کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4640188 1341265 2010 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Convergence analysis of multigrid methods with residual scaling techniques
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Convergence analysis of multigrid methods with residual scaling techniques
چکیده انگلیسی

In this paper, multigrid methods with residual scaling techniques for symmetric positive definite linear systems are considered. The idea of perturbed two-grid methods proposed in [7] is used to estimate the convergence factor of multigrid methods with residual scaled by positive constant scaling factors. We will show that if the convergence factors of the two-grid methods are uniformly bounded by σσ (σ<0.5σ<0.5), then the convergence factors of the W-cycle multigrid methods are uniformly bounded by σ/(1−σ)σ/(1−σ), whether the residuals are scaled at some or all levels. This result extends Notay’s Theorem 3.1 in [7] to more general cases. The result also confirms the viewpoint that the W-cycle multigrid method will converge sufficiently well as long as the convergence factor of the two-grid method is small enough. In the case where the convergence factor of the two-grid method is not small enough, by appropriate choice of the cycle index γγ, we can guarantee that the convergence factor of the multigrid methods with residual scaling techniques still has a uniform bound less than σ/(1−σ)σ/(1−σ). Numerical experiments are provided to show that the performance of multigrid methods can be improved by scaling the residual with a constant factor. The convergence rates of the two-grid methods and the multigrid methods show that the W-cycle multigrid methods perform better if the convergence rate of the two-grid method becomes smaller. These numerical experiments support the proposed theoretical results in this paper.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 234, Issue 10, 15 September 2010, Pages 2932–2942
نویسندگان
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