Fast cubature of high dimensional biharmonic potential based on approximate approximations

We derive new formulas for the high dimensional biharmonic potential acting on Gaussians or Gaussians times special polynomials. These formulas can be used to construct accurate cubature formulas of an arbitrary high order which are fast and effective also in very high dimensions. Numerical tests show that the formulas are accurate and provide the predicted approximation rate O(h8) up to the dimension 10 7. © 2019, Università degli Studi di Ferrara.

Авторы
Lanzara F.1 , Maz’ya V. 2, 3 , Schmidt G.4
Редакторы
-
Издательство
Springer-Verlag
Номер выпуска
2
Язык
Английский
Страницы
277-300
Статус
Опубликовано
Подразделение
-
Номер
-
Том
65
Год
2019
Организации
  • 1 Mathematics Department, Sapienza University, P.le Aldo Moro 2, Rome, 00185, Italy
  • 2 Department of Mathematics, University of Linköping, Linköping, 581 83, Sweden
  • 3 RUDN University, 6 Miklukho-Maklay St., Moscow, 117198, Russian Federation
  • 4 Berlin, Germany
Ключевые слова
Biharmonic potential; Higher dimensions; Multidimensional convolution; Separated representations
Дата создания
24.12.2019
Дата изменения
24.12.2019
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/54926/