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.