کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4967268 1449367 2017 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Factorizing the factorization - a spectral-element solver for elliptic equations with linear operation count
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
پیش نمایش صفحه اول مقاله
Factorizing the factorization - a spectral-element solver for elliptic equations with linear operation count
چکیده انگلیسی
The paper proposes a novel factorization technique for static condensation of a spectral-element discretization matrix that yields a linear operation count of just 13N multiplications for the residual evaluation, where N is the total number of unknowns. In comparison to previous work it saves a factor larger than 3 and outpaces unfactored variants for all polynomial degrees. Using the new technique as a building block for a preconditioned conjugate gradient method yields linear scaling of the runtime with N which is demonstrated for polynomial degrees from 2 to 32. This makes the spectral-element method cost effective even for low polynomial degrees. Moreover, the dependence of the iterative solution on the element aspect ratio is addressed, showing only a slight increase in the number of iterations for aspect ratios up to 128. Hence, the solver is very robust for practical applications.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 346, 1 October 2017, Pages 437-448
نویسندگان
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