The Krylov--Jacobi method: functions of matrices for fractional partial differential equations

Data Seminario: 
Ora Inizio: 
Ora Fine: 
Fabio Durastante
Università di Pisa
Luogo: Sala Seminari Est, Dipartimento di Informatica.
In this talk I discuss briefly some computational issues concerning a Krylov method of rational type for the computation of certain matrix functions occurring in the solution of fractional partial differential equations. Specifically, a new set of poles for the computation of the following functions of symmetric positive definite matrices is introduced:
- fractional power, $f(z) = z^{-\alpha/2}$,
- resolvent of fractional power, $f(z) = (1+\nu z^{\alpha/2})^{-1}$.

The underlying approach permits to efficiently semidiscretize the fractional Laplacian operator on non Cartesian/regular grids exploiting either Finite Differences, Finite Elements, or Finite Volumes schemes, and to employ any appropriate linear multistep method for marching in time.

Numerical experiments on some fractional partial differential equation model problems and comparisons with other methods, including other popular rational Krylov methods, confirm that the proposed approach is promising.

This is a joint work with: L. Aceto, D. Bertaccini, and P. Novati.