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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 sources NASA NTRS DOE OSTI

DOE OSTI2023

Batched Sparse Linear Algebra (Final Report for Subcontract B648960)

This report finalizes design specifications for developing batched kernels for small tensor operations for unassembled matrix-free iterative solvers, batched solvers for partially assembled operators, and batched solvers with support for various sparse formats. The outcome of the project milestones is a set of interfaces to Batched Sparse LA solvers running on hardware accelerators for use in ECP Libraries and Applications. It is part of the development of sparse batched kernels, solvers/preconditioners as well as creating interoperability in xSDK libraries with sparse and dense batched functions to benefit ECP applications. The participants included representatives from ECP libraries (not limited to the xSDK project), applications, and vendors (AMD, Intel, and NVIDIA). Batched sparse linear algebra solvers form the new frontier for algorithmic development and performance engineering. Many applications (ECP and non-ECP alike) require simultaneous solutions of small linear systems of equations that are structurally sparse. To move towards high hardware utilization, it is important to provide these applications with appropriate interfaces to efficient batched sparse solvers running on modern hardware accelerators. We present interface designs in use by HPC software libraries supporting batched sparse linear algebra and the development of sparse batched kernel codes for solvers and preconditioners. We also address the potential interoperability opportunities to keep the software portable between the major hardware accelerators from AMD, Intel, and NVIDIA. The presented interface specifications includes batched band, sparse iterative, and sparse direct solvers. This report summarizes progress in Kokkos Kernels and the xSDK libraries MAGMA, Ginkgo, hypre, SUNDIALS, and SuperLU_dist.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

The Reverse Cuthill-McKee Algorithm in Distributed-Memory

Ordering vertices of a graph is key to minimize fill-in and data structure size in sparse direct solvers, maximize locality in iterative solvers, and improve performance in graph algorithms. Except for naturally parallelizable ordering methods such as nested dissection, many important ordering methods have not been efficiently mapped to distributed-memory architectures. In this paper, we present the first-ever distributed-memory implementation of the reverse Cuthill-McKee (RCM) algorithm for reducing the profile of a sparse matrix. Our parallelization uses a two-dimensional sparse matrix decomposition. We achieve high performance by decomposing the problem into a small number of primitives and utilizing optimized implementations of these primitives. Our implementation shows strong scaling up to 1024 cores for smaller matrices and up to 4096 cores for larger matrices.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Uncertainty quantification in density estimation from background-oriented Schlieren measurements

In this paper, we present an uncertainty quantification methodology for density estimation from background-oriented Schlieren (BOS) measurements, in order to provide local, instantaneous, a posteriori uncertainty bounds on each density measurement in the field of view. Displacement uncertainty quantification algorithms from cross-correlation-based particle image velocimetry are used to estimate the uncertainty in the dot pattern displacements obtained from cross-correlation for BOSs and assess their feasibility. In order to propagate the displacement uncertainty through the density integration procedure, we also develop a novel methodology via the Poisson solver using sparse linear operators. Testing the method using synthetic images of a Gaussian density field showed agreement between the propagated density uncertainties and the true uncertainty. Subsequently, the methodology is experimentally demonstrated for supersonic flow over a wedge, showing that regions with sharp changes in density lead to an increase in density uncertainty throughout the field of view, even in regions without these sharp changes. Lastly, the uncertainty propagation is influenced by the density integration scheme, and for the Poisson solver the density uncertainty on average increases on moving away from the regions where the Dirichlet boundary conditions are specified.

47 OTHER INSTRUMENTATION↗

DOE OSTI2013

Xyce(™) Parallel Electronic Simulator

The Xyce Parallel Electronic Simulator simulates electronic circuit behavior in DC, AC, HB, MPDE and transient mode using standard analog (DAE) and/or device (PDE) device models including several age and radiation aware devices. It supports a variety of computing platforms (both serial and parallel) computers. Lastly, it uses a variety of modern solution algorithms dynamic parallel load-balancing and iterative solvers.! ! Xyce is primarily used to simulate the voltage and current behavior of a circuit network (a network of electronic devices connected via a conductive network). As a tool, it is mainly used for the design and analysis of electronic circuits.! ! Kirchoff's conservation laws are enforced over a network using modified nodal analysis. This results in a set of differential algebraic equations (DAEs). The resulting nonlinear problem is solved iteratively using a fully coupled Newton method, which in turn results in a linear system that is solved by either a standard sparse-direct solver or iteratively using Trilinos linear solver packages, also developed at Sandia National Laboratories.

Source record↗

DOE OSTI2022

Xyce(™) Parallel Electronic Simulator v.7.5

Source record↗

DOE OSTI2013

Xyce(™) Parallel Electronic Simulator v.7.6

Keiter, Eric↗

DOE OSTI2024

Parallel interior-point solver for block-structured nonlinear programs on SIMD/GPU architectures

Here, we investigate how to port the standard interior-point method to new exascale architectures for block-structured nonlinear programs with state equations. Computationally, we decompose the interior-point algorithm into two successive operations: the evaluation of the derivatives and the solution of the associated Karush-Kuhn-Tucker (KKT) linear system. Our method accelerates both operations using two levels of parallelism. First, we distribute the computations on multiple processes using coarse parallelism. Second, each process uses SIMD/GPU accelerators locally to accelerate the operations using fine-grained parallelism. The KKT system is reduced by eliminating the inequalities and the state variables from the corresponding equations. We demonstrate our method's capability on the supercomputer Polaris, a testbed for the future exascale Aurora system. Each node is equipped with four GPUs, a setup amenable to our two-level approach. Our experiments on the stochastic optimal power flow problem show that the reduction method is 50x faster than the sparse linear solver HSL MA57 running in serial on the CPU, and 6x faster than Pardiso running in parallel on CPU on the same number of processes.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

A Segregated Approach for Modeling the Electrochemistry in the 3-D Microstructure of Li-Ion Batteries and Its Acceleration Using Block Preconditioners

Abstract Battery performance is strongly correlated with electrode microstructure. Electrode materials for lithium-ion batteries have complex microstructure geometries that require millions of degrees of freedom to solve the electrochemical system at the microstructure scale. A fast-iterative solver with an appropriate preconditioner is then required to simulate large representative volume in a reasonable time. In this work, a finite element electrochemical model is developed to resolve the concentration and potential within the electrode active materials and the electrolyte domains at the microstructure scale, with an emphasis on numerical stability and scaling performances. The block Gauss-Seidel (BGS) numerical method is implemented because the system of equations within the electrodes is coupled only through the nonlinear Butler–Volmer equation, which governs the electrochemical reaction at the interface between the domains. The best solution strategy found in this work consists of splitting the system into two blocks—one for the concentration and one for the potential field—and then performing block generalized minimal residual preconditioned with algebraic multigrid, using the FEniCS and the Portable, Extensible Toolkit for Scientific Computation libraries. Significant improvements in terms of time to solution (six times faster) and memory usage (halving) are achieved compared with the MUltifrontal Massively Parallel sparse direct Solver. Additionally, BGS experiences decent strong parallel scaling within the electrode domains. Last, the system of equations is modified to specifically address numerical instability induced by electrolyte depletion, which is particularly valuable for simulating fast-charge scenarios relevant for automotive application.

25 ENERGY STORAGE↗

DOE OSTI2016

Educating local radial basis functions using the highest gradient of interest in three dimensional geometries: EDUCATING LOCALIZED RBF-SCHEMES

We present a novel methodology to effectively localize radial basis function approximation methods in three dimensions. The local scheme requires shape parameter-dependent functions that can be used to approximate gradients of scattered data and to solve partial differential operators. The optimum shape parameter is obtained from the highest gradient of interest, where a known analytical function, when boundary conditions are not present, or a shape parameter-free global approximation are used to educate the localized scheme. The later option is applicable to problems where the operator needs to be solved multiple times, like in time evolution or stochastic integration. Past shape parameter's optimizations, for two-dimensional domains, based on the condition number of the interpolant matrix, were unable to provide satisfactory approximations. The applicability of our method is illustrated in the context of an analytical expression interpolation and during a Ginzburg-Landau relaxation of a free energy functional. In general, the optimum shape parameter depends on geometry, node distribution, and density, whereas the approximation errors decrease as the node density and the local stencil size increase. The effective localization of radial basis functions motivates its use in moving boundary problems and accelerates solutions through sparse matrix solvers.

free energy functional↗

DOE OSTI2023

The Kokkos OpenMPTarget Backend: Implementation and Lessons Learned

As the supercomputing landscape diversifies, solutions such as Kokkos to write vendor agnostic applications and libraries have risen in popularity. Kokkos provides a programming model designed for performance portability, which allows developers to write a single source implementation that can run efficiently on various architectures. At its heart, Kokkos maps parallel algorithms to architecture and vendor specific backends written in lower level programming models such as CUDA and HIP. Another approach to writing vendor agnostic parallel code is using OpenMP’s directives based approach, which lets developers annotate code to express parallelism. It is implemented at the compiler level and is supported by all major high performance computing vendors, as well as the primary Open Source toolchains GNU and LLVM. Since its inception, Kokkos has used OpenMP to parallelize on CPU architectures. In this paper, we explore leveraging OpenMP for a GPU backend and discuss the challenges we encountered when mapping the Kokkos APIs and semantics to OpenMP target constructs. As an exemplar workload we chose a simple conjugate gradient solver for sparse matrices. We find that performance on NVIDIA and AMD GPUs varies widely based on details of the implementation strategy and the chosen compiler. Furthermore, the performance of the OpenMP implementations decreases with increasing complexity of the investigated algorithms.

Gayatri, Rahulkumar↗

DOE OSTI2016

Large-scale optimal control of interconnected natural gas and electrical transmission systems

We present a detailed optimal control model that captures spatiotemporal interactions between gas and electric transmission networks. We use the model to study flexibility and economic opportunities provided by coordination. A large-scale case study in the Illinois system reveals that coordination can enable the delivery of significantly larger amounts of natural gas to the power grid. In particular, under a coordinated setting, gas-fired generators act as distributed demand response resources that can be controlled by the gas pipeline operator. This enables more efficient control of pressures and flows in space and time and overcomes delivery bottlenecks. We demonstrate that the additional flexibility not only can benefit the gas operator but can also lead to more efficient power grid operations and results in increased revenue for gas-fired power plants. We also use the optimal control model to analyze computational issues arising in these complex models. We demonstrate that the interconnected Illinois system with full physical resolution gives rise to a highly nonlinear optimal control problem with 4400 differential and algebraic equations and 1040 controls that can be solved with a state-of-the-art sparse optimization solver. (C) 2016 Elsevier Ltd. All rights reserved.

Chiang, Nai-Yuan↗

DOE OSTI2019

Improving resilience of scientific software through a domain-specific approach

Not Available

Reguly, I. Z. (ORCID:0000000243854204)↗

DOE OSTI2014

On Parallel Push-Relabel based Algorithms for Bipartite Maximum Matching

We study multithreaded push-relabel based algorithms for computing maximum cardinality matching in bipartite graphs. Matching is a fundamental combinatorial (graph) problem with applications in a wide variety of problems in science and engineering. We are motivated by its use in the context of sparse linear solvers for computing maximum transversal of a matrix. We implement and test our algorithms on several multi-socket multicore systems and compare their performance to state-of-the-art augmenting path-based serial and parallel algorithms using a testset comprised of a wide range of real-world instances. Building on several heuristics for enhancing performance, we demonstrate good scaling for the parallel push-relabel algorithm. We show that it is comparable to the best augmenting path-based algorithms for bipartite matching. To the best of our knowledge, this is the first extensive study of multithreaded push-relabel based algorithms. In addition to a direct impact on the applications using matching, the proposed algorithmic techniques can be extended to preflow-push based algorithms for computing maximum flow in graphs.

Push-relabel, matching, bipartite↗

DOE OSTI2020

A WKB based preconditioner for the 1D Helmholtz wave equation

Frequency-domain full-wave solutions to the cold-plasma problem have become ubiquitous in the study of radio frequency power in fusion plasmas. However, recent efforts at extreme levels of geometric fidelity have revealed fundamental limits in the problem size that can be solved by typical sparse direct solver based methods. These limits are of particular importance in the 3D study of RF launchers, where the number of degrees of freedom required can exceed 100 million. In such cases, it would be advantageous to solve the system via iterative means, but due to the large null space of the curl-curl operator, the convergence properties of algorithms like GMRES are poor. Here we present a physics-based preconditioner in the form of a WKB solution and demonstrate the iterative solution to the frequency-domain Helmholtz problem in 1D for several cases ranging from satisfying the WKB approximation to strongly violating it.

Green, David↗

DOE OSTI2016

A Novel Centrality Measure for Network-wide Cyber Vulnerability Assessment

In this work we propose a novel formulation that models the attack and compromise on a cyber network as a combination of two parts - direct compromise of a host and the compromise occurring through the spread of the attack on the network from a compromised host. The model parameters for the nodes are a concise representation of the host profiles that can include the risky behaviors of the associated human users while the model parameters for the edges are based on the existence of vulnerabilities between each pair of connected hosts. The edge models relate to the summary representations of the corresponding attack-graphs. This results in a formulation based on Random Walk with Restart (RWR) and the resulting centrality metric can be solved for in an efficient manner through the use of sparse linear solvers. Thus the formulation goes beyond mere topological considerations in centrality computations by summarizing the host profiles and the attack graphs into the model parameters. The computational efficiency of the method also allows us to also quantify the uncertainty in the centrality measure through Monte Carlo analysis.

Centrality↗

DOE OSTI2019

IMPLEMENTATION OF DETAILED CHEMISTRY MECHANISMS IN ENGINE SIMULATIONS

The stiffness of large chemistry mechanisms has been proved to be a major hurdle toward predictive engine simulations. As a result, detailed chemistry mechanisms with a few thousand species need to be reduced based on target conditions so that they can be accommodated within the available computational resources. The computational cost of simulations typically increases super-linearly with the number of species and reactions. This work aims to bring detailed chemistry mechanisms within the realm of engine simulations by coupling the framework of unsteady flamelets and fast chemistry solvers. A previously developed tabulated flamelet model (TFM) framework for nonpremixed combustion was used in this study. The flamelet solver consists of the traditional operator-splitting scheme with variable coefficient ordinary differential equation (ODE) solver (VODE) and a numerical Jacobian for solving the chemistry. In order to use detailed mechanisms with thousands of species, a new framework with the Livermore solver for ODEs in sparse form (LSODES) chemistry solver and an analytical Jacobian was implemented in this work. Results from 1D simulations show that with the new framework, the computational cost is linearly proportional to the number of species in a given chemistry mechanism. As a result, the new framework is 2-3 orders of magnitude faster than the conventional variable coefficient ODE (VODE) solver for large chemistry mechanisms. This new framework was used to generate unsteady flamelet libraries for ndodecane using a detailed chemistry mechanism with 2755 species and 11,173 reactions. The engine combustion network (ECN) spray A experiments, which consist of an igniting n-dodecane spray in turbulent, high-pressure engine conditions are simulated using large eddy simulations (LES) coupled with detailed mechanisms. A grid with 0.06 mm minimum cell size and 22 x 10(6) peak cell count was implemented. The framework is validated across a range of ambient temperatures against ignition delay and liftoff lengths (LOLs). Qualitative results from the simulations were compared against experimental OH and CH2O planar laser-induced fluorescence (PLIF) data. The models are able to capture the spatial and temporal trends in species compared to those observed in the experiments. Quantitative and qualitative comparisons between the predictions of the reduced and detailed mechanisms are presented in detail. The main goal of this study is to demonstrate that detailed reaction mechanisms (similar to 1000 species) can now be used in engine simulations with a linear increase in computation cost with number of species during the tabulation process and a small increase in the 3D simulation cost.

Kundu, Prithwish↗

DOE OSTI2019

symPACK v2.0

SymPACK is a parallel direct solver for sparse symmetric systems of linear equations. SymPACK is implemented for large- scale distributed-memory platforms. It employs several innovative ideas, including the use of an asynchronous task paradigm, one-sided communication, and dynamic scheduling.

Ng, EsmondG↗

DOE OSTI2015

The Development of a Finite Volume Method for Modeling Sound in Coastal Ocean Environment

: As the rapid growth of marine renewable energy and off-shore wind energy, there have been concerns that the noises generated from construction and operation of the devices may interfere marine animals’ communication. In this research, a underwater sound model is developed to simulate sound prorogation generated by marine-hydrokinetic energy (MHK) devices or offshore wind (OSW) energy platforms. Finite volume and finite difference methods are developed to solve the 3D Helmholtz equation of sound propagation in the coastal environment. For finite volume method, the grid system consists of triangular grids in horizontal plane and sigma-layers in vertical dimension. A 3D sparse matrix solver with complex coefficients is formed for solving the resulting acoustic pressure field. The Complex Shifted Laplacian Preconditioner (CSLP) method is applied to efficiently solve the matrix system iteratively with MPI parallelization using a high performance cluster. The sound model is then coupled with the Finite Volume Community Ocean Model (FVCOM) for simulating sound propagation generated by human activities in a range-dependent setting, such as offshore wind energy platform constructions and tidal stream turbines. As a proof of concept, initial validation of the finite difference solver is presented for two coastal wedge problems. Validation of finite volume method will be reported separately.

Coastal↗