کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6933153 867592 2014 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Array-representation integration factor method for high-dimensional systems
ترجمه فارسی عنوان
روش یکپارچگی نمایندگی آرایه برای سیستم های با ابعاد بزرگ
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
چکیده انگلیسی
High order spatial derivatives and stiff reactions often introduce severe temporal stability constraints on the time step in numerical methods. Implicit integration method (IIF) method, which treats diffusion exactly and reaction implicitly, provides excellent stability properties with good efficiency by decoupling the treatment of reactions and diffusions. One major challenge for IIF is storage and calculation of the potential dense exponential matrices of the sparse discretization matrices resulted from the linear differential operators. Motivated by a compact representation for IIF (cIIF) for Laplacian operators in two and three dimensions, we introduce an array-representation technique for efficient handling of exponential matrices from a general linear differential operator that may include cross-derivatives and non-constant diffusion coefficients. In this approach, exponentials are only needed for matrices of small size that depend only on the order of derivatives and number of discretization points, independent of the size of spatial dimensions. This method is particularly advantageous for high-dimensional systems, and it can be easily incorporated with IIF to preserve the excellent stability of IIF. Implementation and direct simulations of the array-representation compact IIF (AcIIF) on systems, such as Fokker-Planck equations in three and four dimensions and chemical master equations, in addition to reaction-diffusion equations, show efficiency, accuracy, and robustness of the new method. Such array-presentation based on methods may have broad applications for simulating other complex systems involving high-dimensional data.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 258, 1 February 2014, Pages 585-600
نویسندگان
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