Architectures And Algorithms For Digital Optical Computing Systems With Applications To Numerical Transforms And Partial Differential Equations

1986 ◽  
Author(s):  
Timothy J. Drabik ◽  
Mark A. Title ◽  
Sing H. Lee ◽  
John A. Neff
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Optical Computing ◽  
Partial Differential ◽  
Computing Systems ◽  
Digital Optical Computing

scholarly journals Applying the Swept Rule for Solving Two-Dimensional Partial Differential Equations on Heterogeneous Architectures

2021 ◽  
Vol 26 (3) ◽  
pp. 52
Author(s):  
Anthony S. Walker ◽  
Kyle E. Niemeyer
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Heterogeneous Computing ◽  
Heat Diffusion ◽  
Fixed Cost ◽  
Two Dimensional ◽  
Partial Differential ◽  
Computing Systems ◽  
Heat Diffusion Equation ◽  
Work Distribution

The partial differential equations describing compressible fluid flows can be notoriously difficult to resolve on a pragmatic scale and often require the use of high-performance computing systems and/or accelerators. However, these systems face scaling issues such as latency, the fixed cost of communicating information between devices in the system. The swept rule is a technique designed to minimize these costs by obtaining a solution to unsteady equations at as many possible spatial locations and times prior to communicating. In this study, we implemented and tested the swept rule for solving two-dimensional problems on heterogeneous computing systems across two distinct systems and three key parameters: problem size, GPU block size, and work distribution. Our solver showed a speedup range of 0.22–2.69 for the heat diffusion equation and 0.52–1.46 for the compressible Euler equations. We can conclude from this study that the swept rule offers both potential for speedups and slowdowns and that care should be taken when designing such a solver to maximize benefits. These results can help make decisions to maximize these benefits and inform designs.

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