The paper discusses new cubature formulas for the Riesz potential and the fractional Laplacian ((-Delta)^{a/2}), (0<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.
Fast computation of the multidimensional fractional Laplacian / Lanzara, Flavia; Maz'Ya, Vladimir; Schmidt, Gunther. - In: APPLICABLE ANALYSIS. - ISSN 0003-6811. - 101:11(2022), pp. 4025-4041. [10.1080/00036811.2021.1986025]
Fast computation of the multidimensional fractional Laplacian
Flavia Lanzara
;
2022
Abstract
The paper discusses new cubature formulas for the Riesz potential and the fractional Laplacian ((-Delta)^{a/2}), (0<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.| File | Dimensione | Formato | |
|---|---|---|---|
|
Lanzara_postprint_Fast-computation_2021.pdf
Open Access dal 06/10/2022
Tipologia:
Documento in Post-print (versione successiva alla peer review e accettata per la pubblicazione)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
358.29 kB
Formato
Adobe PDF
|
358.29 kB | Adobe PDF | |
|
Lanzara_Fast-computation_2021.pdf.pdf
solo gestori archivio
Tipologia:
Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
1.64 MB
Formato
Adobe PDF
|
1.64 MB | Adobe PDF | Contatta l'autore |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
