Determining the space dependent coefficients in space-time fractional diffusion equations via Krylov preconditioning
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911218494603264 |
|---|---|
| author | Ilyas, Asim Khan, Muhammad Faisal Sormani, Rosita L. Tento, Giacomo Serra-Capizzano, Stefano |
| author_facet | Ilyas, Asim Khan, Muhammad Faisal Sormani, Rosita L. Tento, Giacomo Serra-Capizzano, Stefano |
| contents | We consider a time-space fractional diffusion equation with a variable coefficient and investigate the inverse problem of reconstructing the source term, after regularizing the problem with the quasiboundary value method to mitigate the ill-posedness. The equation involves a Caputo fractional derivative in the space variable and a tempered fractional derivative in the time variable, both of order in (0, 1). A finite difference approximation leads to a two-by-two block linear system of large dimensions. We conduct a spectral analysis of the associated matrix sequences, employing tools from Generalized Locally Toeplitz (GLT) theory, and construct the preconditioner guided by the GLT analysis. Numerical experiments are reported and commented, followed by concluding remarks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_16425 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Determining the space dependent coefficients in space-time fractional diffusion equations via Krylov preconditioning Ilyas, Asim Khan, Muhammad Faisal Sormani, Rosita L. Tento, Giacomo Serra-Capizzano, Stefano Numerical Analysis We consider a time-space fractional diffusion equation with a variable coefficient and investigate the inverse problem of reconstructing the source term, after regularizing the problem with the quasiboundary value method to mitigate the ill-posedness. The equation involves a Caputo fractional derivative in the space variable and a tempered fractional derivative in the time variable, both of order in (0, 1). A finite difference approximation leads to a two-by-two block linear system of large dimensions. We conduct a spectral analysis of the associated matrix sequences, employing tools from Generalized Locally Toeplitz (GLT) theory, and construct the preconditioner guided by the GLT analysis. Numerical experiments are reported and commented, followed by concluding remarks. |
| title | Determining the space dependent coefficients in space-time fractional diffusion equations via Krylov preconditioning |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2510.16425 |