کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6915469 1447399 2018 28 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Compressed sparse tensor based quadrature for vibrational quantum mechanics integrals
ترجمه فارسی عنوان
چهارگوشه ی مبتنی بر تانسور فشرده برای انتگرال های مکانیک کوانتومی ارتعاشی
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
چکیده انگلیسی
A new method for fast evaluation of high dimensional integrals arising in quantum mechanics is proposed. The method is based on sparse approximation of a high dimensional function followed by a low-rank compression. In the first step, we interpret the high dimensional integrand as a tensor in a suitable tensor product space and determine its entries by a compressed sensing based algorithm using only a few function evaluations. Secondly, we implement a rank reduction strategy to compress this tensor in a suitable low-rank tensor format using standard tensor compression tools. This allows representing a high dimensional integrand function as a small sum of products of low dimensional functions. Finally, a low dimensional Gauss-Hermite quadrature rule is used to integrate this low-rank representation, thus alleviating the curse of dimensionality. Numerical tests on synthetic functions, as well as on energy correction integrals for water and formaldehyde molecules demonstrate the efficiency of this method using very few function evaluations as compared to other integration strategies.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computer Methods in Applied Mechanics and Engineering - Volume 336, 1 July 2018, Pages 471-484
نویسندگان
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