رهیافت توماس موازی در دینامیک سیالات محاسباتی به‌کمک پردازنده‌های‌گرافیکی – جریان درون حفره

نوع مقاله : مقاله کوتاه

نویسندگان

1 دانشگاه تهران

2 دانشگاه شاهرود

چکیده

در این مقاله سه الگوریتم کاهش‌متناوب، کاهش‌متناوب موازی و رهیافت توماس ‌موازی برای حل دستگاه معادلات سه‌‌قطری به‌کمک پردازنده‌های گرافیکی معرفی و اثر دسترسی هم‌مکان و غیرهم‌مکان به حافظۀ سراسری مورد بحث قرار گرفته‌است. برای ارزیابی توانایی این الگوریتم‌ها، نتایج شبیه‌سازی جریان درون حفره (یک مورد مطالعاتی) با نتایج الگوریتم توماس‌کلاسیک اجراشده روی پردازندۀ مرکزی مقایسه شده‌است. بیشینه افزایش سرعت مشاهده‌شده در سه الگوریتم مذکور (پردازنده‌گرافیکی) در برابر الگوریتم توماس کلاسیک (پردازندۀ مرکزی) به‌ترتیب حدود 4/4، 2/5 و 45/38 می‌باشد. هم‌چنین نشان داده شده است که با دسترسی هم‌مکان، افزایش سرعت حدوداً دوبرابری برای پردازندۀ گرافیکی حاصل می‌شود.

کلیدواژه‌ها

عنوان مقاله [English]

Parallel Thomas Approach in Computational Fluid Dynamics with GPUs- Lid-driven Cavity

نویسندگان [English]

  • pooria akbarzadeh 1
  • Hossein Mahmoodi Darian 1
  • Mohsen Nazari 1
  • Milad Souri 2
1 Tehran University
2 Shahrood University
چکیده [English]

In this paper three algorithms of Cyclic-Reduction, Parallel-Cyclic-Reduction and Parallel-Thomas are introduced to solve the Tridiagonal system of equations using GPUs and the effect of coalesced-memory-access and uncoalesced-memory-access to global memory are studied. To assess the ability of these algorithms, as a case-study the simulation of the lid-driven cavity flow have been compared to the results of Runtimes and physical parameters of the classical Thomas algorithm, executed on CPU. The maximum speed-up of these algorithms against CPU runtime is about 4.4x, 5.2x and 38.5x, respectively. Also, approximately a 2x speed-up achieved in coalesced-memory access on GPU.

کلیدواژه‌ها [English]

  • Parallel Thomas approach
  • Parallel Processing
  • Tridiagonal system of equations
  • Graphic Processor
  • Cyclic Reduction algorithm

مراجع

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