5 papers · 1 filter
Block preconditioning for all-at-once variable-coefficient fractional evolution equations via the GLT analysis
Muhammad Faisal Khan, Stefano Serra-Capizzano
We study a class of nonlocal evolutionary partial differential equations with weakly singular temporal kernel and spatially variable diffusion coefficient. The model is posed on $Ω…
Structure-preserving preconditioning of discrete space-fractional diffusion equations with variable coefficient and θ-Method
Muhammad Faisal Khan, Asim Ilyas, Rolf Krause +2
This paper studies the spectral properties of large matrices and the preconditioning of linear systems, arising from the finite difference discretization of a time-dependent space-…
GLT matrix-sequences and few emblematic applications
Muhammad Faisal Khan
This thesis advances the spectral theory of structured matrix-sequences within the framework of Generalized Locally Toeplitz (GLT) -algebras, focusing on the geometric mean of H…
Determining the space dependent coefficients in space-time fractional diffusion equations via Krylov preconditioning
Asim Ilyas, Muhammad Faisal Khan, Rosita L. Sormani +2
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 pro…
Geometric means of HPD GLT matrix-sequences: a maximal result beyond invertibility assumptions on the GLT symbols
Asiim Ilyas, Muhammad Faisal Khan, Valerio Loi +1
In the current work, we consider the study of the spectral distribution of the geometric mean matrix-sequence of two matrix-sequences formed by Hermitian Positi…