix equation is now 'fast-forwarded' to the 'infinity' iteration, leading to a different matrix equation that can be solved in a single step, thereby presenting the same computational complexity as the Poisson equation. We observe computational speedups of ~10 6 when compared to brute-force omnidirectional integration methods, enabling the treatment of grids of ~10 9 points and potentially even larger in a desktop setup at the time of publication. Further examination of the boundary conditions of our one-shot method shows that omnidirectional pressure integration implements a boundary condition where the boundary points are treated as interior points to the extent that information is available. Finally, we show how the method can be extended from the regular grids typical of particle image velocimetry to the unstructured meshes characteristic of particle tracking velocimetry data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

CHESS 2025: Orthorectified airborne RGB imagery from NEON AOP surveys

This dataset provides Level 1 (L1) and Level 3 (L3) orthorectified Red-Green-Blue (RGB) imagery collected for the 2025 Colorado Headwaters Ecological Spectroscopy Study (CHESS). This high-resolution imagery is a photographic record of red, green, and blue visible light from sunlight reflected off of the Earth’s surface. The data comprise full-color images of the ground surface and are primarily intended to provide context to imaging spectroscopy and light detection and ranging (LiDAR) data. The data were acquired over three study domains in the Upper Gunnison river basin: the upper East River watershed (CRBU); Almont Triangle and Taylor Canyon (ALMO); and Upper Taylor River watershed (UPTA) between 2025-06-13 and 2025-07-15. RGB images were acquired using the PhaseOne IXM-RS150F high-resolution digital camera onboard the National Ecological Observatory Network (NEON) Airborne Observation Platform (AOP). The package data include both an L1 product comprising one camera frame per file and an L3 mosaic aligned to the Universal Transverse Mercator (UTM) Zone 13N grid and the World Geodetic System (WGS) 84 projection. Both products are provided in geotif (.tif) format at 0.1 m ground resolution. The bulk of the imagery was collected during the main CHESS field campaign from June 13 to July 15, 2025. Additional images of a portion of the Upper Taylor (UPTA) domain were collected on September 18, 2025, to fill gaps in imagery identified after the main campaign was complete. RGB camera imagery is not radiometrically calibrated, and therefore pixel values should not be exploited for scientific analysis. Pixel values have undergone a manual adjustment to enhance feature identification. The imagery is rigorously geolocated which does allow for reliable geometric information to be retrieved. To generate the orthorectified imagery, the NEON AOP camera captured visible spectrum in red, green, and blue bands. The raw images were then processed using NEON’s camera orthorectification workflow. A boresight calibration flight was made to build a complete camera, distortion, and alignment model. Color balance/white balance and exposure correction were applied to the raw RGB images. The corrected images were orthorectified by ray-tracing image pixels to a lidar-derived digital surface model (DSM) mesh using the refined camera model, outputting orthorectified raster pixels on a regular grid. Flightline-level data were mosaicked by selecting per-pixel contributions from overlapping orthorectified images using line-of-sight (LOS) zenith angle minimization to reduce edge distortions. CHESS Project Description: The Colorado Headwaters Ecological Spectroscopy Study (CHESS) comprised a multi-week airborne remote sensing and field observation campaign in the Upper Gunnison Basin, Colorado, conducted in June and July of 2025. Airborne remote sensing was conducted by the National Ecological Observatory Network Airborne Observation Platform (NEON AOP), concurrent with a field campaign run by the Rocky Mountain Biological Laboratory (RMBL), the Lawrence Berkeley National Laboratory (LBNL) and SLAC National Accelerator Laboratory Watershed Function Science Focus Area (SFA), and NASA-JPL (Jet Propulsion Laboratory) Earth Surface Mineral Dust Source Investigation (EMIT) program. Between June 10 and July 18, 2025, the NEON AOP flight team collected high-resolution aerial imaging spectroscopy and Light Detection and Ranging (LiDAR) data over three domains: the Upper East River (CRBU), Almont Triangle (ALMO), and the Upper Taylor Basin (UPTA). In coordination with the flights, a field campaign acquired ground-truth observations, including observations of vegetation composition, foliar traits, forest demography, and subsurface properties in 18 core sampling areas within the domains. Additional surface water observations were taken at over 380 point locations. All CHESS campaign datasets can be found within the CHESS ESS-DIVE data portal: https://data.ess-dive.lbl.gov/portals/chess. Funding Acknowledgement: Field and remote-sensing data acquisition was performed under a grant from the National Aeronautics and Space Administration (80NSSC24K1005). This work was also supported by the Watershed Function Science Focus Area at Lawrence Berkeley National Laboratory funded by the US Department of Energy, Office of Science, Biological and Environmental Research under Contract No. DE-AC02-05CH11231.

2018 NEON and 2025 CHESS Campaigns↗
DOE OSTI2025

Virtual element approximations of the time-fractional nonlinear convection-diffusion equation on polygonal meshes

We extend the Virtual Element Method to a two-dimensional unsteady nonlinear convection-diffusion equation characterized by a fractional-order derivative with respect to the time variable. Our methodology is based on three fundamental technical components: a fractional version of the Grunwald-Letnikov approximation, discrete maximal regularity, and the regularity theory associated with non-linearity. We prove the method's well-posedness, i.e., the approximate solution's existence and uniqueness to the time-fractional convection-diffusion equation with a Lipschitz nonlinear source term. The fully discrete scheme inherently maintains stability and consistency by leveraging the discrete maximal regularity and the energy projection operator. The convergence in the L 2 -norm and H 1 -norm to various mesh configurations is validated by numerical results, underlining the practical effectiveness of the proposed method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A framework for discrete optimization of stellarator coils

Designing magnets for three-dimensional plasma confinement is a key task for advancing the stellarator as a fusion reactor concept. Stellarator magnets must produce an accurate field while leaving adequate room for other components and being reasonably simple to construct and assemble. In this paper, a framework for coil design and optimization is introduced that enables the attainment of sparse magnet solutions with arbitrary restrictions on where coils may be located. The solution space is formulated as a 'wireframe' consisting of a mesh of interconnected wire segments enclosing the plasma. Two methods are developed for optimizing the current distribution on a wireframe: Regularized Constrained Least Squares, which uses a linear least-squares approach to optimize the currents in each segment, and Greedy Stellarator Coil Optimization, a fully discrete procedure in which loops of current are added to the mesh one by one to achieve the desired magnetic field on the plasma boundary. Examples are presented of solutions obtainable with each method, some of which achieve high field accuracy while obeying spatial constraints that permit easy assembly.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Fast, Nondestructive and Precise Biomass Measurements Are Possible Using Lidar-Based Convex Hull and Voxelization Algorithms

Light detection and ranging (lidar) scanning tools are available that can make rapid digital estimations of biomass. Voxelization and convex hull are two algorithms used to calculate the volume of the scanned plant canopy, which is correlated with biomass, often the primary trait of interest. Voxelization splits the scans into regular-sized cubes, or voxels, whereas the convex hull algorithm creates a polygon mesh around the outermost points of the point cloud and calculates the volume within that mesh. In this study, digital estimates of biomass were correlated against hand-harvested biomass for field-grown corn, broom corn, and energy sorghum. Voxelization (r = 0.92) and convex hull (r = 0.95) both correlated well with plant dry biomass. Lidar data were also collected in a large breeding trial with nearly 900 genotypes of energy sorghum. In contrast to the manual harvest studies, digital biomass estimations correlated poorly with yield collected from a forage harvester for both voxel count (r = 0.32) and convex hull volume (r = 0.39). However, further analysis showed that the coefficient of variation (CV, a measure of variability) for harvester-based estimates of biomass was greater than the CV of the voxel and convex-hull-based biomass estimates, indicating that poor correlation was due to harvester imprecision, not digital estimations. Overall, results indicate that the lidar-based digital biomass estimates presented here are comparable or more precise than current approaches.

Environmental Sciences & Ecology↗
DOE OSTI2026

Numerical Investigation of Fluid Flow and Space Charge in Liquid Argon Time Projection Chamber (LArTPC) Detectors

Overview This project focused on developing a high-fidelity numerical framework to simulate the multiphysics environment within Liquid Argon Time Projection Chamber (LArTPC) detectors. The primary objective was to characterize the complex interplay between ion transport, background fluid dynamics, and electric field distortions—a critical factor for the calibration and sensitivity of next-generation High Energy Physics experiments, such as DUNE. Technical Achievements The research successfully yielded a hybrid numerical space-charge solver utilizing a Cell-Centered Finite Volume Method (FVM) for ion transport coupled with a Finite Element Method (FEM) for electric potential. Key accomplishments include: • Verification & Validation: The 3-D solver was rigorously verified against 1-D analytical solutions, demonstrating high numerical accuracy in predicting space-charge-induced field deviations. • Field Distortion Analysis: 3D simulations revealed that space charge effects introduce significant non-uniformities in the electric field. Critically, the research identified that background LAr flow velocities, when comparable to ion drift velocities, markedly exacerbate these distortions. • Technology Transfer: The resulting source code and comprehensive user manuals were successfully transferred to collaborators at Fermilab, providing a portable computational tool for the broader scientific community. Challenges and Future Directions While the space-charge solver achieved all performance metrics, the integrated fluid dynamics modeling encountered convergence challenges stemming from the extreme 200-fold disparity in length scales between the detector's 37 mm inlet pipes and the 8-meter global domain. To address this, the project has identified a clear technical pivot toward Hierarchical Geometric Adaptive Mesh Refinement (HG-AMR). By implementing an h-type refinement strategy with hanging nodes, future iterations of this solver will be capable of resolving localized high-gradient inlet flows without the prohibitive computational costs of regular grids. This advancement, combined with data-driven uncertainty quantification based on MicroBooNE-style calibration, will enable the precise modeling of detector responses in large-scale cryogenic environments where direct measurement remains difficult. Impact The computational tools developed under this award provide a foundation for enhancing the energy resolution and spatial reconstruction of noble liquid detectors. By bridging the gap between theoretical fluid dynamics and experimental field calibration, this work supports the DOE’s mission to advance the frontiers of neutrino physics and dark matter detection.

42 ENGINEERING↗
DOE OSTI2024

Arbitrary Order Virtual Element Methods for High‐Order Phase‐Field Modeling of Dynamic Fracture

ABSTRACT Accurate modeling of fracture nucleation and propagation in brittle and ductile materials subjected to dynamic loading is important in predicting material damage and failure under extreme conditions. Phase‐field fracture models have garnered a lot of attention in recent years due to their success in representing damage and fracture processes in a wide class of materials and under a variety of loading conditions. Second‐order phase‐field fracture models are by far the most popular among researchers (and increasingly, among practitioners), but fourth‐order models have started to gain broader acceptance since their more recent introduction. The exact solution corresponding to these high‐order phase‐field fracture models has higher regularity. Thus, numerical solutions of the model equations can achieve improved accuracy and higher spatial convergence rates. In this work, we develop a virtual element framework for the high‐order phase‐field model of dynamic fracture. The virtual element method (VEM) can be regarded as a generalization of the classical finite element method. In addition to many other desirable characteristics, the VEM allows computing on polytopal meshes. Here, we use ‐conforming virtual elements and the generalized‐ time integration method for the momentum balance equation, and adopt ‐conforming virtual elements for the high‐order phase‐field equation. We verify our virtual element framework using classical quasi‐static benchmark problems and demonstrate its capabilities with the aid of numerical simulations of dynamic fracture in brittle materials.

42 ENGINEERING↗
DOE OSTI2024

Spectral Analysis of Regular Material Point Method and its Application to Study High Pressure Reverse Osmosis Membrane Compaction and Embossing

Material Point Method (MPM) is gaining widespread interest in applied continuum mechanics. The fact that all the continuum properties are stored on the particles (or material points) and the governing equations are solved on these material points makes MPM extremely suited to problems involving severe material deformations, such as crack propagation, soil movement, and fluid flows. Despite its popularity, only a few studies have focused on the numerical properties of MPM. This presentation introduces a global spectral analysis of the regular material point method. Contrary to previous studies, the analysis focuses on the numerical properties of the method in the spectral space. The amplification factor is derived as a function of the non- dimensional wave numbers. It provides insights into the stability and dissipative properties of the method for various CFL and Fourier numbers. The effect of the grid shape functions, number of particles per cell and their locations inside the grid cell are also analyzed. The EXAGOOP MPM solver (https://github.com/NREL/Exagoop.git) is developed at the National Renewable Energy Laboratory as a part of the NAWI UHPRO project and is based on the AMReX framework. A single-level, uniform cartesian grid is used as the background mesh, while the particle class in AMReX is used to manage the material point operations. Linear hat and B-splines are used as grid shape functions, while the time integration is performed using explicit Euler time integration. EXAGOOP is both CPU and GPU compatible and has been demonstrated to work well on multiple compute architectures. The performance of EXAGOOP on various computing architectures is presented along with its application to study compaction and embossing of high-pressure reverse osmosis membranes. The MPM solution accurately reproduces the membrane deformation. The deformed pore size and structure simulated using MPM also agree well with experimental SEM images.

material point method↗
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↗