Fast cubature of high dimensional biharmonic potential based on\n Approximate Approximations

2018/09/25 by Flavia Lanzara, Lanzara, Flavia, Vladimir Maz’ya +3
Computer Science · Engineering · #Acoustic Wave Phenomena Research #Aerodynamics and Acoustics in Jet Flows #FOS: Mathematics #Image and Signal Denoising Methods #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1809.09438

openalex publication_date 2018/09/25 · openalex created_date 2022/08/03 · openalex updated_date 2026/07/28

Abstract

We derive new formulas for the high dimensional biharmonic potential acting\non Gaussians or Gaussians times special polynomials. These formulas can be used\nto construct accurate cubature formulas of an arbitrary high order which are\nfast and effective also in very high dimensions. Numerical tests show that the\nformulas are accurate and provide the predicted approximation rate (O(h⁸)) up\nto the dimension 10⁷.\n

Related

• Fast cubature of volume potentials over rectangular domains
• Tensor product approximations of high dimensional potentials
• Construction of an infinite-dimensional family of exact solutions of a three-dimensional biharmonic equation by the hypercomplex method
• On the fast computation of high dimensional volume potentials
• Classification of the stable solution to biharmonic problems in large dimensions