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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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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

SPACE: 3D parallel solvers for Vlasov-Maxwell and Vlasov-Poisson equations for relativistic plasmas with atomic transformations

A parallel, relativistic, three-dimensional particle-in-cell code SPACE has been developed for the simulation of electromagnetic fields, relativistic particle beams, and plasmas. In addition to the standard second-order Particle-in-Cell (PIC) algorithm, SPACE includes efficient novel algorithms to resolve atomic physics processes such as multi-level ionization of plasma atoms, recombination, and electron attachment to dopants in dense neutral gases. SPACE also contains a highly adaptive particle-based method, called Adaptive Particle-in-Cloud (AP-Cloud), for solving the Vlasov-Poisson problems. It eliminates the traditional Cartesian mesh of PIC and replaces it with an adaptive octree data structure. The code's algorithms, structure, capabilities, parallelization strategy, and performance have been discussed. Additionally, typical examples of SPACE applications to accelerator science and engineering problems are described.

43 PARTICLE ACCELERATORS↗
DOE OSTI2021

Parallel Solver Framework for Mixed-Integer PDE-Constrained Optimization

ROL-PEBBL is a C++, MPI-based parallel code for mixed-integer PDE-constrained optimization (MIPDECO). In these problems we wish to optimize (control, design, etc.) physical systems, which must obey the laws of physics, when some of the decision variables must take integer values. ROL-PEBBL combines a code to efficiently search over integer choices (PEBBL = Parallel Enumeration Branch-and-Bound Library) and a code for efficient nonlinear optimization, including PDE-constrained optimization (ROL = Rapid Optimization Library). In this report, we summarize the design of ROL-PEBBL and initial applications/results. For an artificial source-inversion problem, finding sources of pollution on a grid from sparse samples, ROL-PEBBLs solution for the nest grid gave the best optimization guarantee for any general solver that gives both a solution and a quality guarantee.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1991

Parallelized solvers for heat conduction formulations

Based on multilevel partitioning, this paper develops a structural parallelizable solution methodology that enables a significant reduction in computational effort and memory requirements for very large scale linear and nonlinear steady and transient thermal (heat conduction) models. Due to the generality of the formulation of the scheme, both finite element and finite difference simulations can be treated. Diverse model topologies can thus be handled, including both simply and multiply connected (branched/perforated) geometries. To verify the methodology, analytical and numerical benchmark trends are verified in both sequential and parallel computer environments.

Padovan, Joe↗
NASA NTRS1992

Parallel solver for trajectory optimization search directions

A key algorithmic element of a real-time trajectory optimization hardware/software implementation is presented, the search step solver. This is one piece of an algorithm whose overall goal is to make nonlinear trajectory optimization fast enough to provide real-time commands during guidance of a vehicle such as an aeromaneuvering orbiter or the National Aerospace Plane. Many methods of nonlinear programming require the solution of a quadratic program (QP) at each iteration to determine the search step. In the trajectory optimization case, the QP has a special dynamic programming structure. The algorithm exploits this special structure with a divide- and conquer type of parallel implementation. The algorithm solves a (p.N)-stage problem on N processors in O(p + log2 N) operations. The algorithm yields a factor of 8 speed-up over the fastest known serial algorithm when solving a 1024-stage test problem on 32 processors.

Psiaki, M. L.↗
NASA NTRS2012

Development of a Robust and Efficient Parallel Solver for Unsteady Turbomachinery Flows

The traditional design and analysis practice for advanced propulsion systems relies heavily on expensive full-scale prototype development and testing. Over the past decade, use of high-fidelity analysis and design tools such as CFD early in the product development cycle has been identified as one way to alleviate testing costs and to develop these devices better, faster and cheaper. In the design of advanced propulsion systems, CFD plays a major role in defining the required performance over the entire flight regime, as well as in testing the sensitivity of the design to the different modes of operation. Increased emphasis is being placed on developing and applying CFD models to simulate the flow field environments and performance of advanced propulsion systems. This necessitates the development of next generation computational tools which can be used effectively and reliably in a design environment. The turbomachinery simulation capability presented here is being developed in a computational tool called Loci-STREAM [1]. It integrates proven numerical methods for generalized grids and state-of-the-art physical models in a novel rule-based programming framework called Loci [2] which allows: (a) seamless integration of multidisciplinary physics in a unified manner, and (b) automatic handling of massively parallel computing. The objective is to be able to routinely simulate problems involving complex geometries requiring large unstructured grids and complex multidisciplinary physics. An immediate application of interest is simulation of unsteady flows in rocket turbopumps, particularly in cryogenic liquid rocket engines. The key components of the overall methodology presented in this paper are the following: (a) high fidelity unsteady simulation capability based on Detached Eddy Simulation (DES) in conjunction with second-order temporal discretization, (b) compliance with Geometric Conservation Law (GCL) in order to maintain conservative property on moving meshes for second-order time-stepping scheme, (c) a novel cloud-of-points interpolation method (based on a fast parallel kd-tree search algorithm) for interfaces between turbomachinery components in relative motion which is demonstrated to be highly scalable, and (d) demonstrated accuracy and parallel scalability on large grids (approx 250 million cells) in full turbomachinery geometries.

West, Jeff↗
NASA NTRS1995

A General Purpose Sparse Matrix Parallel Solvers Package

A general purpose solver package for constructing and solving a range of sparse linear systems arising from discretization of PDEs on unstructured meshes is developed. Once the sparse symmetric complex matrix is constructed, it can be solved by either a preconditioned bi-conjugate gradient solver, a two-stage Cholesky LDLT factorization solver, or a hybrid solver combining the above two methods.

solver sparse matrix solvers package PDE↗
NASA NTRS1995

A General Purpose Sparse Matrix Parallel Solvers Package

A general purpose solver package for constructing and solving a range of sparse linear systems arising from discretization of PDEs on unstructured meshes is developed. Once the sparse symmetric complex matrix is constructed, it can be solved by either a preconditioned bi-conjugate gradient solver, a two-stage Cholesky LDLT factorization solver, or a hybrid solver combining the above two methods. (More detailed than 95-0127).

solver sparse matrix solvers package PDE↗
NASA NTRS1989

Some fast elliptic solvers on parallel architectures and their complexities

The discretization of separable elliptic partial differential equations leads to linear systems with special block tridiagonal matrices. Several methods are known to solve these systems, the most general of which is the Block Cyclic Reduction (BCR) algorithm which handles equations with nonconstant coefficients. A method was recently proposed to parallelize and vectorize BCR. In this paper, the mapping of BCR on distributed memory architectures is discussed, and its complexity is compared with that of other approaches including the Alternating-Direction method. A fast parallel solver is also described, based on an explicit formula for the solution, which has parallel computational compelxity lower than that of parallel BCR.

Gallopoulos, E.↗
NASA NTRS1989

Some fast elliptic solvers on parallel architectures and their complexities

The discretization of separable elliptic partial differential equations leads to linear systems with special block triangular matrices. Several methods are known to solve these systems, the most general of which is the Block Cyclic Reduction (BCR) algorithm which handles equations with nonconsistant coefficients. A method was recently proposed to parallelize and vectorize BCR. Here, the mapping of BCR on distributed memory architectures is discussed, and its complexity is compared with that of other approaches, including the Alternating-Direction method. A fast parallel solver is also described, based on an explicit formula for the solution, which has parallel computational complexity lower than that of parallel BCR.

Gallopoulos, E.↗
NASA NTRS1995

Algorithms for parallel flow solvers on message passing architectures

The purpose of this project has been to identify and test suitable technologies for implementation of fluid flow solvers -- possibly coupled with structures and heat equation solvers -- on MIMD parallel computers. In the course of this investigation much attention has been paid to efficient domain decomposition strategies for ADI-type algorithms. Multi-partitioning derives its efficiency from the assignment of several blocks of grid points to each processor in the parallel computer. A coarse-grain parallelism is obtained, and a near-perfect load balance results. In uni-partitioning every processor receives responsibility for exactly one block of grid points instead of several. This necessitates fine-grain pipelined program execution in order to obtain a reasonable load balance. Although fine-grain parallelism is less desirable on many systems, especially high-latency networks of workstations, uni-partition methods are still in wide use in production codes for flow problems. Consequently, it remains important to achieve good efficiency with this technique that has essentially been superseded by multi-partitioning for parallel ADI-type algorithms. Another reason for the concentration on improving the performance of pipeline methods is their applicability in other types of flow solver kernels with stronger implied data dependence. Analytical expressions can be derived for the size of the dynamic load imbalance incurred in traditional pipelines. From these it can be determined what is the optimal first-processor retardation that leads to the shortest total completion time for the pipeline process. Theoretical predictions of pipeline performance with and without optimization match experimental observations on the iPSC/860 very well. Analysis of pipeline performance also highlights the effect of uncareful grid partitioning in flow solvers that employ pipeline algorithms. If grid blocks at boundaries are not at least as large in the wall-normal direction as those immediately adjacent to them, then the first processor in the pipeline will receive a computational load that is less than that of subsequent processors, magnifying the pipeline slowdown effect. Extra compensation is needed for grid boundary effects, even if all grid blocks are equally sized.

Vanderwijngaart, Rob F.↗
NASA NTRS1974

Parallel tridiagonal equation solvers

Three parallel algorithms were compared for the direct solution of tridiagonal linear systems of equations. The algorithms are suitable for computers such as ILLIAC 4 and CDC STAR. For array computers similar to ILLIAC 4, cyclic odd-even reduction has the least operation count for highly structured sets of equations, and recursive doubling has the least count for relatively unstructured sets of equations. Since the difference in operation counts for these two algorithms is not substantial, their relative running times may be more related to overhead operations, which are not measured in this paper. The third algorithm, based on Buneman's Poisson solver, has more arithmetic operations than the others, and appears to be the least favorable. For pipeline computers similar to CDC STAR, cyclic odd-even reduction appears to be the most preferable algorithm for all cases.

Stone, H. S.↗
NASA NTRS1991

An efficient massively parallel Euler solver for unstructured grids

A data parallel mesh-vertex upwind finite-volume scheme for solving the Euler equations on triangular unstructured meshes is described. A novel vertex-based partitioning of the problem is introduced which minimizes the computation and communication costs associated with distributing the computation to the processors of a massively parallel computer. Finally, the performance of this unstructured computation on 8K processors of the Connection Machine CM-2 is compared with one processor of a Cray-YMP. The experiments show that 8K processors of the CM-2 achieve approximately 70 percent of the performance of one processor of the Cray-YMP on the unstructured mesh computations described here.

Hammond, Steven W.↗
NASA NTRS2001

A Parallel Multigrid Solver for Viscous Flows on Anisotropic Structured Grids

This paper presents an efficient parallel multigrid solver for speeding up the computation of a 3-D model that treats the flow of a viscous fluid over a flat plate. The main interest of this simulation lies in exhibiting some basic difficulties that prevent optimal multigrid efficiencies from being achieved. As the computing platform, we have used Coral, a Beowulf-class system based on Intel Pentium processors and equipped with GigaNet cLAN and switched Fast Ethernet networks. Our study not only examines the scalability of the solver but also includes a performance evaluation of Coral where the investigated solver has been used to compare several of its design choices, namely, the interconnection network (GigaNet versus switched Fast-Ethernet) and the node configuration (dual nodes versus single nodes). As a reference, the performance results have been compared with those obtained with the NAS-MG benchmark.

Prieto, Manuel↗
NASA NTRS1994

Preconditioned implicit solvers for the Navier-Stokes equations on distributed-memory machines

The GMRES method is parallelized, and combined with local preconditioning to construct an implicit parallel solver to obtain steady-state solutions for the Navier-Stokes equations of fluid flow on distributed-memory machines. The new implicit parallel solver is designed to preserve the convergence rate of the equivalent 'serial' solver. A static domain-decomposition is used to partition the computational domain amongst the available processing nodes of the parallel machine. The SPMD (Single-Program Multiple-Data) programming model is combined with message-passing tools to develop the parallel code on a 32-node Intel Hypercube and a 512-node Intel Delta machine. The implicit parallel solver is validated for internal and external flow problems, and is found to compare identically with flow solutions obtained on a Cray Y-MP/8. A peak computational speed of 2300 MFlops/sec has been achieved on 512 nodes of the Intel Delta machine,k for a problem size of 1024 K equations (256 K grid points).

Ajmani, Kumud↗
NASA NTRS1995

Implementation of a parallel unstructured Euler solver on the CM-5

An efficient unstructured 3D Euler solver is parallelized on a Thinking Machine Corporation Connection Machine 5, distributed memory computer with vectoring capability. In this paper, the single instruction multiple data (SIMD) strategy is employed through the use of the CM Fortran language and the CMSSL scientific library. The performance of the CMSSL mesh partitioner is evaluated and the overall efficiency of the parallel flow solver is discussed.

Morano, Eric↗
NASA NTRS1981

Multigrid solvers on parallel computers

Massively parallel computers, as considered in this investigation, are not yet available. However, a large-scale parallel computer cannot usefully be designed before the hypothetical algorithms which will employ it are studied. Most of the studies of parallel partial differential equations (PDE) solvers are based on solution techniques much slower (on sequential machines) than multigrid methods. Multigrid methods are highly parallelizable. Each of their processes can simultaneously be performed at all grid points. The present investigation is concerned with a preliminary exploration of the potential of multigrid, or, more generally, Multi-Level Adaptive Techniques (MLAT) on computers with many processors. Basic processes are considered, taking into account coarse-grid approximation, relaxation, coarse-grid corrections, full multigrid algorithms, nonlinear problems and eigenvalue problems, fine-to-coarse correction, and chains of problems. Details of parallel multigrid processing are also examined.

Brandt, A.↗