Search NASA⌕ Search

Engineering topics

Gropp, William D.

Publications and source records attributed to Gropp, William D..

12 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

PETSc/TAO Users Manual Revision 3.22

This manual describes the use of the Portable, Extensible Toolkit for Scientific Computation (PETSc) and the Toolkit for Advanced Optimization (TAO) for the numerical solution of partial differential equations (PDEs) and related problems on high-performance computers. PETSc/TAO is a suite of data structures and routines that provide the building blocks for implementing large-scale application codes on parallel (and serial) computers. PETSc uses the MPI standard for all distributed memory communication.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Characterizing the performance of node-aware strategies for irregular point-to-point communication on heterogeneous architectures

Supercomputer architectures are trending toward higher computational throughput due to the inclusion of heterogeneous compute nodes. These multi-GPU nodes increase on-node computational efficiency, while also increasing the amount of data to be communicated and the number of potential data flow paths. In this work, we characterize the performance of irregular point-to-point communication with MPI on heterogeneous compute environments through performance modeling, demonstrating the limitations of standard communication strategies for both device-aware and staging-through-host communication techniques. Presented models suggest staging communicated data through host processes then using node-aware communication strategies for high inter-node message counts. Notably, the models also predict that node-aware communication utilizing all available CPU cores to communicate inter-node data leads to the most performant strategy when communicating with a high number of nodes. Furthermore, model validation is provided via a case study of irregular point-to-point communication patterns in distributed sparse matrix–vector products. Importantly, we include a discussion on the implications model predictions have on communication strategy design for emerging supercomputer architectures.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Modeling Data Movement Performance on Heterogeneous Architectures

The cost of data movement on parallel systems varies greatly with machine architecture, job partition, and nearby jobs. Performance models that accurately capture the cost of data movement provide a tool for analysis, allowing for communication bottlenecks to be pinpointed. Modern heterogeneous architectures yield increased variance in data movement as there are a number of viable paths for inter-GPU communication. In this paper, we present performance models for the various paths of inter-node communication on modern heterogeneous architectures, including the trade-off between GPUDirect communication and copying to CPUs. Furthermore, we present a novel optimization for inter-node communication based on these models, utilizing all available CPU cores per node. Finally, we show associated performance improvements for MPI collective operations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

PETSc Users Manual (Revision 3.15)

This manual describes the use of the Portable, Extensible Toolkit for Scientific Computation (PETSc) for the numerical solution of partial differential equations and related problems on high-performance computers. PETSc is a suite of data structures and routines that provide the building blocks for the implementation of large-scale application codes on parallel (and serial) computers. PETSc uses the MPI standard for all distributed memory communication.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Reducing communication in algebraic multigrid with multi-step node aware communication

Algebraic multigrid (AMG) is often viewed as a scalable [Formula: see text] solver for sparse linear systems. Yet, AMG lacks parallel scalability due to increasingly large costs associated with communication, both in the initial construction of a multigrid hierarchy and in the iterative solve phase. This work introduces a parallel implementation of AMG that reduces the cost of communication, yielding improved parallel scalability. It is common in Message Passing Interface (MPI), particularly in the MPI-everywhere approach, to arrange inter-process communication, so that communication is transported regardless of the location of the send and receive processes. Performance tests show notable differences in the cost of intra- and internode communication, motivating a restructuring of communication. In this case, the communication schedule takes advantage of the less costly intra-node communication, reducing both the number and the size of internode messages. Node-centric communication extends to the range of components in both the setup and solve phase of AMG, yielding an increase in the weak and strong scaling of the entire method.

Computer Science↗
DOE OSTI2018

Exploring the feasibility of lossy compression for PDE simulations

Checkpoint restart plays an important role in high-performance computing (HPC) applications, allowing simulation runtime to extend beyond a single job allocation and facilitating recovery from hardware failure. Yet, as machines grow in size and in complexity, traditional approaches to checkpoint restart are becoming prohibitive. Current methods store a subset of the application’s state and exploit the memory hierarchy in the machine. However, as the energy cost of data movement continues to dominate, further reductions in checkpoint size are needed. Lossy compression, which can significantly reduce checkpoint sizes, offers a potential to reduce computational cost in checkpoint restart. This article investigates the use of numerical properties of partial differential equation (PDE) simulations, such as bounds on the truncation error, to evaluate the feasibility of using lossy compression in checkpointing PDE simulations. Restart from a checkpoint with lossy compression is considered for a fail-stop error in two time-dependent HPC application codes: PlasComCM and Nek5000. Results show that error in application variables due to a restart from a lossy compressed checkpoint can be masked by the numerical error in the discretization, leading to increased efficiency in checkpoint restart without influencing overall accuracy in the simulation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

An implementation and evaluation of the MPI 3.0 one-sided communication interface

The Q1 Message Passing Interface (MPI) 3.0 standard includes a significant revision to MPI’s remote memory access (RMA) interface, which provides support for one-sided communication. MPI-3 RMA is expected to greatly enhance the usability and performance ofMPI RMA.We present the first complete implementation of MPI-3 RMA and document implementation techniques and performance optimization opportunities enabled by the new interface. Our implementation targets messaging-based networks and is publicly available in the latest release of the MPICH MPI implementation. Here using this implementation, we explore the performance impact of new MPI-3 functionality and semantics. Results indicate that the MPI-3 RMA interface provides significant advantages over the MPI-2 interface by enabling increased communication concurrency through relaxed semantics in the interface and additional routines that provide new window types, synchronization modes, and atomic operations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Architecture-Aware Algorithms for Scalable Performance and Resilience on Heterogeneous Architectures. Final Report

With the coming end of Moore's law, it has become essential to develop new algorithms and techniques that can provide the performance needed by demanding computational science applications, especially those that are part of the DOE science mission. This work was part of a multi-institution, multi-investigator project that explored several approaches to develop algorithms that would be effective at the extreme scales and with the complex processor architectures that are expected at the end of this decade. The work by this group developed new performance models that have already helped guide the development of highly scalable versions of an algebraic multigrid solver, new programming approaches designed to support numerical algorithms on heterogeneous architectures, and a new, more scalable version of conjugate gradient, an important algorithm in the solution of very large linear systems of equations.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1996

Parallel Newton-Krylov-Schwarz algorithms for the transonic full potential equation

We study parallel two-level overlapping Schwarz algorithms for solving nonlinear finite element problems, in particular, for the full potential equation of aerodynamics discretized in two dimensions with bilinear elements. The overall algorithm, Newton-Krylov-Schwarz (NKS), employs an inexact finite-difference Newton method and a Krylov space iterative method, with a two-level overlapping Schwarz method as a preconditioner. We demonstrate that NKS, combined with a density upwinding continuation strategy for problems with weak shocks, is robust and, economical for this class of mixed elliptic-hyperbolic nonlinear partial differential equations, with proper specification of several parameters. We study upwinding parameters, inner convergence tolerance, coarse grid density, subdomain overlap, and the level of fill-in in the incomplete factorization, and report their effect on numerical convergence rate, overall execution time, and parallel efficiency on a distributed-memory parallel computer.

Cai, Xiao-Chuan↗
NASA NTRS1992

Domain decomposition methods in computational fluid dynamics

The divide-and-conquer paradigm of iterative domain decomposition, or substructuring, has become a practical tool in computational fluid dynamic applications because of its flexibility in accommodating adaptive refinement through locally uniform (or quasi-uniform) grids, its ability to exploit multiple discretizations of the operator equations, and the modular pathway it provides towards parallelism. These features are illustrated on the classic model problem of flow over a backstep using Newton's method as the nonlinear iteration. Multiple discretizations (second-order in the operator and first-order in the preconditioner) and locally uniform mesh refinement pay dividends separately, and they can be combined synergistically. Sample performance results are included from an Intel iPSC/860 hypercube implementation.

Gropp, William D.↗
NASA NTRS1991

Domain-decomposed preconditionings for transport operators

The performance was tested of five different interface preconditionings for domain decomposed convection diffusion problems, including a novel one known as the spectral probe, while varying mesh parameters, Reynolds number, ratio of subdomain diffusion coefficients, and domain aspect ratio. The preconditioners are representative of the range of practically computable possibilities that have appeared in the domain decomposition literature for the treatment of nonoverlapping subdomains. It is shown that through a large number of numerical examples that no single preconditioner can be considered uniformly superior or uniformly inferior to the rest, but that knowledge of particulars, including the shape and strength of the convection, is important in selecting among them in a given problem.

Chan, Tony F.↗
NASA NTRS1991

Domain decomposition methods in computational fluid dynamics

The divide-and-conquer paradigm of iterative domain decomposition, or substructuring, has become a practical tool in computational fluid dynamic applications because of its flexibility in accommodating adaptive refinement through locally uniform (or quasi-uniform) grids, its ability to exploit multiple discretizations of the operator equations, and the modular pathway it provides towards parallelism. These features are illustrated on the classic model problem of flow over a backstep using Newton's method as the nonlinear iteration. Multiple discretizations (second-order in the operator and first-order in the preconditioner) and locally uniform mesh refinement pay dividends separately, and they can be combined synergistically. Sample performance results are included from an Intel iPSC/860 hypercube implementation.

Gropp, William D.↗