Fast computation of the multidimensional fractional Laplacian. Issue 11 (24th July 2022)

• Record Type: Journal Article
• Authors: Lanzara, Flavia; Maz'ya, Vladimir; Schmidt, Gunther
• Is Part Of: Applicable analysis. Volume 101:Issue 11(2022)
• Page Start: 4025
• Page End: 4041
• Publication Date: 2022-07-24
• Subjects: Multidimensional convolution -- Riesz potential -- fractional Laplacian -- separated representation -- approximate approximations; 65D32 -- 41A30 -- 41A63; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2021.1986025
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : The paper discusses new cubature formulas for the Riesz potential and the fractional Laplacian ( − Δ ) α / 2, 0 < α < 2, in the framework of the method approximate approximations. This approach, combined with separated representations, makes the method successful also in high dimensions. We prove error estimates and report on numerical results illustrating that our formulas are accurate and provide the predicted convergence rate 2, 4, 6, 8 up to dimension 10 4 .