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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Parallel and Distributed Computing

ISSN

0743-7315

e-ISSN

—

Svazek periodika

137

Číslo periodika v rámci svazku

March

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

12

Strana od-do

148-159

Kód UT WoS článku

000510315300012

EID výsledku v databázi Scopus

2-s2.0-85075774593