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arXiv · 2606.25520

Efficient Krylov solvers for inverse source problem in 2D space-time fractional diffusion equation

Asim Ilyas·Stefano Serra-Capizzano
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Abstract

In this work, we consider a two-dimensional time-space fractional diffusion equation with a variable coefficient and investigate the inverse source problem of reconstructing the source term f(x,y) , after regularizing the problem using the quasi-boundary value method to mitigate ill-posedness. A finite difference discretization results in a large-scale linear system with a multilevel Toeplitz-like block structure. We perform a spectral analysis of the associated matrix sequences, employing tools from Generalized Locally Toeplitz (GLT) theory, and construct efficient preconditioners based on the GLT analysis. The proposed preconditioners preserve the multilevel structure of the discretization matrices and leads to a general eigenvalue clustering around one for the preconditioned sequence. Numerical experiments validate the theoretical findings and demonstrate that the proposed approach significantly accelerates the convergence of the GMRES method in reconstructing the source term in the two-dimensional space-time fractional diffusion equation.

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Asim Ilyas, Stefano Serra-Capizzano. 2026-06-24. Efficient Krylov solvers for inverse source problem in 2D space-time fractional diffusion equation. https://arxiv.org/abs/2606.25520

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