arXiv subjects

Shelby Lockhart

Publications and source records attributed to Shelby Lockhart.

5 recordsLinked to original sources

arXiv2022

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. 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.

cs.DC↗

arXiv2022

Performance Analysis and Optimal Node-Aware Communication for Enlarged Conjugate Gradient Methods

Krylov methods are a key way of solving large sparse linear systems of equations, but suffer from poor strong scalabilty on distributed memory machines. This is due to high synchronization costs from large numbers of collective communication calls alongside a low computational workload. Enlarged Krylov methods address this issue by decreasing the total iterations to convergence, an artifact of splitting the initial residual and resulting in operations on block vectors. In this paper, we present a performance study of an Enlarged Krylov Method, Enlarged Conjugate Gradients (ECG), noting the impact of block vectors on parallel performance at scale. Most notably, we observe the increased overhead of point-to-point communication as a result of denser messages in the sparse matrix-block vector multiplication kernel. Additionally, we present models to analyze expected performance of ECG, as well as, motivate design decisions. Most importantly, we introduce a new point-to-point communication approach based on node-aware communication techniques that increases efficiency of the method at scale.

cs.DC↗

arXiv2021

Performance of Low Synchronization Orthogonalization Methods in Anderson Accelerated Fixed Point Solvers

Anderson Acceleration (AA) is a method to accelerate the convergence of fixed point iterations for nonlinear, algebraic systems of equations. Due to the requirement of solving a least squares problem at each iteration and a reliance on modified Gram-Schmidt for updating the iteration space, AA requires extra costly synchronization steps for global reductions. Moreover, the number of reductions in each iteration depends on the size of the iteration space. In this work, we introduce three low synchronization orthogonalization algorithms into AA within SUNDIALS that reduce the total number of global reductions per iteration to a constant of 2 or 3, independent of the size of the iteration space. A performance study demonstrates the reduced time required by the new algorithms at large processor counts with CPUs and demonstrates the predicted performance on multi-GPU architectures. Most importantly, we provide convergence and timing data for multiple numerical experiments to demonstrate reliability of the algorithms within AA and improved performance at parallel strong-scaling limits.

math.NA↗

arXiv2021

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.

cs.DC↗

arXiv2016

Trust-Region Methods for Sparse Relaxation

In this paper, we solve the l2-l1 sparse recovery problem by transforming the objective function of this problem into an unconstrained differentiable function and apply a limited-memory trust-region method. Unlike gradient projection-type methods, which uses only the current gradient, our approach uses gradients from previous iterations to obtain a more accurate Hessian approximation. Numerical experiments show that our proposed approach eliminates spurious solutions more effectively while improving the computational time to converge.

math.NA↗