کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
519033 867635 2011 10 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
An O(N log2N) alternating-direction finite difference method for two-dimensional fractional diffusion equations
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
پیش نمایش صفحه اول مقاله
An O(N log2N) alternating-direction finite difference method for two-dimensional fractional diffusion equations
چکیده انگلیسی

Fractional diffusion equations model phenomena exhibiting anomalous diffusion that cannot be modeled accurately by the second-order diffusion equations. Because of the nonlocal property of fractional differential operators, the numerical methods for fractional diffusion equations often generate dense or even full coefficient matrices. Consequently, the numerical solution of these methods often require computational work of O(N3) per time step and memory of O(N2) for where N is the number of grid points.In this paper we develop a fast alternating-direction implicit finite difference method for space-fractional diffusion equations in two space dimensions. The method only requires computational work of O(N log2N) per time step and memory of O(N), while retaining the same accuracy and approximation property as the regular finite difference method with Gaussian elimination.Our preliminary numerical example runs for two dimensional model problem of intermediate size seem to indicate the observations: To achieve the same accuracy, the new method has a significant reduction of the CPU time from more than 2 months and 1 week consumed by a traditional finite difference method to 1.5 h, using less than one thousandth of memory the standard method does. This demonstrates the utility of the method.


► We develop a fast alternating-direction method for fractional diffusion equations.
► This method reduces computational complexity from O(N3) to O(N logN).
► This method reduces memory from O(N2) to O(N).
► Example runs show the advantages of this method on complexity and storage.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 230, Issue 21, 1 September 2011, Pages 7830–7839
نویسندگان
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