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Spectral analysis and sine transform based preconditioning for a structure preserving stabilized scheme approximating the space-fractional Allen Cahn equation with logarithmic potential
Danyal Ahmad, Stefano Serra-Capizzano, Muhammad Sohaib +1
We consider an initial boundary value problem of the space fractional Allen-Cahn equation with logarithmic Flory-Huggins potential. As an approximation technique, first-order weigh…
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-…
Can the a.c.s. notion and the GLT theory handle approximated PDEs/FDEs with either moving or unbounded domains?
Andrea Adriani, Alec Jacopo Almo Schiavoni-Piazza, Stefano Serra-Capizzano +1
In the current note we consider matrix-sequences of increasing sizes depending on and equipped with a parameter . For every fixed , we assume that eac…
Asymptotic spectral properties and preconditioning of an approximated nonlocal Helmholtz equation with Caputo fractional Laplacian and variable coefficient wave number
Andrea Adriani, Rosita Luisa Sormani, Cristina Tablino-Possio +2
The current study investigates the asymptotic spectral properties of a finite difference approximation of nonlocal Helmholtz equations with a Caputo fractional Laplacian and a vari…
Fractional differential problems with numerical anti-reflective boundary conditions: a computational/precision analysis and numerical results
Ercília Sousa, Cristina Tablino-Possio, Rolf Krause +1
Twenty years ago the anti-reflective numerical boundary conditions (BCs) were introduced in a context of signal processing and imaging, for increasing the quality of the reconstruc…
Fine spectral estimates with applications to the optimally fast solution of large FDE linear systems
M. Bogoya, S. M. Grudsky, S. Serra-Capizzano +1
In the present note we consider a type of matrices stemming in the context of the numerical approximation of distributed order fractional differential equations (FDEs): from one si…
Optimal preconditioning for image deblurring with Anti-Reflective boundary conditions
Pietro Dell'Acqua, Stefano Serra-Capizzano, Cristina Tablino Possio
Inspired by the theoretical results on optimal preconditioning stated by Ng, R.Chan, and Tang in the framework of Reflective boundary conditions (BCs), in this paper we present ana…
A Note on Algebraic Multigrid Methods for the Discrete Weighted Laplacian
S. Serra-Capizzano, C. Tablino Possio
In recent contributions, algebraic multigrid methods have been designed and studied from the viewpoint of the spectral complementarity. In this note we focus our efforts on specifi…
A Proposal of Multigrid Methods for Hermitian Positive Definite Linear Systems enjoying an order relation
Stefano Serra-Capizzano, Cristina Tablino Possio
Given a multigrid procedure for linear systems with coefficient matrices , we discuss the optimality of a related multigrid procedure with the same smoother and the same proje…