کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4627106 1631800 2015 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A multigrid preconditioned numerical scheme for a reaction–diffusion system
ترجمه فارسی عنوان
یک طرح عددی پیشین برای یک سیستم انتشار واکنش چندگانه
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
چکیده انگلیسی

Reaction diffusion operators have been used to model many engineering and biological systems. In this study we consider a reaction diffusion system modeling various engineering and life science problems. There are many algorithms to approximate such mathematical models. Most of the algorithms are conditionally stable and convergent. For a big time step size a Krylov subspace type solver for such models converges slowly or oscillates because of the presence of the diffusion term. Here we study a multigrid preconditioned generalized minimal residual method (GMRES) for such a model. We start with a five point scheme for the spatial integration and a method of lines for the temporal integration of the system of PDEs. Then we implement a multigrid iterative algorithm for the full discrete model, and show some numerical results to demonstrate the dominance of the solver. We analyze the convergence rate of such a multigrid iterative preconditioning algorithm. Reaction diffusion systems arise in many mathematical models and thus this study has many applicabilities.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 254, 1 March 2015, Pages 266–276
نویسندگان
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