کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4963783 1447410 2017 38 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Adaptive finite element method for fractional differential equations using hierarchical matrices
ترجمه فارسی عنوان
روش عنصر محدود سازگار برای معادلات دیفرانسیل کسر با استفاده از ماتریس سلسله مراتبی
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
چکیده انگلیسی
A robust and fast solver for the fractional differential equation (FDEs) involving the Riesz fractional derivative is developed using an adaptive finite element method. It is based on the utilization of hierarchical matrices (H-Matrices) for the representation of the stiffness matrix resulting from the finite element discretization of the FDEs. We employ a geometric multigrid method for the solution of the algebraic system of equations. We combine it with an adaptive algorithm based on a posteriori error estimation. A posteriori error estimation based adaptive algorithm is used to deal with general-type singularities arising in the solution of the FDEs. Through various test examples we demonstrate the efficiency of the method and the high-accuracy of the numerical solution even in the presence of singularities. The proposed technique has been verified effectively through fundamental examples including Riesz, Left/Right Riemann-Liouville fractional derivative and, furthermore, it can be readily extended to more general fractional differential equations with different boundary conditions and low-order terms.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computer Methods in Applied Mechanics and Engineering - Volume 325, 1 October 2017, Pages 56-76
نویسندگان
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