Choice and development of a preconditioner for Newton-GMRES algorithm

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Tezin Türü: Yüksek Lisans

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Mühendislik Fakültesi, Havacılık ve Uzay Mühendisliği Bölümü, Türkiye

Tezin Onay Tarihi: 2015

Öğrenci: YUNUS EMRE MUSLUBAŞ

Danışman: SİNAN EYİ

Özet:

This thesis consists of the choice, application and analysis of a preconditioner for a supersonic flow solution through Newton-GMRES (generalized minimal residual) Krylov subspace method and the comparison of the results with unpreconditioned Newton-GMRES method and Newton’s methods. Three dimensional Euler equations are used for the analysis. These Euler equations are discretized, then solved using Newton’s method and the generalized minimal residual method is used to solve the resulting linear system. The results and the computational time for this Newton-GMRES method approach are then obtained to be compared with those for the same method preconditioned using incomplete lower-upper factorization and the regular Newton’s method. The calculation of the Jacobian matrix necessary for the preconditioner and the Newton’s method is done analytically.