Utilizing Sparsity in the GPU-accelerated Assembly of Schur Complement Matrices in Domain Decomposition Methods

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F25%3A10259205" target="_blank" >RIV/61989100:27740/25:10259205 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1145/3712285.3759904" target="_blank" >https://doi.org/10.1145/3712285.3759904</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1145/3712285.3759904" target="_blank" >10.1145/3712285.3759904</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Utilizing Sparsity in the GPU-accelerated Assembly of Schur Complement Matrices in Domain Decomposition Methods

Popis výsledku v původním jazyce

Schur complement matrices emerge in many domain decomposition methods that can utilize supercomputers to solve complex engineering problems. As most of today&apos;s high-performance clusters&apos; performance lies in GPUs, these methods should also be accelerated. Typically, the offloaded components are the explicitly assembled dense Schur complement matrices used later in the iterative solver for multiplication with a vector. As the explicit assembly is expensive, it adds a significant overhead to this approach of acceleration. It has already been shown that the overhead can be minimized by assembling the Schur complements directly on the GPU. This paper shows that the GPU assembly can be further improved by wisely utilizing the matrix sparsity. In the context of FETI, we achieved a speedup of 5.1 in the GPU section of the code and 3.3 for the whole assembly, making the acceleration beneficial from as few as 10 iterations for subdomains with 1,000-70,000 unknowns.

Název v anglickém jazyce

Utilizing Sparsity in the GPU-accelerated Assembly of Schur Complement Matrices in Domain Decomposition Methods

Popis výsledku anglicky

Schur complement matrices emerge in many domain decomposition methods that can utilize supercomputers to solve complex engineering problems. As most of today&apos;s high-performance clusters&apos; performance lies in GPUs, these methods should also be accelerated. Typically, the offloaded components are the explicitly assembled dense Schur complement matrices used later in the iterative solver for multiplication with a vector. As the explicit assembly is expensive, it adds a significant overhead to this approach of acceleration. It has already been shown that the overhead can be minimized by assembling the Schur complements directly on the GPU. This paper shows that the GPU assembly can be further improved by wisely utilizing the matrix sparsity. In the context of FETI, we achieved a speedup of 5.1 in the GPU section of the code and 3.3 for the whole assembly, making the acceleration beneficial from as few as 10 iterations for subdomains with 1,000-70,000 unknowns.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

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

Projekt

—

Návaznosti

—

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název statě ve sborníku

Proceedings of the International Conference for High Performance Computing, Networking, Storage, and Analysis, SC 2025 :16-21 Nov 2025 : St. Louis, MO, USA

ISBN

979-8-4007-1466-5

ISSN

—

e-ISSN

—

Počet stran výsledku

13

Strana od-do

1464-1476

Název nakladatele

Association for Computing Machinery

Místo vydání

New York

Místo konání akce

St. Louis

Datum konání akce

16. 11. 2025

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

—