Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “conjugate gradient”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Light in the dark forest. Part I. An efficient optimal estimator for 3D Lyman-alpha forest power spectrum

The highly anisotropic nature of the Lyman-alpha (Lyα) forest data introduces a complex survey window function that complicates the measurement of the three-dimensional power spectrum ( P 3D ). In this paper, we present the first fully optimal estimator for P 3D , which exactly deconvolves the survey window function and marginalizes contaminated modes that distort the power spectrum. Our approach adapts optimal estimator techniques developed for the 2D cosmic microwave background data to the 3D case. To achieve computational feasibility, we employ the conjugate gradient method and implement the P 3 M formalism to handle large-scale and small-scale operations separately and efficiently. We validate our estimator using Monte Carlo mocks and Gaussian simulations, demonstrating its accuracy and computational efficiency. We confirm that mode marginalization eliminates distortions arising from quasar continuum errors and delivers robust power spectrum estimation, though it also inflates errors at large scales. This first implementation works in the flat-sky case; we discuss the remaining steps needed to generalize it to the curved-sky case. This formalism offers a foundation for the Lyα forest P 3D measurements and a new path toward cosmological constraints from the Lyα forest data.

Lyman alpha forest↗
DOE OSTI2025

Enabling Scientific Applications with Performance-Portability and High-Productivity for Multi-GPU Programming with JACC.Multi

This work bridges the gap between multi-GPU computing and high-productivity, performance-portable programming solutions. Our goal is to enhance scientific applications with a productive and portable solution—program once, deploy everywhere—for multi-GPU programming with no cost to programmability. To accomplish this, we implemented JACC.Multi, which is part of the Julia for ACCelerators (JACC) performance-portable framework. JACC. Multi is the only high-level, portable metaprogramming solution that targets multi-GPU environments and is integrated in a readily accessible programming language (e.g., Julia language). With transparent GPU-to-GPU communication, JACC. Multi is optimized for scientific application workloads and is portable for NVIDIA and AMD accelerators. For the evaluation, we use two modern multi-GPU systems: Hudson, which features two NVIDIA H100 Hopper GPUs per node, and Frontier, which features four AMD MI250X GPUs per node, each with two Graphics Compute Dies (GCDs) for a total of eight GCDs per node. Additionally, as part of the evaluation, we use JACC (one GPU), MPI+JACC, and JACC. Multi codes that implement well-known and widely used scientific algorithms/kernels such as the conjugate gradient algorithm and an explicit forward Euler solver that requires GPU-to-GPU communication. Overall, JACC. Multi codes achieve better performance than MPI+JACC codes and significant speedups over JACC (one GPU), with up to 1.9× on Hudson and 6× on Frontier.

Valero Lara, Pedro [ORNL] (ORCID:0000000214794310)↗
DOE OSTI2025

ARC-DPA 1-MeV Neutron Fluence Equivalence Model for GaAs

Here, the legacy data used in the production of the American Society for Testing and Materials (ASTM) E722 standard for gallium arsenide (GaAs) were fit with the athermal recombination corrected-displacements per atom (ARC-DPA) model for the development of a novel 1-MeV neutron equivalent fluence metric. Improving on previous work, the coefficients for the ARC-DPA model were optimized using a conjugate gradient method, and the uncertainties in the observed damage in different benchmark neutron fields were sampled to quantify their contribution to the damage metric. The optimized parameters of −0.474 ± 0.03 for b arcdpa and 0.016 ± 0.002 for c arcdpa provided good agreement and indicated that the solution is not sensitive to the corresponding fluence uncertainties. Compared to the current 1-MeV neutron fluence equivalence standard for displacement damage in GaAs, our results indicate that for a thermal reactor neutron environment, displacement damage has been underestimated by around 25% and that the saturation value for the damage efficiency had been higher than previously modeled.

1-MeV equivalent fluence↗
DOE OSTI2022

A Framework for Error-Bounded Approximate Computing, with an Application to Dot Products

Approximate computing techniques, which trade off the computation accuracy of an algorithm for better performance and energy efficiency, have been successful in reducing computation and power costs in several domains. However, error sensitive applications in high-performance computing are unable to benefit from existing approximate computing strategies that are not developed with guaranteed error bounds. While approximate computing techniques can be developed for individual high-performance computing applications by domain specialists, this often requires additional theoretical analysis and potentially extensive software modification. Hence, the development of low-level error-bounded approximate computing strategies that can be introduced into any high-performance computing application without requiring additional analysis or significant software alterations is desirable. In this paper, we provide a contribution in this direction by proposing a general framework for designing error-bounded approximate computing strategies and apply it to the dot product kernel to develop \bf qdot---an error-bounded approximate dot product kernel. Following the introduction of qdot, here we perform a theoretical analysis that yields a deterministic bound on the relative approximation error introduced by qdot. Empirical tests are performed to illustrate the tightness of the derived error bound and to demonstrate the effectiveness of qdot on a synthetic dataset, as well as two scientific benchmarks---the conjugate gradient (CG) and power methods. In some instances, using qdot for the dot products in CG can result in many components being quantized to half precision without increasing the iteration count required for convergence to the same solution as CG using a double precision dot product.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Fast and Scalable FFT-Based GPU-Accelerated Algorithms for Block-Triangular Toeplitz Matrices with Application to Linear Inverse Problems Governed by Autonomous Dynamical Systems

In this work, we present an efficient and scalable algorithm for performing matrix-vector multiplications (matvecs) for block Toeplitz matrices. Such matrices, which are shift-invariant with respect to their blocks, arise in the context of solving inverse problems governed by autonomous systems, and time-invariant systems in particular. In this article, we consider inverse problems that infer unknown parameters from observational data of a linear time-invariant dynamical system given in the form of partial differential equations (PDEs). Matrix-free Newton-conjugate-gradient methods are often the gold standard for solving these inverse problems, but they require numerous actions of the Hessian on a vector. Matrix-free adjoint-based Hessian matvecs require solution of a pair of linearized forward/adjoint PDE solves per Hessian action, which may be prohibitive for large-scale inverse problems. Time invariance of the forward PDE problem leads to a block Toeplitz structure of the discretized parameter-to-observable (p2o) map defining the mapping from inputs (parameters) to outputs (observables) of the PDEs. This block Toeplitz structure enables us to exploit two key properties: (1) compact storage of the p2o map and its adjoint, and (2) efficient fast Fourier transform–based Hessian matvecs. The proposed algorithm is mapped onto large multi-GPU clusters and achieves more than 80% of peak bandwidth on NVIDIA A100 GPUs. Excellent weak scaling is shown for up to 48 A100 GPUs. For the targeted problems, the implementation executes Hessian matvecs within fractions of a second, which is orders of magnitude faster than can be achieved by conventional matrix-free Hessian matvecs via forward/adjoint PDE solves.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

PERKS: a Locality-Optimized Execution Model for Iterative Memory-bound GPU Applications

Iterative memory-bound solvers commonly occur in HPC codes. Typical GPU implementations have a loop on the host side that invokes the GPU kernel as much as time/algorithm steps there are. The termination of each kernel implicitly acts the barrier required after advancing the solution every time step. We propose an execution model for running memory-bound iterative GPU kernels: PERsistent KernelS (PERKS). In this model, the time loop is moved inside persistent kernel, and device-wide barriers are used for synchronization. We then reduce the traffic to device memory by caching subset of the output in each time step in the unused registers and shared memory. PERKS can be generalized to any iterative solver: they largely independent of the solver's implementation. We explain the design principle of PERKS and demonstrate effectiveness of PERKS for a wide range of iterative 2D/3D stencil benchmarks (geomean speedup of 2.12x for 2D stencils and 1.24x for 3D stencils over state-of-art libraries), and a Krylov subspace conjugate gradient solver (geomean speedup of 4.86x in smaller SpMV datasets from SuiteSparse and 1.43x in larger SpMV datasets over a state-of-art library). All PERKS-based implementations available at: https://github.com/neozhang307/PERKS.

Zhang, Lingqi↗
DOE OSTI2025

Extending SEER for Extreme Heterogeneity

Heterogeneous and multi-device nodes are increasingly common in high-performance computing and data centers, yet existing programming models often lack simple, transparent, and portable support for these diverse architectures. The main contribution of this work is the development of novel SEER capabilities to address this challenge by providing a descriptive programming model that allows applications to seamlessly leverage heterogeneous nodes across various device types. SEER uses efficient memory management and can select the proper device[s] depending on the computational cost of the applications. This is completely transparent to the programmer, thereby providing a highly productive programming environment. Integrating extreme heterogeneity into the SEER library as shown with the use of NVIDIA and AMD GPUs simultaneously allows it to expand and exploit the performance possibilities. Our analysis based on the well-known Conjugate Gradient algorithm reports accelerations above 1.5 × on computationally demanding steps of such an algorithm by using both architectures simultaneously.

Teranishi, Keita [ORNL] (ORCID:0000000166472690)↗
DOE OSTI2022

HyKKT

HyKKT (pronounced as "hiked") is a package for solving systems of linear equations of Karush-Kuhn-Tucker (KKT) form, which typically arise in optimization problems, such as optimal power flow analysis. HyKKT uses Cholesky instead of LDL^T factorization and solves the general KKT system to a desired numerical precision via block reduction and conjugate gradient on the Schur complement. Such implementation is more suitable for implementation on graphic processing units (GPUs).

Regev, Shaked↗
DOE OSTI2024

LATTE: Los Alamos TravelTime package based on Eikonal equation

This Fortran code focuses on traveltime computation and tomography based on eikonal equation. Specifically, the package provides three major functionalities: (1) forward modeling of traveltime from single-point or ensemble source based on factorized eikonal equation, (2) adjoint-state first-arrival traveltime tomography based on picked first arrival traveltime using steepest descent, conjugate gradient, or limited-memory BFGS inversion scheme, and (3) adjoint-state joint transmission-reflection tomography based on picked first-arrival and reflection traveltimes. The package applies to forward modeling and tomography based on traveltime in 2D and 3D isotropic regular-grid models. We name this package LATTE – Los Alamos TravelTime package based on Eikonal equation. * The code is for accompanying a journal paper under preparation. The paper will be submitted via LA-UR separately later.

Gao, Kai↗
DOE OSTI2024

pnnl/LAP

A software framework to study, from the performance and energy perspective, the efficacy of GPU-resident parallel Conjugate Gradient (CG) linear solver with different preconditioner options, including Gauss-Seidel, Jacobi, and incomplete Cholesky. We also propose a novel GPU-based preconditioner, in which the triangular solves are approximated by an iterative process

Swirydowicz, Kasia↗
DOE OSTI2024

NeuroFEM

SAND2025-00525O NeuroFEM is a software tool that demonstrates a neuromorphic algorithm for solving finite element problems. It sets up a 2D finite element problem for the Poisson equation on a disk, constructs synaptic matrices, and simulates neural dynamics to solve the resulting sparse linear system. The software illustrates how the algorithm converges to the solution and plots the results, showcasing a neuromorphic counterpart to traditional methods like Conjugate Gradient or GMRES. This tool is designed to highlight the potential of neuromorphic algorithms for solving sparse linear systems, which are prevalent in various computational applications. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

SciDAC↗
DOE OSTI2026

NCCS High Performance GMRES Mixed Precision

HPG-MxP is a software package that performs a fixed number of multigrid preconditioned (using a Gauss-Seidel smoother) Generalized minimal residual (PGMRES) iterations in order to solve a possibly nonsymmetric large sparse linear system of equations. It is designed to be a benchmark to measure a computer's performance for sparse linear algebra workloads typical in scientific computing while allowing the use of mixed precision methods. The solution is required to have convergence characteristics and accuracy similar to double precision GMRES. It is based on the High Performance Conjugate Gradient Benchmark (HPCG) which restricts all implementations to use only the IEEE double precision format (FP64). The original implementation (https://github.com/hpg-mxp/hpg-mxp) was written by Ichitaro Yamazaki, Jennifer Loe, Christian Glusa, Sivasankaran Rajamanickam, Piotr Luszczek, and Jack Dongarra. Please refer to that repository for documentation on the original implementation. This version is maintained by the National Center for Computational Sciences at Oak Ridge National Laboratory. It is highly scalable and optimized for Oak Ridge Leadership Computing Facility (OLCF) systems, particularly Frontier.

Kashi, Aditya [Oak Ridge National Laboratory (ORNL↗
DOE OSTI2024

Advancing attenuation estimation through integration of the Hessian in multiparameter viscoacoustic full-waveform inversion

Accurate seismic attenuation models of subsurface structures not only enhance subsequent migration processes by improving fidelity, resolution, and facilitating amplitude-compliant angle gather generation but also provide valuable constraints on subsurface physical properties. Leveraging full-wavefield information, multiparameter viscoacoustic full-waveform inversion ( Q-FWI) simultaneously estimates seismic velocity and attenuation ( Q) models. However, a major challenge in Q-FWI is the contamination of crosstalk artifacts, where inaccuracies in the velocity model are mistakenly mapped to the inverted attenuation model. While incorporating the Hessian is expected to mitigate these artifacts, the explicit implementation is prohibitively expensive due to its formidable computational cost. In this study, we formulate and develop a Q-FWI algorithm via the Newton-conjugate gradient (CG) framework, where the search direction at each iteration is determined through an internal CG loop. In particular, the Hessian is integrated into each CG step in a matrix-free fashion using the second-order adjoint-state method. We find through synthetic experiments that our Newton-CG Q-FWI significantly mitigates crosstalk artifacts compared with the limited-memory Broyden-Fletcher-Goldfarb-Shanno method and the CG method, albeit with a notable computational cost. In the discussion of several key implementation details, we also determine the significance of the approximate Gauss-Newton Hessian, the second-order adjoint-state method, and the two-stage inversion strategy.

Geochemistry & Geophysics↗
DOE OSTI2023

ORNL_AISD_NiPt

This dataset describes the nickel-platinum (NiPt) solid solution binary alloy, where the two constituent elements nickel (Ni) and platinum (Pt) are randomly placed on the face centered cubic (FCC) crystal structure, with the lattice constant of 3.840 angstroms. The dataset comprises data for three different sizes of the crystal structure: 256 atoms, 864 atoms, and 2,048 atoms, each of which contains 1900 configurations. For each size of the crystal structure, the data set was generated for concentrations ranging from 0at% of Pt to 100at% of Pt in the NiPt binary system, with increasing the concentration of Pt in the system every 5at%. For each one of the chemical compositions, 100 random configurations were generated, each with a different random seed. Each of the output files contains the mass, type, atomic coordinates, energy per atom, and forces in x, y, and z directions respectively. For each atomic configuration, the output was collected every 150 steps during the minimization stage and every 1000 steps during the replica exchange stage. Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [1], which is a molecular dynamics code, was used to generate data for NiPt alloy. The simulation used the interatomic potential for NiPt binary system MEAM_LAMMPS_KimSeolJi_2017_PtNi__MO_020840179467_001 [3] from the OpenKIM library (Open Knowledgebase of Interatomic Models) [2]. This potential was developed based on the second nearest-neighbor modified embedded-atom method (2NN MEAM). The simulation process begins with the generation of the random NiPt structure and follows with the short minimization and replica exchange simulation. The minimization procedure adjusts atomic coordinates and performs energy minimization, which typically leads to a local potential energy minimum. The method used for the minimization was the conjugate gradient algorithm. A short replica exchange (parallel tempering) simulation involves four replicas (ensembles) of a system and follows the minimization stage. Multiple snapshots of the configuration were collected during the minimization and replica exchange stages. NiPt alloy is interesting due to its magnetic and charge transfer properties [4]. The data is provided in three compressed zipped folders: atoms256.zip, atoms864.zip, atoms2048.zip Each zipped folder contains the data that describes crystals of size 256 atoms, 864 atoms, and 2,048 atoms respectively. Each one of the three zipped folders contains the data structured in the following way: -Ni_ground_state.cfg --> atomic configuration for the pure nickel -Pt_ground_state.cfg --> atomic configuration for the pure platinum -Pt#_filtered --> folders containing atomic configurations for #at% concentration of platinum. The folder contains 100 atomic configurations, each saved in a subfolder. Each subfolder named config* is associated with a specific atomic configuration. Each of these subfolders contains files with .cfg format, corresponding to outputs for each atomic configuration The total number of atomic configurations contained in atoms256.zip is 65,046. The total number of atomic configurations contained in atoms864.zip is 63,936. The total number of atomic configurations contained in atoms2048.zip is 61,997. The total number of atomic configurations spanned by the entire dataset is 190,979. References [1] https://www.lammps.org/ [2] https://openkim.org/ [3] https://openkim.org/id/MEAM_LAMMPS_KimSeolJi_2017_PtNi__MO_020840179467_001 [4] El-Gendy, Ahmed A. and Hampel, Silke and Büccchner, Bernd and Klingeler, Rüdiger, Tuneable magnetic properties of carbon-shielded NiPt-nanoalloys, RSC Adv., volume 6, issue 57, pages 52427-52433, 2016, The Royal Society of Chemistry, doi:10.1039/C6RA05910D

36 MATERIALS SCIENCE↗
DOE OSTI2023

ORNL_AISD_NiPt_108atoms

This dataset describes the nickel-platinum (NiPt) solid solution binary alloy, where the two constituent elements nickel (Ni) and platinum (Pt) are randomly placed on the face centered cubic (FCC) crystal structure, with the lattice constant of 3.840 angstroms. The dataset comprises data for crystal structures with 108 atoms with 1,900 configurations. The data set was generated for concentrations ranging from 0at% of Pt to 100at% of Pt in the NiPt binary system, with increasing the concentration of Pt in the system every 5at%. For each one of the chemical compositions, 100 random configurations were generated, each with a different random seed. Each of the output files contains the mass, type, atomic coordinates, energy per atom, and forces in x, y, and z directions respectively. For each atomic configuration, the output was collected every 150 steps during the minimization stage and every 1000 steps during the replica exchange stage. Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [1], which is a molecular dynamics code, was used to generate data for NiPt alloy. The simulation used the interatomic potential for NiPt binary system 'MEAM_LAMMPS_KimSeolJi_2017_PtNi__MO_020840179467_001' [3] from the OpenKIM library (Open Knowledgebase of Interatomic Models) [2]. This potential was developed based on the second nearest-neighbor modified embedded-atom method (2NN MEAM). The simulation process begins with the generation of the random NiPt structure and follows with the short minimization and replica exchange simulation. The minimization procedure adjusts atomic coordinates and performs energy minimization, which typically leads to a local potential energy minimum. The method used for the minimization was the conjugate gradient algorithm. A short replica exchange (parallel tempering) simulation involves four replicas (ensembles) of a system and follows the minimization stage. Multiple snapshots of the configuration were collected during the minimization and replica exchange stages. NiPt alloy is interesting due to its magnetic and charge transfer properties [4]. The data is provided in a compressed zipped folders atoms108.zip. The zipped folder contains the data structured in the following way: - Ni_ground_state.cfg --> atomic configuration for the pure nickel - Pt_ground_state.cfg --> atomic configuration for the pure platinum - Pt#_filtered --> folders containing atomic configurations for #at% concentration of platinum. The folder contains 100 atomic configurations, each saved in a subfolder - Each subfolder named config* is associated with a specific atomic configuration. Each of these subfolders contains files with .cfg format, corresponding to outputs for each atomic configuration The total number of atomic configurations contained in atoms108.zip is 66,132. This dataset is an extension to the dataset ORNL_AISD_NiPt [5] that has been previously released with crystal structures of 256 atoms, 864 atoms, and 2,048 atoms, with the same methodology for data collection. References [1] https://www.lammps.org/ [2] https://openkim.org/ [3] https://openkim.org/id/MEAM_LAMMPS_KimSeolJi_2017_PtNi__MO_020840179467_001 [4] El-Gendy, Ahmed A. and Hampel, Silke and Büchner, Bernd and Klingeler, Rüdiger, Tuneable magnetic properties of carbon-shielded NiPt-nanoalloys, RSC Adv., volume 6, issue 57, pages 52427-52433, 2016, The Royal Society of Chemistry, doi:10.1039/C6RA05910D [5] M. Karabin, M. Lupo Pasini, and M. Eisenbach. ORNL_AISD_NiPt. United States: N. p., 2023. Web. doi:10.13139/OLCF/1958172.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Optimization-based algorithms for nonlinear mechanics and frictional contact

An optimization-based strategy for solving nonlinear mechanics problems is proposed. In contrast to typical nonlinear equation solver algorithms that aim to find zeros in the residual force function, we minimize an energy (or energy-like) function to encourage solutions which are locally stable equilibria. These smooth and potentially non-convex objective functions are minimized using a preconditioned conjugate-gradient trust-region algorithm. Contact is formulated as an inequality constrained minimization problem, and is solved with an augmented Lagrangian algorithm. Friction is included in the approach via a regularized quasi-potential energy, and other dissipative behavior is included through the use of variational constitutive updates. Finally, to accelerate convergence rates for the Lagrange multipliers, we propose a novel multiplier update algorithm utilizing the Fischer-Burmeister function, and demonstrate super-linear solver convergence for some applications.

42 ENGINEERING↗
DOE OSTI2021

Report on hypre performance on AMD GPUs

In this report, the performance of the algebraic multigrid solver used as a preconditioner for conjugate gradient is investigated on 2 nodes of Spock, an early access system at ORNL with 4 MI-100 GPUs and a 64-core Rome CPU per node. We compare GPU and CPU performance for three different diffusion problems using increasing problem sizes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

An Efficient Numerical Algorithm for Solving Coupled Time-Dependent Ginzburg-Landau Equation for Superconductivity and Elasticity

A decoupled finite element algorithm is developed for simulating the vortex dynamics on an elastic superconductor which couples the time-dependent Ginzburg- Landau equation with the complex-valued superconducting order parameter and the vector-valued magnetic potential, and the elasticity equation. We present an iterative algorithm for the decoupled system arising from the time and spatial discretization using a combination of preconditioner, algebraic multigrid method (AMG) and preconditioned conjugate gradient method (PCG). The iterative algorithm allows us to perform large-scale three-dimensional simulations of mesoscale pattern formation during superconducting phase transitions with arbitrary elastic boundary conditions. Here, the performance and efficiency of the algorithm are numerically verified by several benchmark problems, exhibiting up to two orders of magnitude improvement depending on the scale of discrete system compared to the exact solver.

Efficiency↗