مقارنة بعض طرائق كريلوف المسرعة لحل جمل المعادلات الخطية غير المتناظرة كثيرة الأصفار
Abstract
Large sparse non-symmetric linear systems of equations often occur in many scientific and engineering applications. In this paper, we present a comparative study of some preconditioned Krylov iterative methods, namely CGS, Bi-CGSTAB, TFQMR and GMRES for solving such systems. To demonstrate their efficiency, we test and compare the numerical implementations of these methods on five numerical examples. The preconditioners considered here are incomplete LU-decomposition (ILU), Symmetric Successive Over Relaxation (SSOR), and Alternating Direction Implicit (ADI). The ILU preconditioner is shown to be extremely effective in achieving optimal convergence rates for the class of problems considered here. Finally, our results show that the GMRES is the best among the considered iterative methods.
تظهر جمل المعادلات الخطية ، غير المتناظرة ، كثيرة الأصفار ، من مراتب عليا. في العديد من التطبيقات العلمية والهندسية. في هذا العمل، نجري دراسة مقارنة لبعض طرائق كريلوف التكرارية المسرعة وهي الطرائق CGSو Bi-CGSTABو TFQMR و GMRES لحل هذا النوع من جمل المعادلات. المسرعات المدروسة هنا هي تحليل LU غير التام (ILU) و المسرع فوق الاسترخاء المتتالي التناظري (SSOR) و مسرع الاتجاهات الضمنية المتناوبة (ADI). تبين أن المسرع ILU فعال إلى حد كبير في إنجاز معدلات تقارب مثلى من أجل صف المسائل المدروسة هنا. أخيرا، تبين تجاربنا أن طريقةGMRES(10) كانت هي الأفضل بين جميع الطرائق التكرارية المدروسة.
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