کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
519164 867642 2012 25 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Optimal Runge–Kutta schemes for discontinuous Galerkin space discretizations applied to wave propagation problems
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
پیش نمایش صفحه اول مقاله
Optimal Runge–Kutta schemes for discontinuous Galerkin space discretizations applied to wave propagation problems
چکیده انگلیسی

We study the performance of methods of lines combining discontinuous Galerkin spatial discretizations and explicit Runge–Kutta time integrators, with the aim of deriving optimal Runge–Kutta schemes for wave propagation applications. We review relevant Runge–Kutta methods from literature, and consider schemes of order q from 3 to 4, and number of stages up to q + 4, for optimization. From a user point of view, the problem of the computational efficiency involves the choice of the best combination of mesh and numerical method; two scenarios are defined. In the first one, the element size is totally free, and a 8-stage, fourth-order Runge–Kutta scheme is found to minimize a cost measure depending on both accuracy and stability. In the second one, the elements are assumed to be constrained to such a small size by geometrical features of the computational domain, that accuracy is disregarded. We then derive one 7-stage, third-order scheme and one 8-stage, fourth-order scheme that maximize the stability limit. The performance of the three new schemes is thoroughly analyzed, and the benefits are illustrated with two examples. For each of these Runge–Kutta methods, we provide the coefficients for a 2N-storage implementation, along with the information needed by the user to employ them optimally.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 231, Issue 4, 20 February 2012, Pages 2067–2091
نویسندگان
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