Speaker: Fabio Durastante
Affiliation: University of Pisa
Time: Thursday, 28 February 2019, h. 14:00
Place: Sala Seminari Est, Dipartimento di Informatica
Title: The Krylov--Jacobi method: functions of matrices for fractional
partial differential equations
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.
