Fast cubature of high dimensional biharmonic potential based on Approximate Approximations
arXiv:1809.094385 citations
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Provides a fast numerical method for high-dimensional biharmonic potential, relevant for computational mathematics and physics applications.
The paper derives new formulas for high-dimensional biharmonic potential on Gaussians, enabling fast and accurate cubature formulas with O(h^8) approximation rate, tested up to dimension 10^7.
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(h^8)) up to the dimension 10^7.