Batched transpose-free ADI-type preconditioners for a Poisson solver on GPGPUs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F20%3A10243520" target="_blank" >RIV/61989100:27740/20:10243520 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0743731519307609" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0743731519307609</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jpdc.2019.11.004" target="_blank" >10.1016/j.jpdc.2019.11.004</a>

Result language
angličtina
Original language name
Batched transpose-free ADI-type preconditioners for a Poisson solver on GPGPUs
Original language description
We investigate the iterative solution of a symmetric positive definite linear system involving the shifted Laplacian as the system matrix on General Purpose Graphics Processing Units (GPGPUs). We consider in particular the Chebyshev iteration for its reduced global communication. The ADI-type preconditioner involves solving multiple (batched) symmetric positive tridiagonal Toeplitz systems along each coordinate direction. We investigate several variants how to solve these tridiagonal systems, the Thomas algorithm, the Thomas combined with the SPIKE algorithm, and a polynomial approximation of the inverse. We test the various implementations numerically by means of two- and three-dimensional examples. It turns out that a combination of the Thomas algorithm and the approximate inverse leads to a solution that does not need either tiling or transpositions. As such none of the kernels uses an extensive amount of shared memory which yields a very high GPU utilization and more importantly optimal coalesced global memory access patterns. (C) 2019 Elsevier Inc.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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