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.

Authors
Lanzara F.1 , Maz’ya V. 2, 3 , Schmidt G.4
Publisher
Springer-Verlag
Number of issue
2
Language
English
Pages
277-300
Status
Published
Volume
65
Year
2019
Organizations
  • 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
Keywords
Biharmonic potential; Higher dimensions; Multidimensional convolution; Separated representations
Date of creation
24.12.2019
Date of change
24.12.2019
Short link
https://repository.rudn.ru/en/records/article/record/54926/