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Carl Pearson
2017-05-18 08:42:54 -07:00
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@@ -32,7 +32,7 @@ The multilevel fast multiple method (MLFMM) is a key tool for efficiently solvin
The problems are solved using volume integral equations instead of conversion into a corresponding surface-scattering problem through the equivalence principle to support highly inhomogeneous media.
The MLFMM implementation for two-dimensional volumetric scattering problems is realized through matrix operations optimized with shared memory tiling, register tiling, and thread coarsening.
MPI communications are overlapped with GPU kernels to achieve high multi-node parallel efficiency.
The MLFMM is evaluated on current- and next-generation GPU-accelerated supercomputing nodes, where up to 969x speedup is achieved over single-thread CPU execution using 4 NVIDIA P100 graphics processing units.
The MLFMM is evaluated on current- and next-generation GPU-accelerated supercomputing nodes, where up to 969x speedup is achieved over sequential CPU execution using 4 NVIDIA P100 graphics processing units.
\end{abstract}
@@ -60,23 +60,7 @@ This section presents an analysis of the performance of the MLFMM algorithm on d
\subsection{Evaluation Environments}
%\begin{table}{}
%\centering \caption{Evaluation Systems} \label{tab:systems}
%\begin{tabular}{|c|c|c|c|}
%\hline & \textbf{XK Node} & \textbf{XE Node} & \textbf{S822LC} \\
%\hline
%\hline \textbf{CPU 1} & AMD Opteron 6276 & AMD Opteron 6276 & IBM Power8 \\
%\hline \textbf{CPU 2} & -- & AMD Opteron 6276 & IBM Power8 \\
%\hline
%\hline \textbf{GPU 1} & \makecell{K20X \\ (6 GB RAM) } & -- & P100 (16GB RAM) \\
%\hline \textbf{GPU 2} & -- & -- & P100 (16GB RAM) \\
%\hline \textbf{GPU 3} & -- & -- & P100 (16GB RAM) \\
%\hline \textbf{GPU 4} & -- & -- & P100 (16GB RAM) \\
%\hline \textbf{RAM} & 32GB & 64 GB & 512 GB \\
%\hline \makecell{\textbf{CPU-GPU} \\ \textbf{Bus}} & PCIe & -- & NVLink \\
%\hline
%\end{tabular}
%\end{table}
The performance of MLFMM is evaluated on three systems: XE and XK nodes from the Blue Waters supercomputer~\cite{ncsa}, and an IBM S822LC.
Each Blue Waters node is a two-socket system: the XE node has two AMD Opteron 6276 CPUs, each with eight floating-point units, hardware support for 16 executing threads, and 32 GB of RAM.
@@ -159,9 +143,8 @@ A 16-GPU MPI execution is not shown, as only one S822LC was available for evalua
Both XE and S822LC achieve more CPU speedup than they have floating-point units (17x with 32 threads on 16 units for XE, 26x with 160 threads on 20 units for S822LC).
When floating-point units are oversubscribed, they are more fully utilized.
The CUDA implementations leverage well-understood techniques for optimizing matrix operations, including hybrid shared-memory and register tiling, and thread coarsening~\cite{hwu11}
The CUDA implementations leverage hybrid shared-memory and register tiling, and thread coarsening~\cite{hwu11}.
In both systems, using a GPU for MLFMM provides substantial speedup (additional 3.1x on XE/XK, 9.2x on S822LC) over fully utilizing the CPUs.
This speedup justifies the considerable time invested in a CUDA implementation.
Furthermore, nearly linear scaling when using multiple GPUs is also achieved thanks to overlapping all required MPI communication with GPU computation.
This corresponds to a reduction in execution time from approximately 33 seconds to 40 milliseconds on XK nodes, and 28 seconds to 29 milliseconds on S822LC.
@@ -170,22 +153,20 @@ This reflects the slow pace of single-threaded CPU performance improvement.
On the other hand, the P100 GPU in S822LC provides 4.4x speedup over the K20x in XK.
On a per-node basis the four GPUs in S822LC provide 17.9 speedup over the single GPU in XK.
The nearfield kernel is the majority of the MLFMM execution time.
The average kernel-execution speedup moving from K20x to P100 is 5.3x, and the disaggregation kernel speedup is the largest, at 8x.
On both K20x and P100, this kernel's performance is limited by the amount of CUDA shared memory it requires.
In S822LC, the newer Pascal GPU architecture provides 64 KB of shared memory per thread-block rather than the 48 KB on XK, which allows more thread-blocks to run concurrently and provide the disproportionate speedup on that machine.
\section{Conclusions}
This paper presents MLFMM performance results on three types of computer systems: Blue Waters XE and XK nodes, and an IBM S822LC.
MLFMM is realized as matrix operations for excellent performance.
Significant CPU speedup on both systems is achieved with OpenMP, and further eclipsed by CUDA implementations that take advantage of well-understood matrix optimization techniques, up to a speedup of 969x over single-threaded CPU execution on S822LC, bringing execution times from seconds to milliseconds even for large problems.
On modern GPUs, this speedup justifies the significant CUDA time investment.
Significant CPU speedup on both systems is achieved with OpenMP, and further eclipsed by CUDA implementations that take advantage of well-understood matrix optimization techniques.
A speedup of 969x over single-threaded CPU execution is achieved on S822LC, bringing execution times from seconds to milliseconds even for large problems.
This speedup justifies the significant CUDA time investment.
\section*{Acknowledgments}
This work was supported by the NVIDIA GPU Center of Excellence, the NCSA Petascale Improvement Discovery Program, and the IBM-Illinois Center for Cognitive Computing Systems Research (C3SR)- a research collaboration as part of the IBM Cognitive Horizon Network.
This work was supported by the NVIDIA GPU Center of Excellence, the NCSA Petascale Improvement Discovery Program, and the IBM-Illinois Center for Cognitive Computing Systems Research (C3SR).
\bibliographystyle{IEEEtran}
\begin{thebibliography}{99}
@@ -213,7 +194,23 @@ Available: https://bluewaters.ncsa.illinois.edu/hardware-summary.
\vfill \pagebreak
%\begin{table}{}
%\centering \caption{Evaluation Systems} \label{tab:systems}
%\begin{tabular}{|c|c|c|c|}
%\hline & \textbf{XK Node} & \textbf{XE Node} & \textbf{S822LC} \\
%\hline
%\hline \textbf{CPU 1} & AMD Opteron 6276 & AMD Opteron 6276 & IBM Power8 \\
%\hline \textbf{CPU 2} & -- & AMD Opteron 6276 & IBM Power8 \\
%\hline
%\hline \textbf{GPU 1} & \makecell{K20X \\ (6 GB RAM) } & -- & P100 (16GB RAM) \\
%\hline \textbf{GPU 2} & -- & -- & P100 (16GB RAM) \\
%\hline \textbf{GPU 3} & -- & -- & P100 (16GB RAM) \\
%\hline \textbf{GPU 4} & -- & -- & P100 (16GB RAM) \\
%\hline \textbf{RAM} & 32GB & 64 GB & 512 GB \\
%\hline \makecell{\textbf{CPU-GPU} \\ \textbf{Bus}} & PCIe & -- & NVLink \\
%\hline
%\end{tabular}
%\end{table}
%\subsection{Computation Kernel Breakdown}