ISSIQLIK TENGLAMASINI PARALLEL USUL VA CHEKLI AYIRMALAR USULI BILAN SONLI YECHISH: ALGORITMIK TAHLIL VA SOLISHTIRMA
Kalit so'zlar:
issiqlik tenglamasi, parallel hisoblash, chekli ayirmalar usuli, vaqt murakkabligi, CFL sharti, masshtablanishAnnotatsiya
Ushbu maqolada bir o'lchamli issiqlik tenglamasini sonli yechishda qo'llaniladigan ikki usul — parallel hisoblash usuli va chekli ayirmalar usuli (CAU) — algoritmik jihatdan tahlil qilinadi va o'zaro solishtiriladi. Har ikkala usulning vaqt murakkabligi, xotira sarfi, barqarorlik shartlari va masshtablanish imkoniyatlari ko'rib chiqiladi. Tahlil shuni ko'rsatadiki, parallel usul katta o'lchamli masalalar uchun sezilarli darajada samaraliroq bo'lib, p protsessor soni ortishi bilan hisoblash vaqti proporsional kamayadigan bo'lsa, CAU sodda amalga oshirilishi bilan kichik o'lchamli masalalar uchun afzalroqdir.
Foydalanilgan adabiyotlar
[1] Samarskiy A.A. Farq sxemalari nazariyasi. — M.: Nauka, 1977. — 656 b.
[2] Leveque R.J. Finite Difference Methods for Ordinary and Partial Differential Equations. — SIAM, 2007. — 341 p.
[3] Pacheco P.S. An Introduction to Parallel Programming. — Morgan Kaufmann, 2011. — 392 p.
[4] Gropp W., Lusk E., Skjellum A. Using MPI: Portable Parallel Programming with the Message-Passing Interface. — MIT Press, 2014. — 400 p.
[5] Strikwerda J.C. Finite Difference Schemes and Partial Differential Equations. — SIAM, 2004. — 435 p.
